New transmission code with zero correlation zone and modulated information

Abstract

A transmission code for transmission in a transmission channel, wherein the transmission code comprises a sequence of components, each component being able to assume a first component value, a second component value and an idle value, each component representing a transmission slot, the first component value in one of the components representing the transmission of a first transmission symbol in the respective transmission slot, the second component value representing the transmission of a second transmission symbol in the respective transmission slot, the idle value representing the transmission of no transmission symbol in the respective transmission slot, the transmission code comprising a number M of at least two first groups and a plurality of second groups, each first group comprising a number N of at least two components,wherein each component of each first group can assume the first component value and the second component value, wherein all first groups have the same length, wherein each second group comprises only idle values, wherein each two consecutive first groups are separated by one of the second groups, wherein the first groups are designed such that each first group can carry one bit and that the transmission code has a zero-correlation zone property for any M bits carried by the first groups.

Description

field of technology

[0001] The present invention relates to a transmission code and to a method, a device and a computer program for processing such a transmission code. State of the art

[0002] The recently codified IEEE Ultra Wideband (UWB) standard 802.15.4z (IEEE, 2020) prescribes all specifications of a pulsed UWB (IR-UWB) radio used for secure ranging and localization. This standard specifies two types of IR-UWB physical layers: high frequency pulse (HRP) and low frequency pulse (LRP). The HRP type uses encrypted time stamp sequences (STS) for secure ranging. More recently, the next-generation UWB IEEE standard 802.15.4ab, currently under development, also includes ranging integrity fragments that address secure ranging. In both the existing 802.15.4z standard and the proposed 802.15.4ab standard, the UWB packet for secure ranging consists of a deterministic preamble sequence (also called sync pattern) and the encrypted timestamp sequence (STS).While the preamble is used for signal detection (802.15.4z only) and for an unsecure estimation of the early path (shortest distance), the STS is used to verify the security of the distance measurement.

[0003] The general problems of detecting an early peak of a UWB signal will be quickly reviewed here. To detect the arrival time of a UWB message, the received signal is correlated with an expected signal from a specific part of the UWB message, usually the preamble. This correlation of the received UWB signal with an expected signal or template is often referred to as the channel impulse response (CIR), as it provides the arrival time of each path of the transmitted message. The multipath propagation of the UWB message means that the UWB message arrives not just once at the receiver, but once for each different path of the UWB signal from the transmitter to the receiver. Typically, the direct path is the fastest and strongest path, usually referred to as the first or early path. However, in many scenarios, the early path is shielded, e.g.,through a human body, and a longer reflection path is stronger. The strongest path is therefore not necessarily the early path. Thus, the early path could be hidden in the noise from the strongest correlation peak corresponding to a longer path of the UWB message. Not only does noise sometimes make it difficult to identify the early path, but interpulse interference from the different paths also sometimes weakens the correlation of some of the paths, possibly the early path. This is because a first pulse from a first path might be received at the same time as a second pulse from a second path, so the two paths cancel each other out, thus weakening the correlation of a particular path.Another problem with correlating the received UWB signal with the expected UWB signal is that even the autocorrelation of the perfect UWB signal, i.e., the UWB message (part), with itself generates false peaks (also called sidelobes) due to occasional correlations. This is especially the case with random sequences such as the STS. To avoid being confused by these sidelobes and the early paths, the arrival time of the early path is usually determined using special codes with specific properties, such as the presence of a zero-correlation zone (ZCZ) in the CIR, to ensure high sensitivity to the early path. A code with a ZCZ has zero autocorrelation around the main peak, which corresponds to zero delay.A ZCZ of 16 means that at 16 times the interpulse spacing around the main peak, there are no false peaks due to the signal's correlation with itself. That is, at -16 interpulse spacings before and +16 interpulse spacings after the main peak, all peaks correspond to either other paths or other types of noise not associated with this type of false lobe. IPATOV or Gold codes with this property are typically used for the preamble. These codes have the advantage of obtaining a high-quality CIR for the received UWB message and allowing the arrival time of the early path to be determined with high quality. However, these codes are well known to potential attackers, making it easy to spoof the arrival time by sending the preamble earlier.

