Data communication method and system using two hopped carrier frequencies

Abstract

A method for creating and processing a signal waveform, the method comprising: generating, by a first processor, two hopped carrier frequencies, wherein the two hopped carrier frequencies are symmetrical with respect to a third carrier frequency, fm, and wherein a distance between the first and second hopped carrier frequencies, |second hopped carrier frequency – first hopped carrier frequency|, is pre-defined; modulating, by the first processor, the first hopped carrier frequency and the second hopped carrier frequency with a narrow-band waveform, wherein a first signal is a first outcome of the modulation on the first hopped carrier frequency and a second signal is a second outcome of the modulation on the second hopped carrier frequency, converting the modulated first and second hopped carrier frequencies to the central carrier frequency f0; transmitting, by a first transceiver coupled to the first processor, the modulated first signal and the modulated second signal; receiving, by a second transceiver, the transmitted first and second signals, wherein the second transceiver is couplable to a second processor configured to process the received first and second signals; and converting, by the second processor, a first baseband of the modulated first carrier frequency to a central baseband carrier frequency, and a second baseband of the modulated second carrier frequency to the central baseband carrier frequency, wherein the conversion to the central baseband carrier frequency is configured to be applied for each hop applied to the modulated first and second carrier frequencies.

Description

[0001] .

[0002] Airbus Defence and Space GmbH - 1 - 30A-166 109METHOD AND SYSTEM FOR CREATING AND PROCESSING A SIGNAL WAVEFORM FIELD OF THE INVENTION The present invention relates to a method for creating and processing a signal waveform. The method is achieved by selecting a first and a second carrier frequency, modulating the first and second carrier frequencies with a narrowband waveform to generate modulated signals, transmitting the modulated signals, receiving the transmitted first and second signals and converting the received signals. A system is also described for carrying out the method. BACKGROUND TO THE INVENTION The last decade has witnessed a renewed interest for Low Earth Orbit (LEO) constellations to support communication for broadband applications. Mega- Constellations such as Starlink, OneWeb or Kuiper comprising hundreds, if not thousands, of satellites represent some examples. Further announcements for up- coming systems follow almost at a monthly rate, dynamized by the introduction ofthe 5G Non-Terrestrial Network (NTN). Communication is not the only spaceapplication which takes benefit of this trend. Indeed, systems such as Xona, Trustpoint or Centispace, and which also comprise a large number of satellites, are currently designed to support so-called LEO Positioning-Navigation-and-Timing (LEO- PNT). Contrarily to the well-established Global Navigation Satellite Systems (GNSS) such as GPS, Galileo or Beidou operating on a Medium Earth Orbit (MEO) 25000- 30000km altitude, LEO satellites’ altitudes typically vary between 500 and 1200km. Another, main differentiator between GNSS and LEO-PNT system is related to the operational frequencies which not only cover the native L-Band of the GNSS, but also alternative frequencies either in the lower part of the spectrum (VHF, UHF) or the higher part (S-, C-, Ku or even Ka-Band). These alternative frequencies offer new degrees of freedom for the signal design, and especially satisfy a new demand from the end-application sectors, such as Internet-of-Things, Automotive, or other Mass- Market applications. Nevertheless, some signal design constraints, also motivated by chipset manufacturers, who still ask for a certain continuity and interoperability of the proposed LEO-PNT signal waveforms with the GNSS ones, can motivate maintaining the application in a form of Code Division Multiple Access (CDMA). Hence, alternative waveforms, still inheriting of the CDMA features, are proposed, such as the Frequency Hopping Code Division Multiple Access (FH-CDMA), andOrthogonal Frequency Division Multiplex-Code Division Multiple Access (OFDM-. .

[0003] Airbus Defence and Space GmbH - 2 - 30A-166 109CDMA) schemes. Thanks to their wide bandwidth, such CDMA related waveforms are usually suited to enhance accuracy but also robustness against non-intentional or intentional interferences, through the so-called de-spreading process. However, a wider bandwidth typically results in a more complex acquisition step aiming at coarsely estimating both delay (i.e. code) and Doppler state information from the received signal. As an example, a Matched Filter acquisition approach applying a replica having the same waveform as the FH-CDMA may result in a very narrow correlation function, which forces testing a larger number of delay, or equivalently, code hypotheses, resulting from the higher granularity for the code search space, and which directly impacts the computational effort of the user device in an unfavorable manner. Furthermore, Multi-Carrier (MC) and OFDM waveforms are proposed for the new generation of Broadband LEO-communication systems, underthe impulse of the 3GPP (3rd Generation Partnership Project) initiative for 5G non-terrestrial networks (5G NTN). Such waveforms share similarities to the CDMA waveforms, and notably can also offer the large bandwidths necessary for precise ranging, and can therefore also support positioning applications. Considering the above, the application of FH-CDMA or OFDM-CDMA, but also MC and OFDM, waveforms for a LEO-PNT signal may also show two degrading effects on the acquisition performance and / or complexity. Firstly, the larger Doppler caused by the lower satellite altitude may increase the number of Doppler hypotheses to be tested with one higher order of magnitude when compared to GNSS satellites at a Medium Earth Orbit, and transmitted in the legacy L-Band. If the carrier frequency is thenincreased to S-, C- or higher bands, the Doppler excursion may become even larger,therefore increasing further the number of Doppler hypotheses. Hence, in some configurations of LEO-PNT signal acquisition (e.g. defined with the spreading sequence duration, LEO satellite altitude and carrier frequency), the number of Doppler hypotheses to be scrutinized might even exceed the number of delay (i.e. code) hypotheses to be tested, a trend which has not been observed in GNSSs.Reversely, when transmitted in VHF or UHF bands, the delay caused by the piercedatmospheric ionosphere layers may also be larger than in L-band, as the ionospheric delay is inversely proportional to the squared carrier frequency. Therefore, some acquisition techniques might also suffer from this ionospheric delay. The former assessments may be applied for open service signals, i.e. where signal structure and characteristics are publicly available through Signal-in-Space Documents (SIS-ICD). Nowadays, major threats caused by the increased vulnerability of navigation and communication systems to spoofing, meaconing and . .

[0004] Airbus Defence and Space GmbH - 3 - 30A-166 109jamming attacks force adopting counter-measures to take place at the signal design level. Those attacks are particularly efficient during the GNSS signal acquisition, which represents the “Achilles’ heel” of the signal processing chain due to not enough information being available to conduct plausibility checks on the actual originof the signal. Existing techniques based on data- and / or ranging authentication areavailable through the use of meta data obtained after demodulation of the authentication message. Such meta data serving authentication can, for example, comprise keys, signatures, etc. Known techniques comprise the Chimera scheme being applied for the GPS L1C signals, and the TESLA scheme being applied for some specific Galileo signal components. However, these techniques cannot be applied for a cold start acquisition, i.e. when such metadata information is (still) not available, enhancing thus the vulnerability to meaconing and spoofing attacks, depending on the capability of the adversary to repeat incoming signals or to forge spoofing signals with “publicly known” spreading sequences, but also to jamming attacks. One solution to enhance robustness to attacks during the acquisition step consists in applying a fully cyphered spreading code, which hinders the capability of signal forging, and later spoofing, due to the lack of key information necessary to generate a cyphering stream from the spoofer’s side. Direct acquisition asking for massive correlation testing represents the most common technique to acquire GNSS signals modulated with fully cyphered spreading codes, and was firstly applied to GPS P(Y) signals. The chip rate associated with the cyphered stream of chips may, however,be a trade-off between robustness and acquisition complexity. GNSS signals with lowchip rates simplify the acquisition performance as a smaller number of delay, or equivalently, code hypotheses need to be proposed and tested for a “brute force”,i.e. Direct acquisition, scheme on the cyphered spreading code. However, a shorterchip rate results in a smaller spreading factor, which reduces robustness against narrow-band jammers. Furthermore, once acquisition has been achieved for GNSS signals with a low chip rate such signals offer reduced ranging performance. Reversely, higher chip rates may spread further the jamming power during the correlation process to enhance robustness. However, they may also increase theacquisition complexity by a large amount due to the larger number of (cyphered)code hypotheses. In J. Anderson et al, “Cryptographic Ranging Authentication with TESLA, Rapid Rekeying, and a PRF”, a scheme is proposed to strengthen both data and spreading code authentication. The scheme re-uses elements of the TESLA scheme applied for . .

[0005] Airbus Defence and Space GmbH - 4 - 30A-166 109the Galileo OSNMA, but completes it by improving rapid rekeying and spreading sequences authentication. In Anderson, two variants are proposed: The first variant considers a hypothetical GNSS signal comprising an I and a Q component with the following “specialization”: The I component applies repetitive and uncyphered spreading sequences (similar to the GPS C / A or Galileo Open Service sequences) modulated with meta-data serving authentication of ranging and data ofthe Q component. The Q component applies cyphered spreading sequences and datawhich can be deciphered in a delayed manner with meta-data provided by the I component. Hence, the I channel offers real-time positioning and timing, while the Q component ensure an authenticated, but delayed positioning and timing. The second variant considers another hypothetical GNSS signal comprising only one (I) component, and alternating the main features of both the I and Q components of the first variant in a Time-Division Multiplexing (TDM) manner. Here, the spreading sequence layer alternates between repetitive and uncyphered spreading sequences (same as the sequences applied on the I component of first option) and cypheredspreading sequences (same as the sequences applied on the Q component of firstoption). The data layer alternates between the meta-data serving authentication and the authenticated and cyphered navigation message. This second variant shows the advantage of offering a singular component guaranteeing acquisition, tracking, and authenticated ranging and positioning. Thus, this signal component can be easily accommodated with other signal components (not serving authentication) modulated on the same carrier frequency and transmitted by the same satellite.By alternating cyphered spreading sequences (called PRF in Anderson) anduncyphered spreading sequences (used for acquisition), the corresponding signal becomes more robust to spoofing attacks thanks to the cyphered sequence sections. The spreading sequence for acquisition, called “acquisition section” in Anderson simplifies acquisition by applying the same spreading code over several repetitions, and thus enables the reduction of the number of code hypotheses necessary whencompared to the acquisition of the cyphered spreading sequences. The maindrawback of this solution is the periodicity in the acquisition section, i.e. the corresponding spreading code is repeated over the alternations with the cyphered spreading sequences. This represents a signature or watermarking for an attacker who can recognize the corresponding acquisition section, using for example “blind . .

[0006] Airbus Defence and Space GmbH - 5 - 30A-166 109detection techniques”. The knowledge of this signature enables a malicious attacker to detect and jam during the next occurrence of the acquisition section, denying access to the corresponding GNSS signal. Z. Zhou et al, "CBFH: Coherent Binary Frequency-Hopping Multiplexing for BeiDou B2 Signal", published in J. Sun et al. (eds,), China Satellite, proposes to acquire the transmitted signals with a hopping frequency carrier. It is shown that on one side, Frequency Hopping CDMA signals are more robust against jamming attacks and on the other side, offer wide bandwidth signals for improved tracking performance. Zhou proposes to make the combination of coherent and non-coherent signal acquisition to limit the complexity of wide band signals. In particular, Zhou proposesthat the signal input to the acquisition detector be built by combining, in a non-coherent manner, the squared magnitude of the correlations which have been computed over a coherent integration time. However, this solution introduces major losses, such as the so-called squaring losses, degrading the acquisition performance. Furthermore, Zhou does not mention any application of cyphered spreading sequences. Navigation Message Authentication used in, for instance, Galileo (OSNMA modulated on the E1-I / Nav message) provides receivers protection against spoofing at the navigation message level, but does not offer protection to the spreading sequence layer. Indeed, Galileo Open Service spreading sequences remain uncyphered. It is therefore possible to prepare an “attack” by forging signals with known spreading sequences, defeating both signal acquisition and tracking. The ranging authentication is also a known technique against spoofing, but is not feasible for cold start acquisition. As stated, the Chimera scheme proposes cyphering the complete spreading sequence layer of the GPS L1-C, which is composed of different sub-sequences which are all cyphered and serve rapid or slow authentication channels. This fully cyphered spreading sequence layer, however, greatly enhances the complexity of acquisition based on such signals. Furthermore, in some wireless communication systems and / or communication networks, positioning services are provided for a user equipment (UE). The provisionof an accurate but also resilient positioning has been identified as a key feature forcommunication systems and / or communication networks, as is observed in several industrial use cases, such as in the fields of aviation, automotive, manufacturing, . .

[0007] Airbus Defence and Space GmbH - 6 - 30A-166 109logistics, and other industries. This feature can therefore represent a differentiating commercial item in a competitive commercial situation. Additionally, a recrudescence of situations involving unintentional or intentional threats, such as interferers, jammersor spoofers, can affect legacy positioning and navigation and timing (PNT) solutionsand services, wherein the positioning and PNT services may be to Global NavigationSatellite Systems (GNSSs) is currently contemplated. Alternative solutions, enhancing robustness against such threats are therefore highly desirable and investigated. SUMMARY OF THE INVENTION The invention is set out in the independent claims. Preferred embodiments of the invention are set out in the dependent claims. The invention, as disclosed herein, may achieve several goals, and have numerous advantages and technical effects. These are outlined below, and throughout the present disclosure. The skilled person further understands that the described invention may achieve other goals and have further technical effects not explicitly described herein, but will be understood by the skilled person. A first problem solved by the invention, and a corresponding technical effect, disclosed herein is the facilitation of acquisition of wide-band FH-CDMA or OFDM- CDMA signals, and aiding this facilitation by offering a higher immunity during the acquisition process to the Doppler and ionospheric delay increase observed with LEO- PNT systems. The proposed invention will be valuable not only for the acquisition of LEO-PNT signals, but also of GNSS signals, transmitted by satellites at MEO altitudes, and modulated with FH-CDMA or OFDM-CDMA waveforms, even if the Doppler or ionospheric delay increases are less pronounced. Furthermore, an additional advantage of the proposed invention, described throughout, relates to focusing on enhanced robustness against spoofing and jamming, which is also applicable to both LEO-PNT and GNSS systems. A second problem solved by the invention, and a corresponding technical effect, is the ensuring of a robust acquisition of a protected signal, and more particularly a GNSS signal, against spoofing and jamming attacks, without degrading significantly acquisition and ranging performance. . .

[0008] Airbus Defence and Space GmbH - 7 - 30A-166 109A third problem solved by the invention is to give possibility to track signal waveforms applying the proposed scheme, in order to be robust, almost insensitive to, or greatly reduce the effect of, ionospheric delay and Doppler. Furthermore, the proposed invention aims at designing a cyphered signal waveform whose features ensure a very robust acquisition against jamming and spoofing, but which still guarantees an acquisition for a simple receiver architecture with low complexity. According to a first aspect, we describe a method for creating and processing a signal waveform, the method comprising: generating, by a first processor, two hopped carrier frequencies, wherein the two hopped carrier frequencies are symmetrical with respect to a third carrier frequency, fm, and wherein a distance between the first and second hopped carrier frequencies, |second hopped carrierfrequency – first hopped carrier frequency|, is pre-defined; modulating, by the firstprocessor, the first hopped carrier frequency, called f1herein, and the second hopped carrier frequency, called f2herein, with a narrow-band waveform, wherein a first signal is a first outcome of the modulation on the first hopped carrier frequency and a second signal is a second outcome of the modulation on the second hopped carrier frequency, wherein the first and second hopped carrier frequencies are symmetrical with respect to a third carrier frequency, called a middle baseband frequency, fm, herein, and wherein a distance between the first and second hopped carrierfrequency, |second hopped carrier frequency – first hopped carrier frequency|, ispre-defined; transmitting, by a first transceiver coupled to the first processor, the modulated first signal and the modulated second signal; receiving, by a second transceiver, the transmitted first and second signals, wherein the second transceiver is couplable to a second processor configured to process the received first and second signals; and converting, by the second processor, a first baseband frequency of the modulated first carrier frequency to a central baseband carrier frequency, and a second baseband frequency of the modulated second carrier frequency to the central baseband carrier frequency, wherein the conversion to the central baseband carrier frequency is configured to be applied for each hop applied to the modulated first and second carrier frequencies. In the present disclosure, at least one of f1, f2and fmmay be frequencies expressed at baseband. . .

[0009] Airbus Defence and Space GmbH - 8 - 30A-166 109In some examples disclosed herein, the first and / or second carrier frequencies may be hopped carrier frequencies. The skilled person understands how hopping frequencies function, and how hopping is applied to carrier frequencies. In some examples disclosed herein, the selection of the middle baseband frequency, fm, and the distance between the first and second hopped carrier frequencies which are used in the conversion process may depend on the tested delay hypothesis. It is proposed to apply a waveform based on a Frequency Hopping Code Division Multiple Access (FH-CDMA) scheme. However, the skilled person understands that an OFDM-CDMA-based waveform may additionally or alternatively be applied. More specifically, it is proposed to transmit two signals applying FH-CDMA scheme, which, in some examples, show a large frequency excursion of their respective hopped carrier frequencies. This may allow for the provision of good tracking performance, once acquisition is achieved. In some examples, the respective hopped carrier frequencies f1and f2are selected with respect to specific constraints to facilitate acquisition. The constraint may be, for example, that both f1and f2be modulated with a narrow band signal. Additionally or alternatively, if a central carrier frequency, also called “RF carrier” on which the first waveform is modulated and / or converted,is transmitted within a frequency band where ionospheric effects are negligible (C-band and above, for example, or for terrestrial applications for which ionosphere does not play a role, for example) it may be possible to create a pool of hopped frequency distances |f1-f2| and which is associated with a middle baseband frequency fm. In some examples, the central carrier frequency may be known as the “nominal frequency” and may be, for example, 1575.42 MHz in the L1 band. The middle baseband carrier frequency may lie between f1and f2. The first and second hopped carrier frequencies are modulated with the narrow-band signal. As an example: -|f1-f2|=1MHz for fm = 12MHz during the first hop; and- |f1-f2|=3MHz for fm = -4MHz during the second hop; and- |f1-f2|=2MHz for fm = +2MHz during the third hop.- Etc..The skilled person understands that any suitable values may be used in the above, as long as the constraints of the independent claims are complied with. The above may be stored in a lookup table, as described herein, which is accessible by the first and / or second processor. . .

[0010] Airbus Defence and Space GmbH - 9 - 30A-166 109The two hopped carrier frequencies, f1and f2, are each modulated with a narrow- band waveform such as, for example, Binary Phase Shift Keying (BPSK). In particular, the narrow-band waveform may need to occupy a bandwidth which is smaller or significantly smaller than the overall permitted and transmitted bandwidth, so that the benefit in terms of acquisition complexity reduction become advantageous with respect to other more conventional acquisition techniques applying matched filter approach. As example the narrow-band waveform bandwidth may be at least 6, 8 or 10 times smaller than the transmitted bandwidth. Alternatively, any suitable ratio between the narrow-band waveform bandwidth and the transmitted bandwidth may be used in order to achieve the goals of the disclosure as described herein. The method of choosing a ratio will be known to the skilled person, and may depend on the band being used by the user and / or the specifications of the equipment being used by said user. Additionally or alternatively, the waveform may need to comprise a simple correlation function with a single peak, like BPSK or any other suitable waveform scheme. The two hopped carrier frequencies are symmetrical with respect to a middle baseband carrier frequency, fm. This middle baseband carrier frequency may be hopped with a cyphered scheme. Furthermore, the difference |f2-f1|, i.e the absolute value of f2-f1, may depend directly on the middle baseband carrier frequency fmand / or equivalently on the hop index m. Throughout the present description, the term Δf(m) has the meaning of half of the distance between |f2-f1|, that is to say, ^f(m)=|f2-f1| / 2. Throughout this description, when the dependency of f1and f2with respect to the hop index is described, m is omitted in the Δf(m) definition, yielding to Δf, for sake ofsimplification, but it is to be understood that if the offset ^f(m) is hop indexdependent, then both f1and f2will also be hop index dependent (f1(m) and f2(m)). The decision regarding the relationship of Δf(m) with regards to the hop index m may mainly depend on the spectral region, i.e. the frequency band such as, for example, UHF, L-Band, C-Band, Ku-Band, etc., and may especially depend on the ionospheric impact on to the received signal. For example, for frequency bands lower than, or below, C-Band (~5GHz) it may be desirable to keep Δf constant, Δf(m)=Δf in order to take benefit of the further processing steps offering better ionospheric immunity. However, for bands showing a much milder ionospheric activity, it may be possible to let Δf vary and depend on the hop index m, such that an unambiguous relationship between m and Δf exists, in the form of a lookup table, Δf(m)=g(m). This lookup table may be stored in a memory couplable to at least one of the . .

[0011] Airbus Defence and Space GmbH - 10 - 30A-166 109processors and / or transceivers. The memory may be wholly physically, partially physical and partially stored in the cloud, or wholly stored in the cloud. This predefined value of ^f as function of the hop index m may then still permit the advantageous processing of the proposed signals described herein. Having two hopped carrier frequencies which are symmetrical with respect to a middle basebandcarrier frequency, fm, and separated from Δf(m) with respect to this middle basebandcarrier frequency may enable the User Terminal (UT) to proceed with particular embodiments of the invention disclosed herein. As mentioned above, this may allow for robust acquisition against jamming and spoofing while maintaining a simple receiver architecture with low complexity. In some examples, the first and second signals at carrier frequencies f1and f2may be modulated with different spreading sequences noted as akand bk, respectively, both taking the role of the primary spreading sequence layers. Alternatively, the first and second signals may be modulated with a tiered sequence structure. In the case of use of tiered sequences, each symbol of the tiered sequence is constituted of a secondary sequence layer comprising chips (akand bk) modulated with a primary sequence layer (Scnand Sdn). In this case, the sequence ak(respectively Scn) is different to the sequence bk(respectively Sdn) for the first and second signals. Particular embodiments can effectively exploit the primary sequence layer in order to reduce sensitivity to the thermal noise. But still, this may reduce the vulnerability of the method to jamming and spoofing. The first and / or second transceiver may be only a receiver, or only a transmitter. In some examples, there may be a plurality of pairs of first and second signals. That is to say, there may be N pairs of first and second signals. Each of the N signal pairs may fulfil some, or all, of the signal design constraints disclosed herein. If the User Terminal is used in line with the aspects described herein, as a prerequisite, it is considered that the User Terminal will proceed to the generic signal reception and conditioning steps before the processing steps which are specific to the proposed invention. Those early steps may comprise at least one of reception through an antenna, filtering, conditioning, down-converting from the RF carrier to the first baseband frequency or Intermediate Frequency (IF) carrier, and finally conversion in the digital domain with an Analogue-to-Digital Converter (ADC). The skilled person understands that this may allow for the signals to be processed in the baseband domain. . .

[0012] Airbus Defence and Space GmbH - 11 - 30A-166 109As disclosed above, after receiving the first and second signals, the method, in some examples, further comprises: down-converting, by the second processor, a first baseband frequency of the modulated first carrier frequency to the central baseband carrier frequency and up-converting a second baseband frequency of the modulated second carrier frequency to the central baseband carrier frequency, wherein the conversion to the central baseband carrier frequency is configured to be applied for each hop applied to the modulated first and second carrier frequencies. This maymean that the central baseband of each of the hopped carrier frequencies (f1 and f2)are modulated / converted with a narrow-band waveform. In the following, and for sake of simplification, it is considered that f1(and respectively f2) is equal to fm+^f(m) (and respectively fm-^f(m)), so that the conversion of f1(and respectively f2) to the central baseband carrier frequency is a down-conversion (and respectivelyan up-conversion). The waveform may occupy a small bandwidth with respect to theoverall transmitted bandwidth. For example, in the E1-Band, if the transmit bandwidth is 32MHz a narrow-band may not be larger than a 1 / 10 of it, so ~4MHz. The waveform may be a Binary Phase Shift Keying, BPSK(N) waveform and where N represents the normalized chip rate, normalized to fnom= 1.023MCps (such as a BPSK(1) waveform, a BPSK(2) waveform), or any suitable kind of waveform showing a single peak in the correlation function. This may allow for the provision of a simple acquisition of the corresponding waveform. For example, if a BOC(1,1) waveform shows 4MHz of spectral occupancy, like the BPSK(2) waveform, so that it is in line with the 4MHz in the E1-band, this BOC signal would also have multiple peaks, which would make the acquisition of the narrowband signal more complex. However, as mentioned above, the narrow-band waveform bandwidth may be at least 6, 8 or 10 times smaller than the transmitted bandwidth. Alternatively, any suitable ratio between the narrow-band waveform bandwidth and the transmitted bandwidth may be used in order to achieve the goals of the disclosure as described herein. This up / down conversion, which may be applied for each hop, may allow for the processing of the signals (after up / down conversion) at baseband, and with a narrower bandwidth. This may mean that it is possible to reduce the noise bandwidth to this narrow-band, thereby increasing noise robustness, especially after themultiplication step described herein. The first and second signals are signals receivedby the second transceiver before conversion of these signals to the respectivebaseband frequencies via the up- and down-conversion.In the former examples, and throughout the present specification, the term down- conversion (and respectively up-conversion) is applied when removing or wiping-off . .

[0013] Airbus Defence and Space GmbH - 12 - 30A-166 109the fm+^f(m) (and respectively fm-^f(m)) frequency component from the first (andrespectively second) baseband frequency of the modulated first (and respectivelysecond) carrier frequency. This terminology is applied as fm+^f(m) is larger than fm-^f(m) for a positive frequency offset ^f(m), and will be further applied within thepresent specification for sake of consistency and conciseness. In some examples, the method further comprises down-converting, by the second processor, the first baseband of the modulated first carrier frequency; and up- converting, by the second processor, the second baseband of the modulated second carrier frequency, wherein the down-conversion and the up-conversion are applied for each hop applied to the existing waveform by the first waveform In some particularly preferred examples, after receiving the first and second signals, the method further comprises: first filtering, by the second processor, the modulated first and second carrier frequencies with a bandwidth adapted to a spectral occupancy of the narrow-band waveform, in particular, the method further comprising pre-correlating, by the second processor, the first filtered first and secondcarrier frequencies. This may allow for the output of the down / up converted signaland / or the received signals to be filtered with a bandwidth which may, in some examples, be adapted to the spectral occupancy of the narrow-band waveform. This may reduce the noise contribution originating from multiplication as described herein and / or general noise from the outside environment. In some examples, filteredsample streams of the down / up converted signals are pre-correlated before, forexample, multiplication as described herein. In some examples, the bandwidth of thefilter may be adapted in such a way that it fits the narrow-band to not lose a significant amount of power. As an example, if the narrowband waveform is a BPSK(1) with an occupancy of 2MHz with the main lobe comprising ~90% of thepower, a filter of 2MHz or more may be used. In some examples, the down- and up-converting steps mentioned herein may be applied before the first filtering step. Pre-correlation, as mentioned herein, may be advantageous in that by applying a further correlation, it may be possible to reduce the noise bandwidth even further. Before this pre-correlation, the noise bandwidth may equal the bandwidth of the narrow-band waveform (ex: 2MHz for a BPSK(1)). After pre-correlation, the bandwidth may be reduced to the inverse of the pre-correlation time (equal to the spreading code duration). For example, if short codes of 31 chips (e.g. ~0.03ms for a BPSK(1)) are considered, then a bandwidth of 33KHz may be achieved, which is lower than 2MHz. For example, if short codes of 341 chips (e.g. 0.3ms for a BPSK(1)) . .

[0014] Airbus Defence and Space GmbH - 13 - 30A-166 109are considered, then a bandwidth of 3KHz may be achieved which is greatly lower than 2MHz. In some particularly preferred examples, after receiving the first and second signals, the method further comprises: applying a bandpass filtering, by the second processor, to the modulated first and second carrier frequencies with a bandwidth adapted to a spectral occupancy of the narrow-band waveform and with a bandpass bandwidth centered at the first and second carrier frequencies, in particular, the method further comprising (pre-)correlating, by the second processor, the first filtered first and second carrier frequencies and / or applying a conversion to the central baseband carrier frequency of the bandpass filtered, possibly pre-correlated, modulated signals at the first and second carrier frequencies. As stated earlier, this conversion to the central baseband carrier frequency may take the form an down- (and respective up-) conversion for the first (and respective second) carrierfrequency, considering that the first carrier frequency, f1, is larger than f2 in thisexample. The skilled person understands that, in some examples, f2may be larger than f1. In the above particularly preferred example, or indeed any other example describedherein, the correlation with the first and second signals before the down- and up-conversion may be performed with a replica which is converted at the first and second carrier frequencies to ensure spectral consistency. Alternatively, in the above particularly preferred example, or indeed any other example described herein, thecorrelation with the first and second signals after the down- and up- conversion maybe performed with a replica generated at baseband to ensure spectral consistency.In some examples, the first filtering may additionally or alternatively comprise filtering the modulated first and second carrier frequencies with a narrow-band bandpass filter centered at f1and f2. The bandpass filter may allow for the output ofthe down / up converted signal and / or the received signals to be filtered with abandwidth which may, in some examples, be adapted to the spectral occupancy of the narrow-band waveform. In some examples, after receiving the first and second signals, the method further comprises: multiplying, by the second processor, the modulated first carrier frequency with a complex conjugate of the second carrier frequency. That is to say in some particularly advantageous examples of the present specification, the sample stream originating from the first filtered and / or down-converted carrier (f1) and . .

[0015] Airbus Defence and Space GmbH - 14 - 30A-166 109modulated with a narrow-band waveform, with the complex conjugate of the sample stream originating from the second filtered and / or up-converted carrier (f2) may be multiplied. Alternatively, these carriers may only be filtered, may only be pre- correlated, or neither before this multiplication. As an example, one architecture according the present specification may apply the pre-correlation but not any filtering with a narrow-band filters, as the pre-correlation not only enables the de-spreading of the received signals, but also the reduction of the noise bandwidth, as a narrow- band filter would do. This multiplication may mean that the Doppler dependency is no longer a degrading factor when testing the delay hypotheses for acquisition performance. The skilled person understands that this leads to improved signal acquisition. In some examples, the method further comprises forming at least two correlations,by the second processor, by correlating the output of the multiplication with at leasttwo replicas generated for a delay hypothesis derived from an estimated delay hypothesis, wherein the at least two correlations are delayed or advanced to produce different Early and Late correlator channels for the generation of a Delay Lock Loop Discriminator; and multiplying the modulated first carrier frequency with the modulated second carrier frequency without application of a complex conjugate operation; and forming a further correlation, by the second processor, by correlating the output of the multiplication of the modulated first carrier frequency with the modulated second carrier frequency without application of a complex conjugate operation, with a further corresponding replica generated for a delay hypothesis derived from the from the estimated delay hypothesis to produce a Prompt correlator channel for the generation of a Phase Lock Loop Discriminator and / or a Frequency Lock Loop Discriminator, wherein the further correlation and the further replica are different from the at least two correlations and the at least two replicas; and estimating, by the second processor, a code delay, a phase and a frequency of the received first and second signals based on the generated Delay Lock Loop Discriminator, Phase Lock Loop Discriminator and / or Frequency Locked Loop Discriminator In some examples, the method further comprises: forming a first correlation, by the second processor, by correlating the output of the multiplication with a known replica generated for a tested delay hypothesis; forming, by the second processor, a first detector output comprising a magnitude of the first correlation; comparing, by thesecond processor, the first detector output to a first detection threshold;retaining, by the second processor, a coarse delay estimate if: . .

[0016] Airbus Defence and Space GmbH - 15 - 30A-166 109a) the first detector output exceeds the first detection threshold; orb) repeating the formation of the first correlation, the formation of thefirst detector output and the comparison of the first detector output for another tested delay hypothesis if the first detector output does not exceed the first detection threshold; multiplying, by the second processor, the modulated first carrier frequency with the modulated second carrier frequency without application of a complex conjugate operation and the formation of the first correlation by applying the retained coarse delay estimate; forming a second correlation, by the second processor, by correlating the output of the first correlation with an exponential including a tested Doppler hypothesis; forming, by the second processor, a second detector output comprising a magnitude of the second correlation; comparing, by the second processor, the second detector output to a second detection threshold; and retaining, by the second processor, the coarse Doppler estimate if: c) the second detector output exceeds the second detection threshold; ord) repeating the formation of the second correlation, the formation of thesecond detector output and the comparison of the second detector output foranother tested Doppler hypothesis if the second detector output does not exceed the second detection threshold. That is to say, the output of the multiplication, in some examples from both streams, may be correlated with a known replica applying a tested delay (i.e. code) hypothesis. The delay (i.e. code) hypothesis may depend on a typical code search for acquisition. Where the delay (i.e. code) uncertainty domain depends on the a priori uncertainty, the relative distance between satellite and user terminal, implying a propagation delay, may be used as a basis for the delay hypothesis. In a worst-case scenario, all of the delay, or equivalently, code hypotheses may need to be tested. The replica may be generated with a spreading sequence obtained with the product of the spreading sequences modulated on the first and second signals. Furthermore, the overall number of code hypotheses maynot only depend on the delay uncertainty, but also on the number of codehypotheses to be tested per chip waveform, which depends on the permitted code mis-alignment losses. Finally, the delay hypothesis may not only be translated into a code delay hypothesis used to offset the (spreading code) replica accordingly, butalso into an offset of the middle baseband carrier frequency fm and the offset ^fm, asfor both FH-CDMA and OFDM-CDMA signals, both the code and frequency hopping schemes are rigidly tied. In some examples, a detector output may be formed by taking the magnitude (or absolute value squared or magnitude squared) of the correlation. The comparison of the detector output with a first detection threshold may be set according to a specific probability of missed-detection and false alarm, which may support the decision for the tested code hypothesis. The probability of . .

[0017] Airbus Defence and Space GmbH - 16 - 30A-166 109detection and false alarm may impact the typical mean time to acquire. For example, if the first detection threshold is set too low (corresponding to, for example, a PFA of 10%), it may mean that the threshold may be exceeded once every 10 times by a signal originating from noise, rather than the signals that are wished to be acquired. This may then impact / delay the acquisition time. If the threshold is set too high, the probability to see the peak is reduced, as the peak has a lower likelihood of exceeding the threshold. Therefore, the first detection threshold may be set in order to balance these two effects. The correlation function obtained in this process may be similar to one of a CDMA signal modulated with a BPSK waveform and showing a broader peak than the original FH-CDMA, or OFDM-CDMA, signal, or OFDM signals. This broader correlation peak may allow for a reduction in the number of code hypotheses to be tested, when compared to a matched filtered acquisition. Furthermore, in relation to the above-mentioned features, and the features mentioned below, the fact that both hopped carrier frequencies f1and f2may be separated by a constant interval 2^Δf over the complete correlation duration may enable the suppression of the ionospheric contribution in the detector output. For bands showing a much milder ionospheric activity, it may be possible to let Δf vary and depend on the hop index m, such that an unambiguous relationship between m and Δf exists, in the form of a lookup table, Δf(m)=g(m). This lookup table may be stored in a memory couplable to at least one of the processors and / or transceivers. The memory may be wholly physically, partially physical and partially stored in thecloud, or wholly stored in the cloud. This predefined value of ^f as function of thehope index m may then still permit the advantageous processing of the proposed signals described herein. As for the acquisition of the delay (i.e code) hypothesis based on the comparison of the first detector output with a first detection threshold, the setting of the second detection threshold, which is compared to the second detector output, may have to fulfill a balance between the probability of false alarm and the probability of detection for the tested Doppler hypotheses. Furthermore, an overall optimum for the allocation of the PFA and PD for the tested delay (i.e. code) hypothesis and the PFA and PD for the tested Doppler hypothesis may be performed. More precisely, the optimum may be performed by accounting for the overall number of delay (i.e. code) hypothesis and Doppler (hypothesis) tested separately, and to the joint PFA and PD applicable to the delay (i.e. code) and Doppler acquisition. The skilled person understands that any suitable allocation of the corresponding PFA and PD levels for . .

[0018] Airbus Defence and Space GmbH - 17 - 30A-166 109delay (i.e. code) and Doppler testing and the resulting threshold derivation may be used. The present disclosure also allows for a fast acquisition with a minimum overall number of delay (i.e. code) and Doppler hypotheses being tested, thereby making the receiver acquisition processing less complex, but robust against spoofing. In some examples, once acquisition has been achieved, the second processor may also aim at estimating precisely the code delay, carrier phase and frequency of the received signal. For this it will apply the coarse code and Doppler hypotheses estimated from the acquisition phase to enter firstly into a Pull-In, and then into a tracking phase. In conventional receiver architectures, applying scalar tracking structures, several, or any suitable number of correlation functions may be calculated for delays or advances with respect to the prompt correlator channel, and fed to a Delay Locked Loop (DLL) for code delay estimation, to a Frequency Locked Loop (FLL) for carrier frequency estimation and / or to a Phase Locked Loop (PLL) for carrier phase and frequency estimation of each single received signal. Each of those correlation functions is obtained with a replica which is an offset version of the replica generated for the prompt correlator channel derived from the code delay estimated by the DLL. These correlation functions applied for suitable additional delays (atop the one estimated by the DLL) may be calculated based a similar architecture to the delays disclosed herein in relation to acquisition. As for the acquisition architecture, when generating a correlator output corresponding to aspecific code delay value, it may not only be necessary to offset the replica accordingto this value, but also to apply the middle baseband frequency carrier fm and also theoffset ^f(m) corresponding to the corresponding delay estimation, during the down-and up-conversion processes, as for both FH-CDMA and OFDM-CDMA signals, both the code and frequency hopping schemes are rigidly tied. The different correlation output, called Early and Late correlator channels may serve for the production of a so called “discriminator” which is a key element of any DLL. An example of simple discriminator is the non-coherent “Early minus Late” discriminator which is obtained by computing the difference between the squared absolute value of an early correlation function and the squared absolute value of a late correlation function. The distance or spacing between the early or late correlators with respect to the prompt may be a parameter that depends on the receiver configuration, wherein the smaller this parameter is and the better, also considering limitations due to the finite sampling frequency. Typical values for such a parameter are 0.5 chip for low-grade . .

[0019] Airbus Defence and Space GmbH - 18 - 30A-166 109receivers, such as mass-market receivers, and 0.05 chip for high-end receivers. Other discriminators may be the Double-Delta, which is built with two-pairs of early and late correlators computed for two different values of the distance with respect to the prompt channel. In addition to the DLL, a PLL aiming at estimating the phase and frequency of the received signal may also be fed with the prompt correlator channel and apply a specific phase discriminator, such as an atan() or asin() one. A FLL may also be fed with the prompt channel to estimate the frequency carrier directly proportional to the received Doppler. Some adaptations to conventional code delay, carrier phase and frequency locked loops, justified by the particularities of the proposed signal processing scheme, may be necessary and outlined herein. Firstly, the signal phase and frequency (Doppler) information of the output of the complex multiplication between the output of thedown- and up-conversion branches (one of both being complex conjugate), possiblyfollowed by an adapted filter, vanishes. Therefore, and contrarily to a conventionalGNSS receiver, it may not necessary to multiply the output of the complexmultiplication and adapted filter with the sine and cosine functions generated with the output of the carrier (or frequency) loop NCO to de-wipe the corresponding carrier phase and frequency information to generate the Early and Late correlator channels used to generate the non-coherent discriminator of the DLL. Here, only the real and imaginary parts may be necessary for the application to the aforementioned output to produce the so-called In-Phase and Quadrature Phase components necessary to generate the Early and Late correlator channels used to generate the non-coherent discriminator of the DLL. Secondly, because the phase and (Doppler) frequency information disappears from the output of the complex multiplication and possible adapted filter, the PLL or FLL may then not be able to estimate the signal carrier and (Doppler) frequency information. In order to avoid this situation, nocomplex conjugate operation may be applied to one of the Down- or Up- conversionbranches before application of the complex multiplication and possible adapted filter to generate the Prompt correlator channel necessary for PLL or FLL discriminator calculation. In order to produce each delay or advanced correlator channel, each correlator channel may be obtained by applying at least one of the aforementioned processingsteps introduced for the acquisition with the down / up conversion, the low-passfiltering, the complex conjugate multiplication and finally the correlation with a replica, as mentioned herein, wherein the replica has been delayed or advanced according to the specific Early or Late correlator channel configuration. Additionally . .

[0020] Airbus Defence and Space GmbH - 19 - 30A-166 109or alternatively, it may be possible to proceed to a high-pass filter of each channelprocessing the S1 and S2 signals, and then proceed to the down- and up-conversionof the filtered signals. Additionally or alternatively, it may also be possible to introduce a pre-correlation step, as is described herein. In such a case, the replica necessary to feed the pre-correlation may also delayed or advanced according to the specific Early or Late correlator channel configuration. Additionally or alternatively, the adapted filter may be applied after the complex multiplication described herein. The role of the corresponding adapted filter is to suppress potential interfering signals which are also comprised in the received signals. In some examples, the FH-CDMA scheme is adapted with an application of a cyphering scheme to a hopped frequency domain and a spreading code domain of said FH-CDMA scheme. The cyphering may be applied in the hopped frequency domain (resultantly, the apparent “walk” of both hopped frequencies appears unpredictable) and / or in the spreading code domain (resultantly, the corresponding spreading sequence symbols, also called chips, are cyphered). Varying the carrier frequency through a specific and cyphered hopping scheme, not accessible to non- authorised and possibly malicious users, offers another dimension for robustness in addition to the cyphering of the spreading sequences. It thus may complexify the tasks of the spoofer / jammer, especially when considering the capabilities offered by quantum computers. Hence, despite the signal being transmitted over a large bandwidth to be robust against jamming, it may also allow for a fast acquisition with a minimum of delay (i.e. ode) and Doppler hypotheses being tested. In some examples, the first signal to be down-converted is defined by the equation: and the second signal to be up-converted is defined by the equation: . .

[0021] Airbus Defence and Space GmbH - 20 - 30A-166 109 where: M: number of hops during an integration time; Nc: number of cyphered chips during the integration time; Tc: chip period; fm: middle baseband carrier frequency for the hop index m;Δfm: offset frequency relative to the middle baseband (i.e. central) frequency carrierfm, wherein the absolute value of the offset Δfmdepends of the middle baseband carrier frequency fmand / or on the hop index m, where Δfm= g(m), and where g is a function relating the offset Δfmto the hop index m; ^: delay between a satellite and a receiver; p: chip pulse shape; fdm: Doppler of the respective signal at frequency fm+ Δfm; φ1: initial phase offset of the first signal at transmission; φ2: initial phase offset of the second signal at transmission; A1: amplitude of the first signal; A2: amplitude of the second signal; d1: data of the first signal; d2: data of the second signal; ak: kth chip of the first signal; bk: kth chip of the second signal; ^m: 1 or 0 to define potential discontinuity; and ^^^^^(^): contribution of the ionospheric effect at carrier f, and is given by the corresponding expression: ()[ 40.3 × ^^^^^^^^ ^ ^] = −^^ × ^^where: TEC: total electron count; and c0: speed of light. The above signals may be based on the use of two Direct Sequence CDMA Frequency-Hopped (DS / FH) interplexed signals, with said signals being represented by S1 and S2. Should S1 and S2 be simultaneously transmitted, there may be no ^term, no ionospheric term ^^^^^(^) and no Doppler term fdm, in the equations. .

[0022] Airbus Defence and Space GmbH - 21 - 30A-166 109described herein. Said signals may be transmitted symmetrically with respect to a sequence of frequency carriers by the first transceiver. At reception, the two signals S1and S2can be expressed as above. The above may also allow for any hypothesis on the Doppler to not be applied when, for example, the received signal is correlated. In this way, the hypotheses in the delay (and equivalently code)dimension can be tested separately to the hypotheses in the Doppler dimension. Thismay represent a significant reduction of the complexity of the method and scheme when compared to conventional acquisition schemes for which both delay andDoppler hypotheses are tested simultaneously, rather than sequentially.In some examples, in low operational frequencies, Δfmmay be constant, where |Δfm|= Δf. In some examples, the first signal and / or the second signal is transmitted in a continuous or discontinuous manner, in particular wherein the first and second signals are transmitted with a random sleep cycle time sequence. The parameter ^mintroduced in the expressions of S1and S2enables to define the sleeping duty cycle. In the discontinuous case, no signals may be transmitted for some epochs. In particular, if the first signal and / or the second signal is transmitted in a discontinuous manner, the signal may be transmitted during an “on” period, and not transmitted during an “off” period. In some examples, when both the first and second signals are discontinuous, both signals are transmitted simultaneously during an “on” period, and not transmitted during an “off” period. Discontinuous transmission of at least one of the first and second signals may comprise some particular advantages. When both signals are transmitted during the “on” period, the objective of improving acquisition may be achieved, even if tracking could also be done during this period. During the “off” period, there may be two options, either nothing is transmitted, or other signals, considering that two signals may still need to be transmitted, may be transmitted but without any constraints being applied to these additional signals. These periods may be used like the TESLA scheme for tracking and data provision. If OFDM signals are used, it can also be considered that some frames may apply the proposed constraints between the signals S1and S2, while other frames would not. An advantage of the “random sleep” sequence may be like those seen in the TESLA scheme. It is to be understood that in the “random sleep” sequence, during the “off” period, nothing may be transmitted that improves robustness against a jammer or a spoofer, as said jammer / spoofer may ignore the sequencing of sleep periods. In such a case, the tracking, should it be used, may only have to be covered by the S1and S2. .

[0023] Airbus Defence and Space GmbH - 22 - 30A-166 109signals transmitted during the “on” periods. This may not only allow for robust acquisition, but also for robust tracking. Additionally or alternatively, during “off” periods, other signal components S3and S4, which don’t have to fulfill the imposed constraints, and which enable the improvement of some other performance, may be transmitted. This other performance may relate to tracking, robustness to jamming / spoofing during a tracking phase, or any other suitable performance or parameter. In some examples, after receiving the first and second signals, the method further comprises: frequency converting, by the second processor, the first and second signals via down-converting the first signal and up-converting the second signal, based on the middle baseband carrier frequency and the offset frequency, which may depend on the delay hypothesis to be tested during acquisition; second filtering, by the second processor, the frequency converted signals by applying a bandwidth accounting for a chip rate of the frequency converted signals; multiplying, by the second processor, the second filtered first signal with a complex conjugate of the second filtered second signal; correlating, by the second processor, the output of the multiplication with a replica generated by the second processor via the use of a tested code hypothesis, which may directly depend on the delay hypothesis; and calculating, by the second processor, a magnitude of the output of the correlation. That is to say, the received signal may be split into 2 branches through an downconversion (with fm+Δfm) and a up conversion (with fm-Δfm) based on the knowledgeof the hopping carrier frequency fmfor the hop, and the offset frequency Δfmdepending on m. These branches may be further filtered via a bandwidth accounting for the chip rate. In some examples, the bandwidth may be chosen in such a way that it fits the narrow-band to not lose a significant amount of power. As an example, if the narrowband waveform is a BPSK(1) with an occupancy of 2MHz with the main lobe comprising ~90% of the power, a filter of 2MHz or more may be used. The output of the first branch relating to one of the converted signals may be multipliedwith the conjugate of the output of the other branch. The output of themultiplication may then be correlated with a replica generated for a given tested code hypothesis which may directly depend on the delay hypothesis. The magnitude of the correlation output may then be calculated. In some examples, the correlation step comprises the equation: . .

[0024] Airbus Defence and Space GmbH - 23 - 30A-166 109 where:r(t): generated replica; and^̂: code delay hypothesis also called code hypothesis; and the calculation step comprises the equation: where: CAF: Cross-Ambiguity Function, wherein the CAF may be used for a validation for the proposed tested code hypothesis, and wherein the CAF is compared with a first detection threshold configured to be set according to a specific probability of missed detection and / or false alarm; and CCF: Cross Correlation Function. The output of the multiplication is correlated with a replica generated for a given tested code delay hypothesis, ^̂, and the CAF may serve as a validation for the proposed tested hypothesis. The comparison of the detector output with a first detection threshold may be set according to a specific probability of missed-detection and false alarm, via the CAF, and may support the decision for the tested code hypothesis. The probability of missed detection and false alarm may impact the typical mean time to acquire. For example, if the first detection threshold is set too low (corresponding to, for example, a PFA of 10%) it may mean that the threshold may be exceeded once every 10 times by a signal originating from noise, rather than the signals that are wished to be acquired. This may then impact / delay the acquisition time. If the threshold is set too high, the probability to see the peak is reduced, as the peak has a lower likelihood of exceeding the threshold. Therefore, the threshold may be set in order to balance these two effects. The skilled person understands that any suitable threshold may be used. In some examples, after receiving the first and second signals, the method further comprises: pre-correlating, by the second processor, the first and second signals with short wherein the first to be correlated is defined and the second signal to be pre-correlated is defined by:. .

[0025] Airbus Defence and Space GmbH - 24 - 30A-166 109 where: M: number of hops during an integration time; Nc: number of cyphered chips during the integration time; Tc: chip period; fm: middle baseband carrier frequency for the hop index m; Δfm: offset frequency relative to the middle baseband frequency carrier fm, wherein the absolute value of the offset Δfm depends on the middle baseband carrier frequency fm and / or on the hop index m, where Δfm= g(m), and where g is a function relating the offset Δfm to the hop index m; ^: delay between a satellite and a receiver; p: chip pulse shape; fdm: Doppler of the respective signal at frequency fm+ Δfm; φ1: initial phase offset of the first signal at transmission; φ2: initial phase offset of the second signal at transmission; A1: amplitude of the first signal; A2: amplitude of the second signal; d1: data of the first signal; d2: data of the second signal;ak: kth chip of the first signal;bk: kth chip of the second signal; ^m: 1 or 0 to define potential discontinuity; Ns: a length of the short codes; Scn: nthchip of the short code for the first signal; and Sdn: nthchip of the short code for the second signal. When applying a pre-correlation, then the correlation step applied to the output of the multiplication between the output of the two branches, one being complex conjugate, may be carried out with a replica generated with the product of the secondary codes described herein. In order to reduce undesired noise contributions, the noise bandwidth may be reduced before, for example, the multiplication step. For this purpose, a pre-correlation with very short code (Scn and Sdn) is applied. Additionally or alternatively, this may allow for the ionospheric delay vanishing from the output of the method. Alternatively, short codes may be used, or codes of any suitable length. This pre-correlation may enable for the reduction of the noise bandwidth from, for example, MHz (2 MHZ for a BSPK(1)) down to a few KHz (the . .

[0026] Airbus Defence and Space GmbH - 25 - 30A-166 109inverse of the short code duration). This reduction may improve the acquisition performance for the method and system described herein obtained via complex multiplication as mentioned herein. The short code, taking the role of the primary code, is preferably periodic and / or modulated with another code, called a secondary code which may be random and / or generated with a cyphering algorithm. Therefore, if the length of the short code is too long, the secondary code may have a lower rate of cyphered chips, which can have some negative consequences with respect to robustness to spoofers. So, the code length may be chosen such that there is a suitable trade-off between acquisition performance and robustness against spoofers. In some examples, in low operational frequencies, Δfmmay be constant, where |Δfm|= Δf. In some examples, the method further comprises: third filtering, by the second processor, the first and second signals with a bandpass filter by applying a bandwidth adapted to a spectral occupancy of the narrow-band waveform and a bandpass bandwidth centered at the first and second carrier frequencies; fourth converting the third filtered signals via down-converting the first filtered signal and up-converting the second filtered signal; in particular further pre-correlating, by the second processor, the filtered and converted first signal and the filtered and converted second signal; multiplying, by the second processor, the filtered and converted first signal with a complex conjugate of the filtered and converted second signal; and calculating, by the second processor, a magnitude of the output of the correlation. That is to say, the received signal may be split into 2 branches throughan down conversion (with fm+Δfm) and a up conversion (with fm-Δfm) based on theknowledge of the hopping carrier frequency fmfor the hop, and the offset frequency Δfm. These branches may be further bandpass filtered via a bandwidth accounting forthe chip rate. In some examples, the bandwidth may be chosen in such a way that itfits the narrow-band to not lose a significant amount of power. As an example, if the narrowband waveform is a BPSK(1) with an occupancy of 2MHz with the main lobe comprising ~90% of the power, a filter of 2MHz or more may be used. The output of the first branch relating to one of the converted signals may be multiplied with theconjugate of the output of the other branch. The magnitude of the correlationoutput may then be calculated. In some examples, the correlation step comprising correlating the output of the multiplication with a generated replica may also apply to the above example. In some examples, the multiplying step comprises the equation: . .

[0027] Airbus Defence and Space GmbH - 26 - 30A-166 109 where: SN: the fourth filtered first signal;SP: the fourth filtered second signal; andCCF: Cross Correlation Function; and the calculation step comprises the equation: In the above equations, the contribution of the ionosphere delay is not shown for simplicity of representation. However, the same mathematical developments could show the corresponding ionospheric delay vanishing from the detector output as shown above for the “Spectral Folded Acquisition with Pre-Conversion to Baseband” concept. The output of the multiplication is correlated with a replica generated for a given tested code delay hypothesis, and the CAF and CCF may serve as a validation for the proposed tested hypothesis. The comparison of the detector output with a first detection threshold may be set according to a specific probability of missed-detection and false alarm, via the CAF and CCF, and may support the decision for the tested code hypothesis. The reduction of noise and / or multipath via use of the pre- correlation may lead to the CAF being limited by the CCF. The probability of missed detection and false alarm may impact the typical mean time to acquire. For example, if the first detection threshold is set too low (corresponding to, for example, a PFA of 10%) it may mean that the threshold may be exceeded once every 10 times by a signal originating from noise, rather than the signals that are wished to be acquired. This may then impact / delay the acquisition time. If the threshold is set too high, the probability to see the peak is reduced, as the peak has a lower likelihood of exceeding the threshold. Therefore, the threshold may be set in order to balance these two effects. However, any suitable threshold may be used as deemed suitable by the user. In some examples, a subset of the first and / or second signals are modulated with a known data pattern, the method further comprising: selecting, by the first processor, the subset of first and / or second signals; ignoring, by the second transceiver, the . .

[0028] Airbus Defence and Space GmbH - 27 - 30A-166 109subset of first and / or second signals, wherein the entirety of the first and second signals are symmetrical with respect to the third carrier frequency. This may be used in, for example, OFDM schemes, or combined with any of the aspects described herein. Contrarily to FH-CDMA signals, which transmit only a subset of carriers modulated with the pulse shape, p(t), OFDM signals exploit and transmit all carriers, called sub- carriers in a 5G context. Nevertheless, to ensure satisfactory acquisition and tracking of the OFDM signals some specific sub-carriers may not be modulated with “random” data, but rather with a known data pattern. Such sub-carriers modulated with known sequences are called pilot sub-carriers. The above features may consist of selecting such pilot sub-carriers, ignoring the sub-carriers modulated with data, while still satisfying the symmetry between the pair of sub-carriers with respect to a central sub-carrier. The data of the sub-carriers may be real data, and not pseudo-data. The other sub-carriers may be used for the communication traffic, while the non-ignored sub-carriers are the sub-carriers described herein, and may be used to initiate the link in, for example, acquisition and / or tracking etc. By doing so, and ignoring the sub-carriers dedicated to the communication, it may be possible to apply the above- mentioned feature to the first aspect. In some examples, where a subset of the first and / or second carrier frequencies are modulated with a known data pattern, the method further comprising: selecting, by the first processor, the subset of first and / or second carrier frequencies; ignoring, by the second transceiver, the subset of first and / or second carrier frequencies, wherein the entirety of the first and second carrier frequencies are symmetrical with respect to the third carrier frequency. According to a second aspect, we describe a system comprising: a first transceiver and a second transceiver; a first memory couplable to the first transceiver and a second memory couplable to the second transceiver; and a first processor couplable to the first memory and first transceiver, and a second processor couplable to the second memory and second transceiver, wherein the first and second processors are configured to undertake the method steps of the first aspect. This system may use any known processor and / or memory and / or receiver. Advantages of the present disclosure may be as follows:- To ensure immunity of the method and / or system to ionospheric delay. .

[0029] Airbus Defence and Space GmbH - 28 - 30A-166 109- To ensure immunity of the method and / or system detector for delay hypothesistesting to Doppler- The large bandwidth of the FH-CDMA scheme strengthens pseudo-range trackingperformance.- The specific constraint regarding the known offset ^fm between each of the hoppedcarrier frequencies and the middle baseband carrier frequency, fm, enables the implementation of a specific signal processing scheme which permits a fast acquisition with a minimum overall number of delay (i.e. code) and Dopplerhypotheses being tested, therefore making the receiver acquisition processing lesscomplex but robust against spoofing. It is to be noted that the offset ^fm may be constant, especially for low frequency bands where ionosphere activity is pronounced, or may depend on the hop index m for those frequency bands where ionosphere activity is milder.- The large bandwidth of the FH-CDMA scheme strengthens robustness againstjamming (by spreading the corresponding jamming power).- The cyphering applied to both directions of the FH-CDMA scheme strengthensrobustness against a spoofer / spoofing. The cyphering applied to both directions of the FH-CDMA scheme may strengthen robustness against a spoofer / spoofing and may reduce the detectability of specific acquisition sections which could be used to jam the received signal during such sections to hinder signal acquisition. Furthermore, the invention in the present disclosure may be extended to applications exploiting OFDM waveforms, such as, for example, 5G / 6G NTN applications. It is clear to a person skilled in the art that the statements set forth herein may be implemented under use of hardware circuits, software means, or a combination thereof. The software means can be related to programmed microprocessors or ageneral computer, an ASIC (Application Specific Integrated Circuit) and / or DSPs(Digital Signal Processors). For example, the processing unit may be implemented atleast partially as a computer, a logical circuit, an FPGA (Field Programmable Gate Array), a processor (for example, a microprocessor, microcontroller (µC) or an array processor) / a core / a CPU (Central Processing Unit), an FPU (Floating Point Unit), NPU (Numeric Processing Unit), an ALU (Arithmetic Logical Unit), a Coprocessor (further microprocessor for supporting a main processor (CPU)), a GPGPU (General Purpose Computation on Graphics Processing Unit), a multi-core processor (for parallel . .

[0030] Airbus Defence and Space GmbH - 29 - 30A-166 109computing, such as simultaneously performing arithmetic operations on multiple main processor(s) and / or graphical processor(s)) or a DSP. It is further clear to the person skilled in the art that even if the herein-described details will be described in terms of a method, these details may also be implemented or realized in a suitable device, a computer processor or a memory connected / coupled to a processor, wherein the memory can be provided with one or more programs that perform the method, when executed by the processor. Therefore, methods like swapping and paging can be deployed. Even if some of the aspects described above have been described in reference to the method, these aspects may also apply to the system and vice versa. Additionally, the steps of any method described herein may take place in a differentorder to the order described and / or some steps may take place simultaneously.BRIEF DESCRIPTION OF THE DRAWINGS These and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures, wherein like reference numerals refer to like parts, and in which:Figure 1 shows a flow chart of a method of creating and processing asignal waveform according to an embodiment as described herein;Figure 2 shows a flow chart of a method of creating and processing asignal waveform according to an embodiment as described herein;Figure 3 shows a flow chart of a method of creating and processing asignal waveform according to an embodiment as described herein;Figure 4 shows a flow chart of a method of creating and processing asignal waveform according to an embodiment as described herein; . .

[0031] Airbus Defence and Space GmbH - 30 - 30A-166 109Figure 5 shows a diagram of discontinuous transmission of two signalsaccording to an embodiment as described herein;Figure 6 shows a spectrogram of Frequency Hopping Code DivisionMultiple Access with discontinuous transmission according to an embodiment as described herein;Figure 7 shows a flow chart of Spectral Folded Acquisition with Pre-Conversion to Baseband according to an embodiment as described herein;Figure 8 shows a CCF of Spectral Folded Acquisition with Pre-Conversionto Baseband signal according to an embodiment as described herein;Figure 9 shows a CAF of a Spectral Folded Acquisition with Pre-Conversion to Baseband signal according to an embodiment as described herein;Figure 10 shows a flow chart of Spectral Folded Acquisition with Pre-Conversion to Baseband and Pre-Correlation according to an embodiment as described herein;Figure 11 shows a flow chart of Spectral Folded Acquisition with Pre-Conversion to Baseband according to an embodiment as described herein;Figure 12 shows a block diagram of a system for of creating andprocessing a signal waveform according to an embodiment as described herein; andFigure 13 shows a block diagram of a tracking architecture of the receiveraccording to an embodiment as described herein;Figure 14 shows a time-frequency grid for a generic layout of an OFDMframe defined at 3GPP level according to an embodiment asdescribed herein; . .

[0032] Airbus Defence and Space GmbH - 31 - 30A-166 109Figure 15 shows an illustrative parametrization for a PFL comprising asingle PRS resource according to an embodiment as describedherein;Figure 16 shows a time-frequency grid of the second level of macro-granularity according to an embodiment as described herein;Figure 17 shows a representation of a parametrization according to anembodiment as described herein.Figures 18 and 19 show symmetric time-frequency grids according to anembodiment as described herein;Figure 20 shows an increased bandwidth signal according to anembodiment as described herein; andFigures 21 and 22 show time-frequency grids according to an embodiment asdescribed herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Figure 1 shows a flow chart of a method of creating and processing a signal waveform according to an embodiment as described herein. The method comprises generating S110 two hopped carrier frequencies which are symmetrical with respect to a third carrier frequency, fm, also called a middle baseband carrier frequency herein, and wherein a distance between the first andsecond carrier, |second carrier frequency – first carrier frequency|, is pre-defined.The spectral support occupied by the two hoped carrier frequencies over time mayhave a transmit bandwidth of several 10MHz in order to offer satisfactory rangingperformance, as in the L-Band, for example, where the transmit bandwidth is typically 20 to 50 MHz. In some particular examples, the middle carrier frequency fmis relative to the nominal carrier frequency f0 (fm= 10 MHz, f0=1575.42MHz andf1=11MHz, f2=9MHz for ^fm= 1MHz). The method further comprises modulating S115, by the first processor, the hopped carrier frequencies with a narrow-band waveform, and converting the modulated first . .

[0033] Airbus Defence and Space GmbH - 32 - 30A-166 109and second carrier frequencies to the central carrier frequency f0. As mentionedabove, this may enable the User Terminal, UT, to proceed with particular embodiments of the invention disclosed herein. The narrowband waveform may have a frequency occupation equal to a 10thof the transmit bandwidth, i.e. an order of magnitude smaller. Additionally or alternatively, the narrowband waveform may have a simple autocorrelation shape which may facilitate acquisition by, for example,showing only one main peak of ACF (such as BPSK or SRC signals), rather than aBinary Offset Carrier (BOC) waveform showing more ACF peaks. However, the skilled person understands that any suitable ratio between the narrowband waveform frequency and the transmit bandwidth may be used such as, for example, 1 / 6 or 1 / 8. The method further comprises transmitting S120, by a first transceiver coupled to the first processor, the modulated first signal and the modulated second signal, resulting in a Frequency Hopping Code Division Multiple Access, FH-CDMA. The FH- CDMA signal may allow for the provision of good tracking performance, once acquisition is achieved, and may offer higher robustness against jammers, but more importantly, spoofers who may use methods such as meaconing and repeaters. Thetransmission may be similar to GNSS, using a broadcast transmission scheme. Thetransmission may comprise multibeam, as seen in SATCOM. That is to say there may be one S1 / S2signal per beam, although there may be multiple signals per beam in some examples. In some examples, the first transceiver may only be a transmitter. The method further comprises receiving S125, by a second transceiver, the transmitted first and second signals, wherein the second transceiver is couplable to asecond processor configured to process the received first and second signals. Insome examples, the second transceiver may comprise a GNSS-like receiver and / or may comprise a hemispheric antenna pattern and / or a matched filter (correlation- based) processor. The second transceiver may be, or comprise, an OFDM UT terminal which may use typically known FFT techniques to retrieve at least one symbol from the sub-carrier. In some examples, the second transceiver may only be a receiver. A first baseband frequency, derived from the received RF signal, of the modulated first carrier frequency is converted S130, by the second processor, to the central baseband carrier frequency, and a second baseband frequency, derived from the received RF signal, of the modulated second carrier frequency is converted S130 to the central baseband frequency. Throughout the present specification, whenever the term “baseband” is used, it is to be understood to mean the “baseband frequency”. . .

[0034] Airbus Defence and Space GmbH - 33 - 30A-166 109The method may then additionally comprise one or more of the following steps: The modulated first and second carrier frequencies may be filtered S135 with a bandwidth adapted to a spectral occupancy of the narrow-band waveform filtering, by the second processor, in particular, the method further comprising pre-correlating S140, by the second processor, the first filtered first and second carrier frequencies. In some examples, this filtering S135 may be undertaken by a low-pass filter. The modulated first carrier frequency may be multiplied S145, by the second processor, with a complex conjugate of the second modulated carrier frequency. An output of the multiplication S145 may be correlated S150, by the second processor, with a known replica. As in a standard acquisition of the GNSS, as would be known by the skilled person, several (offset) code hypotheses may be proposed depending on the code / time uncertainty. For each delay, or equivalently, code hypothesis, the replica may be an offset version (delayed / advanced) of a sequence which is generated with respect to the local time of the receiver / second transceiver. For each delay hypothesis the appropriate conversion parameters are defined, as would be understood by the skilled person. In the case that no cyphering is applied on the S1and / or S2signals, the typical example of repetitive spreading sequences can be applied in GNSS: e.g. Gold code for GPS. This may mean that the signal S1may be modulated with a first repetitive code akand the signal S2may be modulated with a second repetitive code bk. S1and S2may fulfill the “^fm” conditions described herein. The product of akand bkmay be another repetitive code ck, which may then be used to generate the replica used to correlate the output of the complex multiplication to form the detector. In some examples, akand bkmay not be repetitive, but the product, ck, may be repetitive. In some examples, akand bkmay not be repetitive, but the product, ck, may not be repetitive, but known to support the generation of the replica. A second correlation comprising the steps following the first correlation may also be performed in a manner similar to that described above, with this second correlation relating to a course Doppler estimate, wherein the input for this coarse Doppler estimate is the output of the first correlation, with this output being correlated with an exponential including a tested Doppler hypothesis. A first detector output comprising a magnitude of the correlation may be formed S155 by the second processor. The first detector output may be the absolute value or the squared absolute value of the correlation between the complex conjugate . .

[0035] Airbus Defence and Space GmbH - 34 - 30A-166 109multiplication output S145 and the code ck. In order to increase the SNR of the detector, it may be possible to further non-coherently combine several of the (elementary) first detector outputs, all generated with the same code hypothesis. The first detector output may be compared S160 with a first detection threshold, by the second processor. The coarse delay and Doppler estimates described above may be retained (S165) by the second processor. The method of figure 1 may apply S110 a waveform based on a Frequency Hopping Code Division Multiple Access (FH-CDMA) scheme. More specifically, the method may transmit S120 two signals applying the FH-CDMA scheme, and may show a large frequency excursion of the hopped carrier frequencies, which in turn may provide good tracking performance once acquisition is achieved, and whose respective hopped carrier frequencies f1and f2may be selected with respect to specific constraints to facilitate acquisition. The constraint may be, for example, both f1and f2be modulated with a narrow band signal. Additionally or alternatively, if a middle baseband carrier frequency (the third carrier frequency described herein) is within a frequency band where ionospheric effects are negligible (C-band and above, for example) it may be possible to create a pool of distance |f1-f2| and which is associated with a third hopped frequency fm. As an example:- |f1-f2|=1MHz for fm = 12MHz during first hop; and- |f1-f2|=3MHz for fm = -4MHz during second hop; and- |f1-f2|=2MHz for fm = +2MHz during third hop.In particular, the two hopped carrier frequencies (f1and f2) may each be modulated S115 with a narrow-band waveform such as, for example, BPSK, and may be symmetrical with respect to a middle baseband carrier frequency, fm. This may mean that the f1and / or f2and / or fmis (implicitly) hopped with a cyphered scheme. Furthermore, the difference |f2-f1| may be kept constant to 2^Δf. As both hopped carrier frequencies may be symmetrical with respect to a middle baseband carrierfrequency, which is separate from Δf, this may enable the UT to undertake furthersteps of the method as disclosed herein. The central baseband each of the hopped carrier frequencies, f1and f2, may bemodulated S115 with a narrow-band waveform. This narrow-band waveform may be. .

[0036] Airbus Defence and Space GmbH - 35 - 30A-166 109the same for both f1 and f2, or different for f1 and f2. This modulation may be appliedfor each hop of f1and / or f2and / or fm, or for a subset of the respective signals.The output of the down / up converted signal may be filtered S135 with a bandwidthadapted to the spectral occupancy of the narrow-band waveform used in theprevious modulation step S115 to reduce the noise contribution originating frommultiplication in at least one of the following steps. As an option, a pre-correlation S140 of the sample streams as output of the filtered signals may be applied before multiplication. In some examples, the bandwidth of the filter may be adapted in such a way that it fits the narrow-band to not lose a significant amount of power. As an example, if the narrowband waveform is a BPSK(1) with an occupancy of 2MHz with the main lobe comprising ~90% of thepower, a filter of 2MHz or more may be used. In some examples, the down- and up-converting steps mentioned herein may be applied before the first filtering step. The sample stream originating from the respectively filtered S135 and down- converted S130 carrier, f1, and modulated S120 with a narrow-band waveform may be multiplied S145 with the complex conjugate of the sample stream originating from the respectively filtered S135 and up-converted carrier S130, f2,which weremodulated S115 with the narrow-band waveform. In some examples, the samplestream originating from f2may be multiplied S145 with the complex conjugate of f1. In some examples, both of these scenarios may happen. The output of the multiplication S145 from both streams may be correlated S150 with a known replica applying a specific tested code hypothesis, and may form S155 a first detector output by taking the magnitude (or absolute value squared ormagnitude squared or any other suitable output) of the correlation. In someexamples, the tested delay (or code) hypothesis may also be applied to the middle baseband frequency, fm, for the hop, and the offset frequency Δfm. This may be due to the fact that for both FH-CDMA and OFDM-CDMA signals, both the code and frequency hopping schemes are rigidly tied. The first detector output may then be compared S160 with a first detection threshold replica, and the first detection threshold may be set according to specific probability of missed-detection and false alarm and may support the decision for the tested code hypothesis. The probability of detection and false alarm may impact the typical mean time to acquire. For example, if the first detection threshold is set too low (corresponding to, for example, a PFA of 10%) it may mean that the first detection threshold may be . .

[0037] Airbus Defence and Space GmbH - 36 - 30A-166 109exceeded once every 10 times by a signal originating from noise, rather than the signals that are wished to be acquired. This may then impact / delay the acquisition time. If the first detection threshold is set too high, the probability to see the peak is reduced, as the peak has a lower likelihood of exceeding the threshold. Therefore, the first detection threshold may be set in order to balance these two effects. However, any suitable first detection threshold may be used according to the present conditions and / or capabilities of the equipment being used. The correlation function, which may be obtained by the above method, may be similar to the function of a CDMA signal modulated with a BPSK waveform, and showing a broader peak than the original FH-CDMA, or OFDM-CDMA, signal, or OFDM signals. This broader correlation peak may permit for a (large) reduction in the number of code hypotheses to be tested, when compared to a matched filtered acquisition, thereby leading to a more computationally efficient method. It is further shown through mathematical developments, as shown below, that the Doppler dependency vanishes in the multiplication step S145. This further reduces the overall number of hypotheses as it is possible to test separately the delay (i.e. code) hypotheses on one side, and the Doppler hypothesis on the other side yielding an overall number of hypotheses equal to the sum of the delay and Doppler hypotheses, while the overall number of delay and Doppler hypotheses in a conventional acquisition scheme is the multiplication of the delay and Doppler hypotheses. This lessens the computational and hardware requirements needed to undertake the method. Furthermore, as both hopped carrier frequencies f1and f2are separated by a constant interval 2^Δf over the complete correlation duration in some examples, this may enable the suppression of the ionospheric contribution in the detector output, further lessening the computational and hardware requirements needed to undertake the method. Figure 2 shows a flow chart of a method of creating and processing a signal waveform according to an embodiment as described herein. The method of figure 2 relates to a so-called “Spectral Folded Acquisition with Pre- Conversion to Baseband” concept. This concept is based on the use of two Direct Sequence CDMA Frequency-Hopped (DS / FH) interplexed signals, S1and S2, transmitted symmetrically, about a middle frequency, by a sequence of frequency carriers by the first transceiver. . .

[0038] Airbus Defence and Space GmbH - 37 - 30A-166 109At reception by the second transceiver, and the down-converted and up-converted first and second signals, wherein the first and second signals are converted fromtheir respective RF carrier frequencies fo to the central baseband carrier frequency,the two signals S1and S2can be expressed as Equation 1 and Equation 2. Here neither multipath, nor noise, are considered. where:M: number of hops during an integration time;Nc: number of cyphered chips during the integration time; Tc: chip period; fm: middle baseband carrier frequency for the hop m; Δfm: offset frequency relative to the middle baseband frequency carrier fm, whereinthe absolute value of the offset Δfm depends of the middle baseband carrierfrequency fm and / or on the hop index m, where Δfm= g(m), and where g is a function relating the offset Δfm to the hop index m; ^: delay between a satellite and a receiver; p: chip pulse shape; fdm: doppler of the respective signal at frequency fm+ Δfm; φ1: initial phase offset of the first signal at transmission; φ2: initial phase offset of the second signal at transmission; A1: amplitude of the first signal; A2: amplitude of the second signal; d1: data of the first signal; d2: data of the second signal; ak: kth chip of the first signal; bk: kth chip of the second signal; . .

[0039] Airbus Defence and Space GmbH - 38 - 30A-166 109^m: 1 or 0 to define potential discontinuity; and ^^^^^(^): contribution of the ionospheric effect at carrier f, and is given by the corresponding expression: 40.3 × ^^^^^( )[ ] ^^^ ^ ^ = −^^ × ^^Here TEC represents the total electron count in units of TECU (1 TECU =1E16 e / m²) and varies between few 10s of TECU during calm ionospheric periods to 1000 TECU for active ionospheric periods, and c0 represents the speed of light (c0=3e8m / s).By replacing ^^^^^(^)[^] in the carrier f with f0+fm^Δfm. where f0 represents thecentral carrier frequency (e.g. 1575.42MHz for the GPS L1 or Galileo E1 signals), the following approximation is yielded: The skilled person understands that any suitable central carrier frequency may be used. At reception by the second transceiver, the typical signal conditioning steps, known to the skilled person, may take place within the applied analogue and digital front- end. This may comprise at least one of: -Analogue filtering- Amplification with the Automatic Gain Control- Down-conversion from Radio Frequency (RF) carrier, down to IntermediateFrequency (IF) carrier or based band. -Analogue to digital conversion (ADC)- Digital FilteringThe above steps are common and generic for most GNSS receivers. Some variants regarding application of the filtering in the analogue or digital domain, or the down- conversion scheme can also be stated but have no impact on the present disclosure, as will be understood by the skilled person. The skilled person is aware of such modifications and may undertake such modifications as they see fit. The skilled person also understands that for a typical receiver, the filtered bandwidth (either in . .

[0040] Airbus Defence and Space GmbH - 39 - 30A-166 109the analogue or digital domain) is usually equal to the transmitted bandwidth to exploit the transmitted FH-CDMA signals. At least one of the following steps may also be undertaken by the method described herein. The converted signal is further frequency converted S210 by splitting said signal into2 branches through a down-conversion (with fm+Δfm) and an up-conversion (with fm-Δfm) based on the knowledge of the middle baseband carrier frequency fmfor the hop, and the offset frequency Δfm. This yields two signals, SNand SP: Equation 3: Equation 4: At this stage, the resulting signals may occupy a spectral bandwidth directly proportional to the chip rate.A (digital) filtering S220 of the down- and respective up-converted signal may thenbe applied with a bandwidth accounting for the chip rate. Considering, for example, a BPSK(1) as a signal waveform p(t), then a typical filtering bandwidth would be 2.046MHz, when considering the main lobe of the corresponding spectral occupancy of the BPKS(1). The skilled person understands that other waveforms and bandwidths may be used. The next step may consist of multiplying S230 the output of the first branch, SN, with the conjugate of the output of the second branch, SP, as shown in Equation 5 and . .

[0041] Airbus Defence and Space GmbH - 40 - 30A-166 109Equation 7. Equation 6 supports mathematical developments related to the argument of the product signal with focus on the ionospheric term. Equation 5 of Equation 6 (Argument of the exponential comprising the Ionospheric term): In a next step, the output of the multiplication may be correlated S240 with a replica generated, r(t), for a given tested code delay hypothesis, ^̂, as expressed in Equation 8. Equation 8: In a final step, the magnitude of the correlation output may be calculated S250 (alternatively a squared magnitude could also be applied or any other suitable output), leading to a Cross-Ambiguity Function, CAF, defined by Equation 9, andwhere the argument ∆^ = ^ − ^̂ is the coarse code hypothesis error.Equation 9: The CAF may serve as validation for the proposed tested hypothesis, and the comparison of the detector output with a first detection threshold set according to . .

[0042] Airbus Defence and Space GmbH - 41 - 30A-166 109specific probability of missed-detection and false alarm may support the decision for the tested code hypothesis. It results from Equation 7 and Equation 9 that through the following process:- The Doppler dependency disappears; and- The ionospheric dependency disappears as the term be factorized over all frequency hops since the offset frequency, Δfm, relative to the middle baseband frequency carrier fm has the same amplitude over the hops, and therefore vanishes in the application of absolute value operator for the CAF calculation. It results from Equation 9 that the “Spectral Folded Acquisition with Pre-Conversion to Baseband” concept can test the delay hypothesis separately from the Dopplerhypothesis, which vanishes thanks to the ^^(^ − multiplication. The “*” sign here signifies the conjugate of the function. The only constraint is that the two hopping sequences are symmetric to a known frequency carrier sequence, fm, which is the case since Δfm takes either +Δf or -Δf. Furthermore, both PRN codes ak and bk may be random and set by the user of the method, but with the constraint that the product spreading code ck=ak x bk may be periodic, or known to the user in order to allow for the replica signal described herein to be generated. Figure 3 shows a flow chart of a method of creating and processing a signal waveform according to an embodiment as described herein. The flow chart of figure 3 relates to a “Spectral Folded Acquisition with Pre-Conversion to Baseband and Pre-Correlation” concept.A possible limitation of the “Spectral Folded Acquisition with Pre-Conversion to Baseband” concept mentioned above is the introduction of an inflated noise causedby the signal multiplication ^^(^ − In order to reduce thecorresponding noise contribution of the detector output, it is proposed to reduce the noise bandwidth before the aforementioned multiplication. For this purpose, a pre- . .

[0043] Airbus Defence and Space GmbH - 42 - 30A-166 109correlation S320 with very short code, Scnand Sdn, is applied before the signal multiplication. At reception by the second transceiver, and the down-converted and up-converted first and second signals, wherein the first and second signals are converted from their respective RF carrier frequencies foto the baseband, the two signals S1and S2applying respective short codes can be expressed by Equation 10 and Equation 11. Equation 10: With:- Scn: nth chip of short code signal 1- Sdn: nth chip of short code signal 2In the above equations, the contribution of the ionosphere delay is not shown forsimplicity of representation. However, the same mathematical developments could show the corresponding Ionospheric delay vanishing from the detector output as shown above for the “Spectral Folded Acquisition with Pre-Conversion to Baseband” concept. The same initial processing steps as for “Spectral Folded Acquisition with Pre- Conversion to Baseband” scheme apply, to this present concept, with: - At reception, the typical signal conditioning steps, as mentioned above in relation to figure 2, take place within the analogue and digital front-end. -further converting S310 the received first and second signals by splitting thereceived first and second signals into 2 branches through an down conversion (with. .

[0044] Airbus Defence and Space GmbH - 43 - 30A-166 109fm+ Δfm) and a up conversion (with fm-Δfm) based on the knowledge of the middle-based frequency carrier fmfor the hop, and the offset frequency Δfm. -The (digital) filtering S330 of the down- and up-converted signal being achievedwith a width accounting for the chip rate. A difference with respect to the above-described “Spectral Folded Acquisition with Pre-Conversion to Baseband” concept is a pre-correlation S320 of each signal with the very short code (Scnand Sdn). For this pre-correlation, a code search and Doppler search are applied, but are limited in terms of time processing with a low number of code delay and Doppler hypotheses due to the short code, and the short Doppler range over the short code duration. It is effectively shown that the Doppler Mis-alignment losses expressed in [dB] are equal to 20*log10(sinc(Tcoh^^Dopp)) where Tcohis the coherent integration time in the pre-correlation process, and equal to the short code duration, ^Dopp is the distance between consecutive Doppler hypotheses, also called Doppler bin width. For example, to limit the Doppler mis-alignment losses to 0.91dB, ^Dopp =(1 / 2)^1 / Tcoh, and to limit the Doppler mis-alignment losses to 3.92dB ^Dopp=(1 / 4)^1 / Tcoh. The former expression shows that that short code duration authorizes a wider Doppler bin width. As an example, for a short code of341 chips (resp. 31 chips) and a chip rate of 1MCps, Tcoh ^ 0.3ms (resp. Tcoh ^30^s)and ^Dopp =1.5KHz (^Dopp =15KHz) for a maximal Doppler mis-alignment loss to3.92dB. For GNSS signals, where the typical span is 6KHz, it is shown that 4 (resp.1)Doppler hypotheses are necessary, which is one or more order of magnitudes smaller than the number of Doppler hypotheses to be tested in more conventional GNSS receivers. The output of the pre-correlated (Equation 14 and Equation 17) branches are again called Snand Sp. The next step after the (digital) filtering S330 consists of multiplying S340 the output of the branches, Sn, with the conjugate of the output of the second branch Spas shown in Equation 18. Here neither multipath, nor noise leading to a CAF limited to the CCF defined by Equation 19 are considered for sake of simplification. Similar to the flow chart of figure 2, in a final step the magnitude of the correlation output may be calculated S350. Equation 12 below corresponds to the down-converted S1signal, and Equation 13 corresponds to the replica comprising the short code, but also to the Doppler hypothesis fd’applied during the pre-correlation process, considering, as stated above, that the number of Doppler hypotheses fd’is relatively small, and is correlated in Equation 14. Similarly, Equation 15 below corresponds to the up-converted S2signal, and Equation 16 corresponds to thereplica comprising the short code but also to the Doppler hypothesis fd’, and iscorrelated in Equation 17 . .

[0045] Airbus Defence and Space GmbH - 44 - 30A-166 109Equation 12: Equation 13: Equation 14: Equation 15: Equation 16: 17: Equation 19: When applying a pre-correlation, then the correlation step applied to the output of the multiplication between the output of the two branches, one being complex . .

[0046] Airbus Defence and Space GmbH - 45 - 30A-166 109conjugate, and defined by Equation 18, may be carried out with a replica generated with the product of the secondary codes, ^^^^described herein. Figure 4 shows a flow chart of a method of creating and processing a signal waveform according to an embodiment as described herein. Contrarily to FH-CDMA signals, which transmit only a subset of carriers modulated with the pulse shape, p(t), OFDM signals exploit and transmit all carriers, called sub- carriers in a 5G context. Nevertheless, to ensure satisfactory acquisition and tracking of the OFDM signals some specific subcarriers are not modulated with “random” data, but rather with a known data pattern. Such sub-carriers modulated with known sequences are called Pilot subcarriers. The above features may consist of selectingS410 such pilot sub-carriers, ignoring S420 the sub-carriers modulated with data,while still satisfying the symmetry between the pair of sub-carriers, f1and f2, with respect to a middle baseband subcarrier, fm. By doing so, and ignoring the sub- carriers dedicated to the communication, it may be possible to apply the above- mentioned feature to the concepts mentioned in relation to at least figures 2 and 3. Figure 5 shows a diagram of discontinuous transmission of two signals according to an embodiment as described herein. Figure 6 shows a spectrogram of Frequency Hopping-Code Division Multiple Access with discontinuous transmission according to an embodiment as described herein. Figure 5 illustrates the two signals S1and S2, as described above, being transmitted from a single satellite. At each epoch ti, each signal is modulated by one or more chips (either overlaid with a data symbol or representing a pure pilot). The two signals, illustrated with a white circle and a black circle, are symmetric versus aknown hopping frequency carrier sequence fm (illustrated with a vertical line,) alsocalled a middle baseband carrier frequency. The two signals S1and S2can be continuous or discontinuous, meaning that in the discontinuous case, no signal is transmitted for some epochs. For clarity, the pulse shape, p(t), of the signals and the corresponding spectral occupancy are not represented in the figures, but only the occurrences of the dedicated signals in the time-frequency domain. The two signals S1and S2can be continuously or discontinuously transmitted with a random “sleep cycle” time sequence as shown in Figures 5 and 6. Figure 7 shows a flow chart of Spectral Folded Acquisition with Pre-Conversion to Baseband according to an embodiment as described herein. . .

[0047] Airbus Defence and Space GmbH - 46 - 30A-166 109As can be seen in figure 7, S1and S2, as described herein, are received by a transceiver which, in this example, comprises an antenna. The signals are then processed by the RF and digital front-end before being split into two branches, wherein one branch comprises an IF down-conversion and the other an IF up- conversion. The respective signals are then digitally filtered, as described herein, and two signals, SNand SPare output. The corresponding digital filter is a Low-Pass (LP) filter. One of the signal SN(t) or SP(t) is then passed to a complex conjugate operation performed by the processor. The decision for the application of the complex conjugate operation to either the SN(t) or SP(t) signal is arbitrary and does not impact the main objective of the proposed scheme described herein. In figure 7, it is applied to the up-conversion branch, yielding S*P(t), although it is to be understood that it can be applied to the down-conversion branch. The signals SNand S*P(t) are then multiplied, yielding [SN^S*P(t)]. The product signals, SNand S*P(t), are then filtered once again via adapted digital filtering, yielding [SN(t)^S*P(t)]Filter. The role of the corresponding adapted digital filter is to suppress potential interfering signals which are also comprised in the received signals. It is noted that the adaptedfilter may be omitted in some variants of architectures for the second processorwithout significantly impacting the main objective of the proposed scheme described herein. The product, and possibly filtered, signal, [SN(t)^S*P(t)]Filter,is then input into a conventional correlation block and which comprises a code and waveform generator, a shift register, a complex multiplication and an integrate and dump operation. The role of the code generator is to produce a code replica, called r(t),comprising chip values according to the spreading sequence. In the case ofuncyphered spreading sequences, the code is usually periodic and can, for example, be a Gold Code for the GPS signals, or a randomly optimized code for the E1-B and E1-C signals. In the case the spreading sequence is cyphered, then an additional cyphering algorithm is comprised in the corresponding code generator block. This code generator also comprises a waveform generator in order to modulate the generated stream of chips with the appropriate BPSK waveform, BOC waveform, or any other suitable type of waveform, such as an OFDM waveform, which is then applied in a matched filter. The code generator receives information regarding the delay hypothesis to be applied for the code tested hypothesis. This yields a shift of the corresponding code replica which is correlated to the signal [SN(t)^S*P(t)]Filter. It is outlined herein that the tested delay hypothesis in the acquisition process will not only impact the production of the shifted code replica, but also impact the selection of the middle baseband frequency fmand also the offset ^f(m), as the hop frequency and the chip values applied in the code replica are rigidly related in FH-CDMA . .

[0048] Airbus Defence and Space GmbH - 47 - 30A-166 109schemes. This is also true for OFDM signals, where the sub-carrier plays the role ofthe hop frequency. Finally, the product of the code replica and the signal [SN(t)^S*P(t)]Filteris fed to an Integrate and Dump block to finally compute the correlation function for the tested delay hypothesis. The magnitude of the corresponding correlation function is then compared to a threshold set according to specified PFA and PD levels. Alternatively, the squared magnitude of the correlation function can also be taken for later comparison and is acquisition architecture dependent. If the magnitude of the correlation function does not exceed the corresponding threshold, then another code delay hypothesis is tested, yielding on one side another setting of the middle baseband frequency fm, and also of the offset ^f(m), and on the other side, another shift of the generated code replica. This process is repeated until the magnitude of the correlation function exceeds the first detection threshold. In that case, it is considered that the receiver coarsely knows the delay hypothesis, called ^^^^^,^^^^^^. Then, the corresponding code delay value is kept and / or stored to produce a replica which is used for the next step of the signal acquisition, namely the coarse estimation of the Doppler. On the right part of Figure7, the additional blocks corresponding to the coarse Doppler estimation arerepresented. T First the signals SN(t) and SP(t) are produced by applying the correct estimation of the delay, which enables the middle baseband frequency fmtobe set accordingly, and also the offset ^f(m). Contrarily to the coarse codeestimation, no complex conjugate operation is applied to the signal SP(t). Indeed, it is shown that the complex conjugate operation yields the wipe-off of the Doppler information, which is now used for coarse Doppler estimation. Therefore, both signals SN(t) and SP(t) are multiplied directly, and eventually filtered, with an adapted filter, [SN(t)^SP(t)]Filter. Then, the code replica generated with correct and coarse code hypothesis, is then correlated to the [SN(t)^SP(t)]Filtersignal. The output of the correlation calculated for the correct and coarse code hypothesis is multiplied with an exponential whose argument is set according to a specific Dopplerhypothesis, and is also shifted with the correct and coarse acquisitionhypothesis The reason for the factor 4 in the aforementioned expression of the argument of the exponential term is that the output of the [SN(t)^SP(t)]Filtersignal depends on the Doppler with a factor twice larger than for conventional Doppler acquisition techniques. Again, the magnitude of the multiplication output is calculated and compared to a second detection threshold set according to the PFA and PD. If the magnitude of the product does not exceed the second threshold, then another Doppler hypothesis is tested. Else, the Doppler hypothesis is considered as the correct coarse hypothesis to be retained for later phases of the signal processing, such as the pull-in and the tracking. . .

[0049] Airbus Defence and Space GmbH - 48 - 30A-166 109In the above description, a single correlation has been applied to compute the magnitude compared with the detection threshold. In order to improve detection and acquisition performance, it is possible to extend the Signal to Noise Ratio (SNR) of the detector input by non-coherently combining different correlations. The combination of coherent and non-coherent integrations to produce acquisition detector input over a so-called dwell-time is a typical technique used to improve acquisition performance. Furthermore, other methods applying Fast Fourier Transform, FFT, can also be applied in order to produce the correlation output in a more efficient way. The FFT algorithm, which may be stored in the herein mentioned memory and executed by the respective processor with the replica signal, then also acts as an input for the correlation step mentioned herein. The skilled person understands that an FFT is a typical known method to calculate the correlation in, forexample, GNSS. An inverse FFT is then performed in order to produce thecorrelation function, defined as (IFFT(FFT([^^(^ − ^) × ^∗^ (^ − ^)]) x conj(r(^ − ^^^^^)) and,in this example, a square of the magnitude is calculated, although it could be a non-squared magnitude, or any other suitable calculation.In the present specification, the first part of the method, i.e. the down / up conversion, filtering, pre-correlation (optional), complex conjugate multiplication, correlation, and detector output, may enable for the delay (i.e. code) to be tested “separately” from the Doppler, as the Doppler term is suppressed. Once the delay (i.e. code) is acquired it is then possible to concentrate on the Doppler hypothesis. To conclude, in place of testing both code and Doppler simultaneously, yielding to NDelayx NDopplertests, where NDelaycorresponds to the number of Delay hypotheses, and where NDopplercorresponds to the number of Doppler hypotheses, the codesearch may be completed first, and then the Doppler search is completed. The leadsto only NDelay+ NDopplerhypotheses being tested and so, a large reduction in the complexity. Figure 8 shows a CCF of Spectral Folded Acquisition with Pre-Conversion to Baseband signal according to an embodiment as described herein. In relation to the above, the CAF would be limited to the one-dimension CCF of the square of the pulse shape, p², illustrated in Figure 8, as the Doppler dependency vanishes. The peak of the CCF is quite broad, as seen in figure 8, with respect to the peak of a CCF corresponding to a wide-band FH-CDMA signal which would be obtained with a matched filter approach (i.e. the replica has the same pulse shape as the incoming FH-CDMA). Therefore, this yields a lower number of correlators to be . .

[0050] Airbus Defence and Space GmbH - 49 - 30A-166 109applied in the time (code / delay) domain, resulting in a lower complexity in both hardware and software. Figure 9 shows a CAF of a Spectral Folded Acquisition with Pre-Conversion to Baseband signal according to an embodiment as described herein. To demonstrate the validity of the concept, two signals are transmitted with a Doppler of 1 KHz, the CAF presented in Figure 9 shows the search Doppler is 0 while Doppler is usually, in this example, 1 KHz in reality, although other frequencies maybe used. It is a major advantage to have a long integration time despite the fastchange of the Doppler of the LEO satellites. Figure 10 shows a flow chart of Spectral Folded Acquisition with Pre-Conversion to Baseband and Pre-Correlation according to an embodiment as described herein.As can be seen in figure 10, S1 and S2, as described herein, are received by atransceiver which, in this example, comprises an antenna. The graph in the upper left of the figure shows Power Spectral Density of the received signal, with frequency on the x-axis and Power Spectrum dBW / Hz on the y-axis. It can be seen that the graph is most symmetrical about a middle baseband frequency, i.e. the middle baseband carrier frequency, fm. The signals are then processed by the RF and digital front-end before being split into two branches, wherein one branch comprises an IF down-conversion and the other an IF up-conversion. The respective signals are then digitally filtered and pre- correlated via respective short codes, as described herein. The graphs below the pre- correlation signifier are CAF graphs, similar to the graph seen in figure 9. Two signals, SNand SP, are output after the pre-correlation. The signals are then combined and filtered once again via adapted digital filtering, with the graphs showing time on the x-axis and amplitude on the y-axis for each signal, and then a combined graph. The combined signal is then input into a conventional correlation block whose objective is to correlated the output of the multiplied and possibly filtered signals SNand S*P, with a replica signal generated for the delay hypothesis to be tested. The magnitude, or alternatively the squared magnitude, of the output of the correlation is applied, and a comparison with a threshold is performed to validate, or not validate, the tested delay hypothesis. The graph shown on the right of this portion is a CCF graph, similar to the one seen in figure 8. Similar to the . .

[0051] Airbus Defence and Space GmbH - 50 - 30A-166 109above, this method reduces the overall number of tested hypotheses to NDelay+ NDopplerand so, a large reduction in the complexity. Furthermore, this method enables the noise bandwidth to be reduced before the multiplication operation, thanks to the pre-correlation with short codes. Figure 11 shows a flow chart of Spectral Folded Acquisition with Pre-Conversion to Baseband according to an embodiment as described herein. Here, it can be seen that many of the blocks of the flow chart correspond to the blocks described above. However, in figure 11, the step of filtering (with a bandpass filter) precedes the conversion step. Figure 12 shows a block diagram of a tracking architecture of the receiver according to an embodiment as described herein. This is applied to the second processor, and aims at tracking the received signals generated by the first processor, in order to estimate precisely the code delay, the carrier phase and frequency which are used later as observables for positioning. This architecture applies so-called scalar tracking loops, where each received and tracked signal corresponds to a dedicated DigitalReceiver Channel.The following main blocks on Figure 12 are described in more details: • On the left part, the common building block of a typical receiver is shown, which comprises a receiver antenna and a receiver analogue and digital front-end. Thisbuilding block has the same functionalities and is shared to the one applied for theacquisition of the received signal generated by the first processor.• Then, on this figure three repetitions of the pair of Down and Up-conversionbranches, followed by a Low Pass (LP) digital Filtering are shown. these branches can be distinguished from each other with the selection of the middle baseband frequency fmand also of the offset ^f(m) whose values depend on one side on the precise delay estimated by the Delay tracking loops and on the other side on the Early, Late or Prompt correlator channels necessary to generate the code delay, the carrier phase and the carrier frequency discriminators presented hereafter. Tosupport the selection of the appropriate middle baseband frequency fm and also ofthe offset ^f(m) values as function of the aforementioned delays, Look-Up-Tables (LUT) are used. For the prompt correlator channel, the values for the middle . .

[0052] Airbus Defence and Space GmbH - 51 - 30A-166 109baseband frequency fm,Pand the offset ^f(m,P) are the ones corresponding to the estimate of the code delay ^(t) estimated at epoch t, since the middle basebandfrequency fm and the offset ^f(m) on one side, and the chip values of the promptreplica on the other side are rigidly bound in the FH-CDMA scheme. For the Early (resp. Late) correlator channel, the values for the middle baseband frequency fm,E(resp. fm,L) and the offset, ^f(m,E) (resp. ^f(m,L)) are the values corresponding to the estimate of the code delay ^(t) estimated at epoch t and advanced (resp. delayed) of half the so-called Early-Late Spacing (ELS). Here, the rigid relationbetween the middle baseband frequency fm,E (resp. fm,L) and the offset ^f(m,E) (resp.^f(m,L)) on one side, and the chip values of the Early (resp. Late) replica needsagain to be considered. For both pairs of down and up-conversion branches,corresponding to the Early and Late correlator channels, an additional operation of complex conjugate is applied here on the down-conversion branch (but can also be applied on the up-Conversion branch). This complex conjugate operation is not applied on the pair of up and down-conversion branches corresponding to the Prompt correlator channel as explained here after. Then for all three pairs ofbranches, the output of the down- and up- conversion branches (containing also thedigital filter and eventually the complex conjugate operations according to the above) are multiplied between each other, and the output of the multiplication is fed to an adapted filter. The roles of the LP filter and adapted filters are identical to the ones applied in the architecture for the acquisition implemented in the second processor of the received signal generated by the first processor. In particular, the adapted digital filter can also be omitted (i.e. no filtering, “all pass” filter) without impacting substantially the main objectives of the proposed scheme described herein. Furthermore, a similar architecture would be obtained by proceeding first to a Band-Pass Digital Filtering and then an down- and up-conversion, as explained for thearchitecture for the acquisition of the received signal. • Distinction is now made with respect to the role and processing of the output of the adapted digital filter corresponding to the Early and Late correlator channels and which will serve for the tracking of the code delay, and the role and processing of the output of the adapted digital filter corresponding to the prompt correlator channel and which will serve for the tracking of the carrier phase and frequency. In the following SE(t) (resp. SL(t)) is defined as the output of the adapted filter corresponding to the Early (resp. Late) correlator channels, while SP(t) is defined as the output of the adapted filter corresponding to the Prompt correlator channel. All signals SE(t), SP(t) and SL(t) serve as input to the Digital Tracking Channels of the Early, Prompt and Late correlator channels. . .

[0053] Airbus Defence and Space GmbH - 52 - 30A-166 109^ Concentrating of the Digital Tracking Channel corresponding to the promptcorrelator channel. In a first step the digital signals, SP(t) are multiplied on one side by a sine function whose argument is the remaining carrier plus the estimation of the carrier phase, and on the other side by a cosine function whose argument is again the remaining carrier plus the estimation of the carrier phase. The carrier phase estimate is materialized thanks to a Carrier NCO which is fed with a control signal originating from the Phase Lock Loop filter implemented in the Receiver Processor. The signal at the output of the sine function is usually called the I-Component of the tracked channel (for In-Phase) while the signal at the output of the cosine function isusually the called the Q-Component of the tracked channel (for Quadrature Phase).^ Regarding the Digital Tracking Channel corresponding to the Early and Latercorrelator channels, the multiplication with the sine and cosine functions with arguments produced by the carrier NCO is not necessary, as it is shown that the signals SE(t) and SL(t) no longer depend on the carrier phase (and neither on the Doppler). Nevertheless, since they are still complex signals, then the real part (resp. imaginary part) of the corresponding SE(t) and SL(t) signals respectively called the I- Component and the Q-Components as for the Digital Tracking Channel for the Prompt correlator channel are extracted for later DLL processing.^ Then each of the I- and Q-components are multiplied by different shifted versionsof the prompt replica which represents the best estimate of the received signal. On the proposed figure, three main replicas are built per the I or Q component: the early, the prompt and the late replica (it must be noted that other receiverimplementations consider 5 or even more shifted replicas). The output of themultiplication is then integrated and dumped to provide the correlator outputs necessary for the DLL and PLL, processed in the Receiver Processor block. The Digital Receiver Processor implements the DLL discriminators and a digital filter to produce a command to the code NCO. This means that altogether, 6 correlator channels are fed to the receiver processor: The Early-In Phase EI, the Prompt-In Phase PI, the Late-In Phase LI, the Early-Quadrature Phase EQ, the Prompt-Quadrature Phase and the Late- Quadrature Phase LQ. To build the required replicas,a code generator aims at generating code sequences which are later shifted according to the Early, Prompt and Late offsets, built into the 3-bit shift register block. This code generator also comprises a waveform generator in order to modulate the replica signal with the appropriate BPSK or BOC waveform or any other waveforms, such as an OFDM waveform, and is then applied in a matched filter. The . .

[0054] Airbus Defence and Space GmbH - 53 - 30A-166109Code generator is disciplined by an NCO which receives control signal from the DLL running in the Receiver Processor (in the same manner than the Carrier NCO received control signal from the PLL running in the Receiver Processor). In the former description, it is also possible to implement a FLL, and especially an FLL discriminator, in place of a PLL in the receiver processor, if only information for the frequency is needed but not the phase. It is noted that the application of the proposed embodiment for tracking received signals is not only limited to scalar tracking architectures but can also be extended to Vector Tracking architectures (not disclosed herein). This alternative type of architecture applies a Kalman Filter fed by the Early, Late and Prompt Componentsfor each of the N received signals, and produces an estimate of the user position andvelocity which can be translated into an estimate of the code and phase delay for each of the N received signals. Those estimates then serve controlling the code and carrier NCOs shown on Figure 12. The following equations justify the proposed processing steps applied for the digital tracking channel corresponding to the prompt correlator channel. The expression the argument product of SN(t-^) and SP(t-^) is:Equation 1 (demodulation):^^(^ − ^)^^(^ − ^)^^.^^^^^^^= ^^^^^^^^^^^^^^^ (^^^^^)^ ^^^^^(^)^^(^)^^^(^^^^^)^^^^^^^^ ^^(^) ⊗ ^ ^^^^^(^ − ^^^ − ^)^^^ To demodulate the data, either the data applied on S1 (resp. S2) must be known so that the Data on S2 (resp. S1) can be retrieved from the phase derived from thesignal ^^(^ − ^)^^(^ − ^), or one of the signals S1 or S2 must be Data free (Pilot Signal).The argument of the exponential term in the term^^(^ − ^)^^(^ − ^)can be derived as follows:=^2^^^ ^ ^^ − ^ +^^.^^^^^ ^ ^^^^ ^^^.^^^^^ ^ ^^^ ^ ^ ^(1 − 2^)^ + ^2^ ^^ ^^ − ^ +^ ^^1 − 2^ ^^= ^2^^^^ ^(^ − ^) + ^2^^^40.3^^^^ 40.3^^^^ ^^40.3^^^^ Δ^^^ ^ ^^^ ^ − ^2^^^^ ^ ^ ^ ^ ^2 ^ − ^2^^^^ ^ ^ ^ ^ ^2^ ^^^^^^^^^^^^^^^+^2^^^ ^(^ − ^) + ^2^^^ ^40.3^^^^ ^^40.3^^^^ ^^ ^ ^40.3^^^^ Δ^^^ ^ ^^^ ^ − ^2^ ^^ ^ ^ ^ ^2 ^ + ^2^ ^^ ^ ^ ^ ^2^ ^^^^^^^^^^^^^^^= ^2^^^ ^(^ − ^) + ^2^^^ ^ ^40.3^^^^ ^+ ^2^^^ ^ ^40.3^^^^ ^^2Δ^^ ^ + ^2^^^ ^(^ − ^) + ^ ^40.3^^^^ ^^^^ ^ ^ ^ ^2^ ^^ ^ ^^ ^^^^^^^^^^^^^+ ^2^^^ ^40.3^^^^ ^^^ ^ ^ ^−2^ ^^^^^^^. .

[0055] Airbus Defence and Space GmbH - 54 - 30A-166 109= ^4^^^ ^ ^^ −40.3^^^^ ^^^ ^ + ^ (1 − 2)^ ^^^^^^It can be verified that through the multiplication (without complex conjugate operation) the term ^^(^ − ^)^^(^ − ^)ois now Doppler dependent (contrarily to ^^(^ − ^)^^(^ − ^)∗)o depends on the ionosphere through the term − 2^ ^ )^ Therefore, it is possible to use the product ^^(^ − ^)^^(^ − ^), eventually filtered in order to feed the PLL or FLL discriminator, as in a conventional receiver architecture in order to track the signal carrier phase and / or frequency. The phase due to ionosphere effects, and present in the term ^^^.^^^^^^ ^(1 − 2^ ^ )^ may be evaluated for each fmthanks to the knowledge of the TEC through external models, such as the Nequick G and Klobuchar Ionospheric models applied respectively for the Galileo and GPS systems, or additional internal processing. The knowledge of the phase delay due to the ionosphere then enables for the reduction of the ionospheric dependency for further processing of the ^^(^ − ^)^^(^ − ^)term in the FLL and PLL. Figure 13 shows a block diagram of a system for of creating and processing a signal waveform according to an embodiment as described herein. Here, it can be seen that there is a transmission device 1000 comprising a processor 1002, a memory 1004 and a transceiver 1006. There is also a reception device 1100 comprising a processor 1102, a memory 1104 and a transceiver 1106. The skilled person understands that any suitable transmission protocol may be used to transfer information and / or data and / or signals between the two devices 1000, 1100 via the transceivers 1006, 1106. The respective memories 1004, 1104 may store instructions which, when executed by the respective processors, 1002, 1102, cause the steps of the method described herein to be undertaken. In some examples, the transceiver 1006 of the transmission device 1000 may be a transmitter and / or the transceiver 1106 of the reception device 1100 may be a receiver. In addition, or as an alternative, to the above, the following may apply. The most recent communication systems and / or communication networks can employ a multi-carrier (MC) modulation technique. Here, Orthogonal Frequency Division Multiplexing (OFDM) signals are used as one well-established example of signals . .

[0056] Airbus Defence and Space GmbH - 55 - 30A-166 109generated with MC techniques, where the information may be modulated in subcarriersover the available bandwidth, and in symbols. More precisely, the generation of anOFDM carrier signal may consist in adding a number of orthogonal sub-carriers whichhave each been modulated with data at baseband.Two main types of modulation encoding are typically applied, with the quadratureamplitude modulation (QAM) or phase-shift keying (PSK) techniques. The resultingcomposite signal may then be modulated onto the carrier frequency. Recent terrestrialand non-terrestrial communication methods, and especially the methods for 4th, 5thand more recent 6thGeneration cellular network technology (4G, 5G and 6G) apply OFDM modulated signals, whose physical layer is defined and described in the standardizations under the initiative of 3rd Generation Partnership Project (3GPP).These standards apply a similar arrangement of OFDM signal layout in both time andfrequency domains.More specifically, the nucleic time domain element is called the symbol, wherein theduration is inverse to the sub-carrier spacing (SCS). The next granularity level, stillapplied in the time domain, is the slot which contains different symbols, the sub-framewhich contains different slots, and finally the frame which contains several sub-frames.The exact number of slots per sub-frame and sub-frames per frame is 4G, 5G or 6Gdesign dependent. As an example, in the 4thGeneration, the down-link signal OFDM frame layout comprises frame of 10ms, sub-frames of 1ms and slots of 0.5ms. The frame layout forthe 5th and 6th generations offers higher flexibility for the setting of these threeparameters in combination to the sub-carrier spacing value, meaning that multiple setsof symbols, slots, sub-frames and frame durations are authorized.The definition of the range which can be spanned by each parameter, and theconstraint existing between those parameters, are described in 3GPP standardizationworks as part of the so-called numerology. The combination of sub-carriers (in the frequency domain) and OFDM symbols (in the time domain) constitute a so-calledresource grid. The smallest unit of the resource grid, also called a Resource Element(RE), then comprises one subcarrier in frequency domain and one OFDM symbol intime domain. The next OFDM granularity is defined by the resource block (RB). In 4G,12 adjacent sub-carriers and 14 symbols constitute an RB. However, in 5G and 6G, theresource block may only be defined in the frequency domain, and may constitute 12adjacent sub-carriers, but may not be constrained in the time domain to offer more. .

[0057] Airbus Defence and Space GmbH - 56 - 30A-166 109flexibility. Still in 5G and 6G, a slot may still constitute 14 symbols, for (all) pre-definednumerologies. The final main component defined in the 3GPP is the so-called Bandwidth Part (BWP).The BWP is a mechanism which divides the full bandwidth in contiguous partitions.Each part comprises contiguous Physical Resource Blocks (PRB). This mechanismenables the application of different numerologies, thus offering different narrowbandor wideband services within the complete bandwidth. One preferable constraint for a 5G terrestrial network is that at any given time, only one BWP may be activated and transmitted to a UE in the downlink, and vice versa in the up-link.Figure 14 shows a time-frequency grid for a generic layout of an OFDM frame definedat the 3GPP level according to an embodiment as described herein. Figure 14 alsographically shows the different elements for the slots, sub-frames, frames, sub-carriersand resource blocks within such a generic layout.To ensure access to the data contained in the OFDM frame, standardizations define reference signals which fulfill several functions as part of the communication protocol between nodes. This concerns the synchronization, and the channel sounding, as wellas the node location. Here, one node refers to a network device such as a terrestrialbase station, or a non-terrestrial 5G or 6G transmitter such as, for example, a satelliteor High-Altitude Platform Station (HAPS), but nodes may also refer to the user terminals. Typical cases of inter-node communication comprise a transmitting base station, satellite or HAPS and a receiving user terminal for so-called down-link (DL) communications, or vice versa a transmitting user terminal and a receiving base station, satellite or HAPS for so-called up-link (UL) communications. Other inter-node communications englobe so-called side-link (SL) communications occurring between two user terminals, or two network devices, such as two satellites, two base stations, or a satellite and a HAPS to cite few exemplary combinations.The aforementioned reference signals may comprise known synchronization patterns,also called synchronization sequences, which are transmitted along the OFDM frame.Resource elements dedicated to the corresponding synchronization sequences arereferred to herein as synchronization resource elements, while resource elementsdedicated to the data, transmitted between two nodes are referred to as data resourceelements. . .

[0058] Airbus Defence and Space GmbH - 57 - 30A-166 109In the example of 4G and 5G standards, PSS (Primary Synchronization Signal) and SSS (Secondary Synchronization Signal) are two synchronization sequences transmitted inthe down-link which may support the search of the (terrestrial) cell containing the basestation serving later for communication exchange. Similarly, in 4G standardization the Cell Specific Reference Signal (CRS) transmitted in the up-link may support channel estimation, cell identification, and synchronization. In the 5G and 6G standardizationthese functions may be allocated to different synchronization sequences and ULsignals, for example with the Sounding Reference Signal (SRS) to solely support singlechannel estimation. In another preferred example, the Position Ranging Signal (PRS)introduced in the 5G and 6G standards may support a UT positioning and timing service based on time-of-arrival (ToA) between transmitting node and user terminal for the down-link. The accuracy level of the receiving node localization depends on the final usage ofnode position information. For example, this information can be used to supportcommunication management assignment, registration or authentication between theuser terminal and the network device. As an example, localization accuracy satisfyingsuch communication management is typically expressed in 100s of meters or evenkilometers for communication between the satellites, such as Low Earth Orbit (LEO) satellites and the user terminal. However, if a positioning service has to be provided by the communication system and infrastructure, atop the communication one, accuracy levels may be expressed in decameters, or at a meter level. In such cases.the PRS, and especially the ToA derived from its exploitation, may represent the mainenabler for such as positioning service. However, exploitation of other sequences, such as SSS or CRS, is not excluded to support such as positioning service.In the following, the application of the aforementioned scheme is applied for the PRS,accounting for the parametrization defined at 3GPP level. Nevertheless, thecorresponding principle is not restricted only to the PRS, but can also be applied andextended to other reference signals and related resource elements of the corresponding synchronization sequences, or even to a combination of synchronizationresource elements and data resource elements to a satisfy the symmetricity conditionhighlighted later in this description. Finally, the proposed invention, as describedherein, could also apply to amendments to 5G and 6G standardizations to, for example,authorize at least a subset of the parameters to change over time, or even to introducenew parameters, with the main goal to “reveal” a symmetric characteristic in thefrequency domain as part of the time-frequency grid. . .

[0059] Airbus Defence and Space GmbH - 58 - 30A-166 109To support the application of the proposed scheme to OFDM PRS defined in the 5G and 6G standards, parameter definitions taken from the 3GPP numerology may be used herein.Firstly, the minimal component of the time-frequency grid, which may permit derivinga time-of-arrival measurements, is called the PRS resource. Initially introduced for 5Gnew radio terrestrial networks, each PRS resource may be associated to a beam of thetransmitter, wherein the beam is steered towards a specific sector which may, in someexamples, comprise User Equipment to be localized. Therefore, a simple scenario mayconsist in allotting one PRS resource to one beam or sector, and to schedule the corresponding transmissions (and therefore PRS resource) in a time divisionmultiplexing, (TDM), manner over the beams, or sectors. To improve positioningperformance of each UE located in a specific sector, the multiple transmissions overtime of PRS resources may share the same characteristics, which represents astraightforward solution. In order to ease the definition of those successive PRS resource transmissions for each sector (i.e. beam) and over the sectors (i.e. beams),a periodicity of the corresponding transmission pattern has been introduced in 3GPP.The skilled person also understands that the notion of sector and beam for new radioterrestrial network is applicable also for non-terrestrial networks such as HAPS or satellites, whose payload can also implement an antenna forming different beams.The formalism defined in 3GPP, and used to describe the mechanism to place thedifferent PRS resources within the time frequency grid, is described below. The wholeof the time-frequency resources allocated within an OFDM frame to generate a PRS iscalled a PRS positioning frequency layer (PFL). A PFL may be defined as a collectionof PRS resource sets, and a PRS resource set may preferably comprise a collection ofPRS resources. A single PRS resource typically corresponds to one slot in the time domain, and multiple RBs in the frequency domain. The PRS resource set may represent the periodicity of the corresponding pattern of PRS resource, i.e. slots,pattern which repeats over the frame. The PFL may be characterized by three mainparameters with the Sub-Carrier Spacing (SCS), the Cyclic Prefix, and the PRS Point A,which represents the lowest sub-carrier of the reference resource block which may be used to define all subsequent sub-carriers and RB allot to a PRS resource. The description given to the allocation of those different PRS resources within the time- frequency grid is made at different time and frequency scales, starting from the highest time granularity units i.e. frame, slot, bandwidth and ending to the lowest ones with the resource block. . .

[0060] Airbus Defence and Space GmbH - 59 - 30A-166 109The first level of macro-granularity in the time-domain may relate to allocation of thePRS resource within the frame. Here the same activation pattern of the PRS RB blockswithin the slot may be repeated over the different slots constitutive of the frame. Thisallocation may be supported with the following parameters:^^^^^^^^: This parameter is called the PRS resource Set Period and expresses the number of PRS resources or slots corresponding to one resource set instance. ^^^^^^^^^^^: This parameter is called the PRS resource Set Offset and represents an offset expressed in unit of slots relative to start of the PRS resource set. In some examples,no slot within this offset contains any PRS resources. As an example, if ^^^^^^^^^^is setto 0, the first slot of the PRS resource set may comprise one PRS RB, which maycorrespond to a “0-based” convention.^ ^ ^^^^^^^^^,^^^ : This parameter is called the PRS resource Offset and represents anadditional offset applied to the first PRS resource Slot and is defined relative to ^ ^^^ ^^^^^^(also using the “0-based” convention).^ : This parameter is called the PRS Resource Repetition and represents thenumber of slots comprising a PRS resource slots belonging to one PRS resource set.^ ^ ^^^^^^ : This parameter is called the PRS Resource Time Gap and represents thenumber of slots free of PRS resource between two consecutive slots comprising PRS resource. Therefore, each resource set may comprise ^^^^^^^minus values.Figure 15 shows an illustrative parametrization for a PFL comprising a single PRSresource according to an embodiment as described herein. This may correspond toone “beam”, as described above.Here, 3 PRS resource set instances are highlighted. Each PRS resource set in thisexample comprises ^^^^^^^= 10 slots. The allocation of PRS resource starts at the 2ndslot (^^^^^^^^^^^= 1). The PRS resource set comprises ^^^^^^ =3 PRS resource slots. Thefirst slot of the PRS resource starts after a ^^^^^^^^^^,^^^= 2, the second slot of the PRS resource set starts after a ^^^^^^^^^^,^^^= 5 and finally the third slot of the PRS resource set starts after a ^^^^^^^^^^,^^^ = 7. Therefore, the PRS Resource Time Gap between thetwo first PRS resource slot comprises = 2 slots free of PRS resource slots, while . .

[0061] Airbus Defence and Space GmbH - 60 - 30A-166 109the PRS resource time gap between the second and third PRS resource slot occurrences comprise = 1 free of PRS resource slots.The second level of macro-granularity in the frequency-domain may relate to theallocation of the PRS resource within the bandwidth, and may be supported by thefollowing parameters: ^^^^: represents the number of physical resource blocks (PRBs) allocated for all PRS resources in a PRS resource set.^ ∶ This parameter is called the Resource Block Offset and represents the startingPRB index (applying the “0-based convention”) of all PRS resources in a PRS resourceset. This offset may be expressed relative to common resource block 0 (CRB 0)comprising the PRS Point A. Figure 16 shows a time-frequency grid of the second level of macro-granularityaccording to an embodiment as described herein. That is to say, figure 16 highlightsthe above parameters.The third level may relate to the micro-granularity in the time and frequency domainand more precisely may relate to which REs, or equivalently sub-carriers and symbols,of the resource block and slot are modulated with the PRS sequence. The followingparameters may be used:^ ^ ^^^^^^^^ : This parameter is called the Symbol Start and defines the first PRS modulatedsymbol of each PRS resource. It may be expressed relative to the first symbol of theslot (also applying the “0-Based convention”). ^^^^^: This parameter represents the number of consecutive PRS modulated symbols in a slot.^ ^^^^^^^^ : This parameter defines the density allocation of the sub-carriers modulated with PRS symbols. As an example, if ^^^^^^^^ = 2, one sub-carrier of every two sub- carriers is modulated with PRS information.^ ^^^^^^^^^^: This parameter represents the starting RE offset in a unit of sub-carrier (alsoapplying the “0-Based convention”) applicable to first symbol of the PRS resource. Therelative RE offsets of the second and ^^^^further PRS symbols of the slot may be . .

[0062] Airbus Defence and Space GmbH - 61 - 30A-166 109defined relative to this ^ ^^^^^^^^^ , as shown in the following table. In some examples, thisparameter is dependent on the RB used. ^^^^^^^^ Symbol Numbers within the Downlink PRS Resource Allocation 01 2 3 4 5 6 7 8 9 10 112 0 1 0 1 0 1 0 1 0 1 0 14 0 2 1 3 0 2 1 3 0 2 1 36 0 3 1 4 2 5 0 3 1 4 2 512 0 6 3 9 1 7 4 10 2 8 5 11Figure 17 shows a representation of a parametrization according to an embodiment asdescribed herein. Here ^^^^^^^^^is set to 2, meaning that the first symbol comprising PRS RE is the third symbol. Furthermore, the ^^^^is set to 7 meaning that 7 consecutive symbols of the slot comprise PRS RE. Then the ^^^^^^^^^^parameter is set to 1 meaning that the overallComb pattern is shifted by 1 sub-carrier. Finally, a ^^^^^^^^ =4 pattern is selectedmeaning that from the above table, the starting RE for the first symbol is not shiftedupwards, the starting RE for the second symbol is shifted 2 sub-carriers upwards, the starting RE for the third symbol is shifted 1 sub-carrier upwards, the starting RE forthe fourth symbol is shifted 3 sub-carriers upwards, and the remainder of the startingREs for the remaining symbols shown in Figure 17 are shifted, or not shifted, accordingto the same numbering convention seen within the figure. All other REs of each symbolare shifted 4 sub-carriers upwards (as ^ ^^^^^^^ =4) until the 12 sub-carriers of the RB isreached. For those REs which exceed the 12 sub-carriers of the RB, a modulo(X,12)operation may be applied, and the remainder may be set at bottom of the RB.To complete the former summary of the 3GPP mechanism to assign PRS resources,muting is described below. The muting permits non-transmission to specific PRS slots.Two main mechanisms are offered. The first mechanism may enable all PRS resourcesand slots as part of a resource set instance to be muted. In other words, no PRSresource (slot) may be transmitted for this set. A vector, called ^^^^^^^, may comprisebinary values, one per PRS resource set instance. A “0” means that the correspondingPRS resource slots of the PRS resource set instance are muted, while a “1” means thatthey are transmitted. When introducing the additional parameter ^^^^^,^^^^^ (integer)the muting pattern may then be defined by the vector ^^^^^^^which does not applyto single PRS resource set instances, but to ^^^^^,^^^^^ consecutive instances. The . .

[0063] Airbus Defence and Space GmbH - 62 - 30A-166 109second mechanism does not apply the muting to the complete PRS resource set instances, but to the individual PRS resource slots. A vector, called ^^^^^^^, maycomprise binary values, one per PRS resource (slot) instance. A “0” means that thecorresponding PRS resource slot is muted, while a “1” means that it is transmitted.The corresponding muting pattern defined within the PRS resource set may berepeated over the frame. A further extension of the muting mechanism consists incombining the individual muting patterns obtained with the first and second mechanism, following a bit-wise AND logic.In view of the above description of the parametrization enabling the generation andassignment of the PRS synchronization sequence within the time-frequency gridachieved, this parametrization may then be used to be applied to the invention, asdescribed herein, to 5G or 6G PRS signals. Here, the main objective is to identify andset specific parameters to create a symmetry of the pattern in the time-frequency grid,with the symmetry, in some examples, being applied in the frequency direction. Thissymmetry can be obtained with respect to a fixed frequency value, but can additionallyor alternatively be obtained with respect to a frequency value, which may vary overtime to reduce vulnerability with respect to signal forging attacks (i.e. spoofing).Furthermore, in order to enhance robustness, the above may only be accessible to areduced number of users.Figures 18 and 19 show symmetric time-frequency grids according to an embodimentas described herein. Figure 20 shows an increased bandwidth signal according to anembodiment as described herein.In particular, figure 18 shows two contiguous RBs ( ^^^ = 2 ) using the sameparametrization. In this example, a Comb-2 is applied, with ^ ^^^^^^^^^ = 0. A symmetryaxis set at 11.5 sub-carriers relative to the lowest frequency of the first RB, which mayserve as middle baseband carrier frequency, fm, described herein.Figure 18 also shows upper and lower frequency bands which are symmetric withrespect to the symmetry axis. The central frequency of both upper and lower frequencybands is respectively called f1 and f2, as described herein. These frequencies fm, f1 andf2 can then use the same methods and conventions described herein for thecorresponding OFDM signal. In some examples, such as the one shown on the Figure18, the frequencies fm, f1 and f2 may not be aligned to the sub-carrier frequencies. Analternative parametrization maybe be proposed to solve this issue, and where, ^^^^ ^^^^^^may be set to 0 for the first RB while setting ^^^^^^^^^^to 1 for the second RB, yielding . .

[0064] Airbus Defence and Space GmbH - 63 - 30A-166 109to the time-frequency grid seen in figure 19, also for ^^^ = 2. Here, all threefrequencies fm, f1 and f2 are aligned to the grid of sub-carrier frequencies. It is notedthat proposing different values of ^^^^^^^^^^over the resource blocks may represent a deviation to legacy 3GPP standardization, but is considered as accommodable in new releases. This principle can be repeated for more than 2 RBs. This may allow for theoverall bandwidth of the OFDM (PRS) signal and of the narrow-band waveform to beincreased, and where the narrow-band waveform has been introduced earlier. As anexample, figure 20 shows such an increase of the actual bandwidth To further support the adaptation of the proposed invention to 5G and 6G signals, it isrecalled that such 5G and 6G standardizations consider the modulation of a Pseudo- Random Noise sequence onto the sub-carrier, which in the case of the PRS is a Gold- Sequence having up to 231binary symbols. The actual sequence symbol modulated oneach sub-carrier depends on the RB. Therefore, both pre- and post-correlation foldingacquisition techniques, as described above, can be implemented considering that thesequences modulated on the sub-carrier of the both upper and lower frequency bands play the same role as the m-sequences akand bk, as described herein. To further enhanced robustness of the proposed OFDM waveform based on the 5Gand 6G standardization, the following features are also described.Figure 21 shows a time-frequency grid according to an embodiment as described herein.The first feature may consist in ensuring that the middle baseband carrier frequencyfm, i.e. axis of symmetry, is time dependent. A high variability of fm may be achievedby changing the value of fmevery symbol. Relaxation of the variability can be achievedby changing fm every slot or sub-frame. Figure 21 represents, for example, a variabilityat slot rate. A possible implementation of a time-dependent middle baseband carrierfrequency, based on the 3GPP parametrization, comprises extending the definition ofthe muting pattern, which is now also applied in the frequency dimension. A mutingmechanism for the above may comprise at least one of the following parameters:- ^^^^^^^^^^^^,^^^is a vector comprising an offset relative to the Point PRS A. This parameter may permit defining the middle baseband carrier frequency fmvarying over the slots. This offset is preferably expressed in a unit of RB, and also applies a “0-Based convention”. Each element may define an offsetapplicable to the PRS resource slot. This vector may comprise ^^^^^^^values. . .

[0065] Airbus Defence and Space GmbH - 64 - 30A-166 109- ^^^^^^^^^^^^,^^^is a vector comprising the offset relative to ^^^^^^^^^^^^,^^^. It may permit specifying the position, equal to ^^^^^^^^^^^^,^^^ + ^^^^^^^^^^^^,^^^of the lower RB of the cluster comprising ^^^^^^^^^RBs at a frequency f1 larger than fm, and may permit specifying the position equal to ^^^^^^^^^^^^,^^^− ^^^^^^^^^^^^,^^^of the upper RB of the cluster comprising ^^^^^^^^^RBs at a frequency f2lower than fm. This offset is preferably expressed in a unit of RB, and also applies a “0-Based convention”. This vector may comprise ^^^^^^^values. -^^^^^^^^^is a vector comprising the number of resource blocks, transmitted on each side of fm, i.e. around the frequencies f1and f2, and which are not muted. This may mean that for each slot, 2^^^^^^^^^^RBs are not muted. This offset is preferably expressed in a unit of RB. This vector may comprise ^^^^^^^values. It is possible to derive the frequencies, f1 and f2, from the parameters described above. For each slot, among the ^^^^^^^PRS resources, or slots, the frequency f1 is preferably equal to / 2)]^RBs offset relative to the PRS A. Similarly, for each slot, among the ^^^^^^^PRS resources, or slots, the frequency f is preferably equal to / 2)]^RBs relative to the Point PRS A. Figure 21 represents an example for the application of the updated muting scheme.Here, ^^^^^^^=5 consecutive PRS resource blocks are considered for illustration. For each slot, 2x^^^^^^^^^ =4 RBs are not muted. For the first slot, they are located at 2 RBs(=[^^^^^^^^^^^^,^^^ + (^^^^^^^^^ / 2)]=1+2 / 2) on each side of the central carrier fm which is offset of ^^^^^^^^^^^^,^^^ = 9 RBs with respect to PRS Point A. For the second slot,they are located at ^^^^^^^^^^^^,^^^= 2 RBs on each side of the central carrier fm which is offset of ^^^^^^^^^^^^,^^^ = 3 RBs with respect to PRS Point A. For the third slot, theyare located at ^^^^^^^^^^^^,^^^= 2 RBs on each side of the central carrier fm which is offset of ^^^^^^^^^^^^,^^^ = 6 RBs with respect to PRS Point A. For the fourth slot, theyare located at ^^^^^^^^^^^^,^^^= 2 RB on each side of the central carrier fm which is offset of ^^^^^^^^^^^^,^^^ = 5 RBs with respect to PRS Point A. Finally, for the fifth slot,they are located at ^^^^^^^^^^^^,^^^= 2 RB on each side of the central carrier fm which is offset of ^^^^^^^^^^^^,^^^ = 7 RBs with respect to PRS Point A. All other RBs are thenmuted. The actual transmitted RBs, showing a variation in the frequency domain, mayguarantee that the time-dependent middle baseband carrier frequency fm are the oneswhich are not muted. . .

[0066] Airbus Defence and Space GmbH - 65 - 30A-166 109Figure 22 shows a time-frequency grid according to an embodiment as describedherein.A second feature which may support direct application of the proposed invention tothe 5G and 6G OFDM waveform is the possibility to set the frequency interval |f2-f1| as time dependent. The corresponding time variability can also be at symbol, slot orsub-frame rate, as for the fm, but it is preferable that the inter-frequency interval |f2-f1| does not change more rapidly than fm and, in a particularly preferred example, thesame change rate for |f2-f1| as for fmmay be applied. Similar to the above-describedfeatures, time varying |f2-f1| is especially suited for a higher carrier frequency of thecommunication signal, where ionospheric effects are mild or negligible. Here again, a possible implementation of a time-dependent middle baseband carrier frequency,based on the 3GPP parametrization, consists of using the capability to mute certainRBs over time.Figure 22, based on figure 21, represents one example of an 5G- / 6G based waveformshowing both a variation of the middle baseband carrier frequency fm and the inter-frequency interval, |f2-f1|, at the same rate (slot rate). For each slot, 2x^^^^^^^^^=4RBs are not muted. For the first slot, they are located at ^^^^^^^^^^^^,^^^= 2 RBs (=[^^^^^^^^^^^^,^^^ + (^^^ ^^^^^^ / 2)] =1+2 / 2) on each side of the central carrier fm whichis offset of ^^^^^^^^^^^^,^^^ = 9 RBs with respect to PRS Point A. For the second slot,they are located at 2 RBs on each side of the central carrier fm which is offset of^^^^^^^^^^^^,^^^ = 3 RBs with respect to PRS Point A. For the third slot, they are located each side ofthe central carrier fmwhich is offset of ^^^^^^^^^^^^,^^^ = 6 RBs with respect to PRS PointA. For the fourth slot, they are located at ^^^^^^^^^^^^,^^^= 1 RB (=[^^^^^^^^^^^^,^^^+ (^^^^^^^^^ / 2)] =0+2 / 2) on each side of the central carrier fm which is offset of^^^^^^^^^^^^,^^^ = 5 RBs with respect to PRS Point A. Finally, for the fifth slot, they arelocated eachside of the central carrier fmwhich is offset of ^^^^^^^^^^^^,^^^ = 7 RBs with respect toPRS Point A. The actual transmitted RBs, showing a variation in the frequency domain,and therefore may guarantee that the time-dependent middle baseband carrierfrequency fm and frequency interval |f2-f1| are the ones which are not muted.A third possible feature may guarantee enhanced robustness of the proposedwaveform derived from 5G or 6G signals generated according to standardization. Thismay consist in ensuring that some of the parameters necessary to generate thiswaveform are cyphered and therefore less accessible for unauthorized users. This may . .

[0067] Airbus Defence and Space GmbH - 66 - 30A-166 109concern the method to generate both sequences m-sequences akand bkso that theirproduct ck=ak x bk may be periodic and / or known to the user in order to allow for thereplica. This may also concern the mechanism used to ensure variability of the middlebaseband carrier frequency fm and / or inter-frequency interval, |f2-f1|, or equivalentlythe muting pattern through the applications of the three parameters ^^^^^^^^^^^^,^^^, ^^^^^^^^^^^^,^^^and ^^^^^^^^^, or finally the existing or adapted parameters defined in 3GPP standardization, such as ^^^^^^^^^^. This mechanism could also be obtained with a cyphering algorithm whose generative keys area known by authorized users. No doubt many other effective alternatives will occur to the skilled person. It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art and lying within the scope of the claims appended hereto. .

Claims

.Airbus Defence and Space GmbH - 67 - 30A-166 109CLAIMS1. A method for creating and processing a signal waveform, the methodcomprising: generating (S110), by a first processor, two hopped carrier frequencies, wherein the two hopped carrier frequencies are symmetrical with respect to a third carrier frequency, fm, and wherein a distance between the first and second hoppedcarrier frequencies, |second hopped carrier frequency – first hopped carrierfrequency|, is pre-defined; modulating (S115), by the first processor, the first hopped carrier frequency and the second hopped carrier frequency with a narrow-band waveform, wherein a first signal is a first outcome of the modulation (S115) on the first hopped carrier frequency and a second signal is a second outcome of the modulation (S115) on the second hopped carrier frequency, converting the modulated first and second hopped carrier frequencies to the central carrier frequency f0; transmitting (S120), by a first transceiver coupled to the first processor, the modulated first signal and the modulated second signal; receiving (S125), by a second transceiver, the transmitted first and second signals, wherein the second transceiver is couplable to a second processor configured to process the received first and second signals; and converting (S130), by the second processor, a first baseband of the modulated first carrier frequency to a central baseband carrier frequency, and a second baseband of the modulated second carrier frequency to the central baseband carrier frequency, wherein the conversion to the central baseband carrier frequency is configured to be applied for each hop applied to the modulated first and second carrier frequencies.

2. The method of claim 1, wherein the converting (S130) further comprises:down-converting, by the second processor, the first baseband frequency of the received first signal of the modulated first carrier frequency to the central baseband frequency; and up-converting, by the second processor, the second baseband frequency of the received second signal of the modulated second carrier frequency to the central baseband frequency, wherein the down-conversion and the up-conversion are applied for each hop of the transmitted first and second signals. ..Airbus Defence and Space GmbH - 68 - 30A-166 1093. The method as claimed in claim 1, after receiving (S125) the first and secondsignals, further comprising: first filtering (S135), by the second processor, the modulated first and second carrier frequencies with a bandwidth adapted to a spectral occupancy of the narrow- band waveform, in particular, the method further comprising pre-correlating (S140), by the second processor, the first filtered first and second carrier frequencies.

4. The method of any one of the preceding claims, after receiving (S125) thefirst and second signals, further comprising: multiplying (S145), by the second processor, the modulated first carrier frequency with a complex conjugate of the modulated second carrier frequency.

5. The method of any one of the preceding claims, after receiving (S125) thefirst and second signals, further comprising: pre-correlating (S320), by the second processor, the first and second signals with respective short codes, wherein the first signal to be pre-correlated is defined by:and the second signal to be pre-correlated is defined by:where: M: number of hops during an integration time; Nc: number of cyphered chips during the integration time; Tc: chip period; fm: middle baseband carrier frequency for the hop m; Δfm: offset frequency relative to the middle baseband frequency carrier fm, wherein the absolute value of the offset Δfm depends of the middle baseband carrier frequency fm and / or on the hop index m, where Δfm= g(m), and where g is a function relating the offset Δfm to the hop index m; ^: delay between a satellite and a receiver; ..Airbus Defence and Space GmbH - 69 - 30A-166 109p: chip pulse shape; fdm: doppler of the respective signal at frequency fm+ Δfm; φ1: initial phase offset of the first signal at transmission; φ2: initial phase offset of the second signal at transmission; A1: amplitude of the first signal; A2: amplitude of the second signal; d1: data of the first signal; d2: data of the second signal; ak: kth chip of the first signal; bk: kth chip of the second signal; ^m: 1 or 0 to define potential discontinuity; Ns: a length of the short codes; Scn: nthchip of the short code for the first signal; and Sdn: nthchip of the short code for the second signal.

6. The method of any one of the preceding claims, further comprising:forming at least two correlations, by the second processor, by correlating the output of the multiplication (S145) with at least two replicas generated for a delay hypothesis derived from an estimated delay hypothesis, wherein the at least two correlations are delayed or advanced to produce different Early and Late correlator channels for the generation of a Delay Lock Loop Discriminator; and multiplying the modulated first carrier frequency with the modulated second carrier frequency without application of a complex conjugate operation; and forming a further correlation, by the second processor, by correlating the output of the multiplication of the modulated first carrier frequency with the modulated second carrier frequency without application of a complex conjugate operation, with a further corresponding replica generated for a delay hypothesis derived from the from the estimated delay hypothesis to produce a Prompt correlator channel for the generation of a Phase Lock Loop Discriminator and / or a Frequency Lock Loop Discriminator, wherein the further correlation and the further replica are different from the at least two correlations and the at least two replicas; and estimating, by the second processor, a code delay, a phase and a frequency of the received first and second signals based on the generated Delay Lock Loop Discriminator, Phase Lock Loop Discriminator and / or Frequency Locked Loop Discriminator.

7. The method of any one of claims 1 to 5, further comprising:..Airbus Defence and Space GmbH - 70 - 30A-166 109forming a first correlation (S150), by the second processor, by correlating the output of the multiplication (S145) with a known replica generated for a tested delay hypothesis; forming (S155), by the second processor, a first detector output comprising a magnitude of the first correlation; comparing (S160), by the second processor, the first detector output to a first detection threshold; retaining (S165), by the second processor, a coarse delay estimate if: a) the first detector output exceeds the first detection threshold; orb) repeating the formation of the first correlation (S150), the formation ofthe first detector output (S155) and the comparison of the first detector output (S160) for another tested delay hypothesis if the first detector output does not exceed the first detection threshold; multiplying, by the second processor, the modulated first carrier frequency with the modulated second carrier frequency without application of a complex conjugate operation and the formation of the first correlation (S150) by applying the retained coarse delay estimate; forming a second correlation, by the second processor, by correlating the output of the first correlation (S150) with an exponential including a tested Doppler hypothesis; forming, by the second processor, a second detector output comprising a magnitude of the second correlation; comparing, by the second processor, the second detector output to a second detection threshold; and retaining (S165), by the second processor, a coarse Doppler estimate if: c) the second detector output exceeds the second detection threshold; ord) repeating the formation of the second correlation, the formation of thesecond detector output and the comparison of the second detector output for another tested Doppler hypothesis if the second detector output does not exceed the second detection threshold.

8. The method of any one of the preceding claims, wherein an FH-CDMA schemeis adapted with an application of a cyphering scheme to a hopped frequency domain and a spreading code domain of said FH-CDMA scheme.

9. The method of any one of the preceding claims, when dependent on claim 2,wherein the first signal to be down-converted is defined by the equation:..Airbus Defence and Space GmbH - 71 - 30A-166 109and the second signal to be up-converted is defined by the equation:where: M: number of hops during an integration time; Nc: number of cyphered chips during the integration time; Tc: chip period; fm: middle baseband carrier frequency for the hop m;Δfm: offset frequency relative to the middle baseband frequency carrier fm, whereinthe absolute value of the offset Δfm depends of the middle baseband carrier frequency fm and / or on the hop index m, where Δfm= g(m), and where g is a function relating the offset Δfm to the hop index m; ^: delay between a satellite and a receiver; p: chip pulse shape; fdm: doppler of the respective signal at frequency fm+ Δfm; φ1: initial phase offset of the first signal at transmission; φ2: initial phase offset of the second signal at transmission; A1: amplitude of the first signal; A2: amplitude of the second signal; d1: data of the first signal; d2: data of the second signal; ak: kth chip of the first signal; bk: kth chip of the second signal; ^m: 1 or 0 to define potential discontinuity; and ^^^^^(^): contribution of the Ionospheric effect at carrier f, and is given by the corresponding expression: ()[ 40.3 × ^^^^^^^^ ^ ^] = −^^ × ^^..Airbus Defence and Space GmbH - 72 - 30A-166 109where: TEC: total electron count; and c0: speed of light.

10. The method of any one of the preceding claims, whereinthe first signal and / or the second signal is transmitted (S120) in a continuous or discontinuous manner, in particular wherein the first and second signals are transmitted (S120) with a random sleep cycle time sequence.

11. The method of claim 9 or 10, after receiving (S125) the first and secondsignals, further comprising: frequency converting (S210), by the second processor, the first and second signals via down-converting the first signal and up-converting the second signal to the central baseband frequency, based on the middle baseband carrier frequency and the offset frequency; second filtering (S220), by the second processor, the frequency converted signals by applying a bandwidth accounting for a chip rate of the frequency converted signals; multiplying (S230), by the second processor, the second filtered first signal with a complex conjugate of the second filtered second signal; correlating (S240), by the second processor, the output of the multiplication with a replica generated by the second processor via the use of a tested code delay hypothesis; and calculating (S250), by the second processor, a magnitude of the output of the correlation.

12. The method of any one of claims 6 to 11, wherein the correlation step (S240)comprises the equation:where: r(t): generated replica; and ^̂: code delay hypothesis; and the calculation step (S250) comprises the equation:where: ..Airbus Defence and Space GmbH - 73 - 30A-166 109CAF: Cross-Ambiguity Function, wherein the CAF is a validation for the proposed tested hypothesis, and wherein the CAF is configured to be set according to a specific probability of missed detection and / or false alarm; and CCF: Cross Correlation Function.

13. The method of claim any one of claims 2 to 5 or 7 to 11, wherein themultiplying step (S340) comprises the equation:where: SN: the fourth filtered first signal; SP: the fourth filtered second signal; and CCF: Cross Correlation Function; and the calculation step (S350) comprises the equation:where: CAF: Cross-Ambiguity Function14. The method of any one of the preceding claims, wherein a subset of the firstand / or second carrier frequencies are modulated (S115) with a known data pattern,the method further comprising: selecting (S410), by the first processor, the subset of first and / or second carrier frequencies; ignoring (S420), by the second transceiver, the subset of first and / or second carrier frequencies, wherein the entirety of the first and second carrier frequencies are symmetrical with respect to the third carrier frequency.

15. The method of any one of the preceding claims, wherein the signal waveformis an Orthogonal Frequency Division Multiplex, OFDM, signal waveform, and whereinthe two hopped carrier frequencies are symmetrical with respect to the third carrierfrequency in a frequency dimension of the OFDM signal waveform.

16. The method of claim 15, wherein the OFDM signal waveform is parameterizedby at least one of: ..Airbus Defence and Space GmbH - 74 - 30A-166 109^^^^^^^^^ which defines the first positioning reference signal, PRS, modulated symbol ofa PRS resource in the OFDM signal waveform;^^^^ which defines a number of consecutive PRS modulated symbols in a slot of theOFDM signal waveform; ^^^^^^^^ which defines a density allocation of sub-carriers of the OFDM waveformmodulated with PRS symbols; and ^^^^^^^^^^ which defines a starting resource element, RE, offset in a unit of sub-carrierapplicable to first symbol of the PRS resource, wherein ^^^^^^^^^^is dependent on a Resource Block, RB, used to define a granularity of the OFDM signal waveform; ^^^^^^^^^^^^,^^^ which defines a vector comprising an offset relative to the PointPosition Ranging Signal, PRS, A;^^^^^^^^^^^^,^^^ which defines a vector comprising the offset relative to ^^^^^^^^^^^^,^^^; and ^^^^^^^^^ which defines a vector comprising a number of RBs transmitted on each sideof fmwhich are not muted; andwherein the two hopped carrier frequencies are symmetrical with respect to the thirdcarrier frequency in the frequency dimension of the OFDM signal waveform based onthe at least one parameter.

17. A system comprising:a first transceiver (1006) and a second transceiver (1106); a first memory (1004) couplable to the first transceiver (1006) and a second memory (1104) couplable to the second transceiver (1106); and a first processor (1002) couplable to the first memory (1004) and first transceiver (1006), and a second processor (1102) couplable to the second memory (1104) and second transceiver (1106), wherein the first and second processors (1002, 1102) are configured to undertake the method steps of any one of claims 1 to 16. .

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