[0004] For this reason, the additional STS is used to secure the input timing. The STS is part of the UWB-HRP frame. It consists of a binary sequence generated by a random number generator, such as AES 128, which is then convolved with a predetermined pulse shape and upconverted to the desired carrier frequency. To avoid interference between pulses, the STS transmits each bit only every eighth pulse position. This creates a ZCZ of seven pulses, but this is not sufficient to robustly use the STS for input timing (measuring the early path). Since the attacker does not have the random number, the STS can be used to authenticate the sender, i.e., for security. This can be achieved, for example, by cross-correlation between the received signal and the expected STS code.

[0005] Separating the preamble for accurate input timing and the STS for security is currently the only way to achieve robust, secure input timing. However, this separation also has some disadvantages. For example, an attacker could easily anticipate the preamble to spoof a previous path and then use specialized guessing attacks to overcome the security provided by the STS. Another disadvantage is that the hardware must process both the preamble and the STS, which increases hardware complexity.

[0006] The preamble actually serves not only to measure the arrival time, but also to detect a UWB message in the receiver and / or to synchronize the receiver with the sender. The new standard also seeks preambles for detecting UWB messages suitable for multi-user environments. Since the current standard uses the same preamble for all users, the receiver detects all messages in the vicinity from all users, resulting in unnecessary energy consumption. It is therefore desirable for the receiver to only detect UWB messages addressed to it.

[0007] The article "Are LAS codes a miracle?" by Stanczak et al., published in 2001, constructs loosely synchronized codes (LS codes) based on Golay pairs. These LS codes have a ZCZ and can be used to determine the CIR or to detect the arrival time. However, LS codes cannot carry information without destroying the ZCZ properties, and another random STS is required to make ranging secure. Similar disclosures for LS codes using Golay pairs can be found in US2007 / 168841A1, US2020 / 014526A1, in the article "Construction and Application of OVSF-ZCZ originated from LS and GO Sequences" by Chao Zhang et al., and in the article "Sequence Sets in Wireless Communication Systems: A Survey" by Velazquez-Gutierrez et al.

[0008] Orthogonality features are also used in CDMA modulation. The article "A novel ternary CDMA code for TPSK modulation scheme" by Che Kyun et al. discloses data transmission codes for orthogonal data transmission in multi-user systems.

[0009] Thus, state-of-the-art secure ranging requires a code for input timing (e.g., the preamble) and another code for security verification (usually an STS code). This requires additional processing hardware in the receiver and opens up opportunities for attacks on the secure ranging. However, no transmission code is currently known that exhibits a ZCZ property for robust input timing or CIR determination and that allows modulating information to verify the security of the input timing. Brief description of the invention

[0010] It is an object of the invention to solve one or all of the problems described above.

[0011] The object is achieved by a transmission code according to claim 1 and by a method for processing such a transmission code and a device and a program for processing such a transmission code.

[0012] The object is achieved by a transmission code for transmission in a transmission channel, wherein the transmission code comprises a sequence of components, wherein each component can assume a first component value, a second component value and an idle value, wherein each component represents a transmission slot, wherein the first component value in one of the components represents the transmission of a first transmission symbol in the respective transmission slot, the second component value represents the transmission of a second transmission symbol in the respective transmission slot, wherein the idle value represents the transmission of no transmission symbol in the respective transmission slot, wherein the transmission code comprises a number M of at least two first groups and a plurality of second groups, wherein each first group comprises a number N of at least two components,wherein each component of each first group can assume the first component value and the second component value, wherein all first groups have the same length, wherein each second group comprises only idle values, wherein each two consecutive first groups are separated by one of the second groups, wherein the first groups are designed such that each first group can carry one bit and that the transmission code has a zero-correlation zone property for any M bits carried by the first groups, wherein the zero-correlation zone preferably has a width of W corresponding to the minimum number of idle values ​​of each of the second groups or the minimum length of each of the second groups.

[0013] The object is further achieved by a computer program comprising instructions which, when executed on a processor, are to carry out the steps of the method described above.

[0014] The object is further achieved by a device which is designed to carry out the steps of the method described above.

[0015] The problem is further solved by a system of transmitter and receiver, where the transmitter sends a transmission code to the receiver as described above.

[0016] According to the prior art, fixed (non-information-bearing) codes are provided with grouped symbols that exhibit a ZCZ property, such as LS codes. Alternatively, information can be transmitted using individual symbols separated by idle values ​​to obtain a ZCZ property for information carrying codes such as STS. The present invention proposes to combine these two concepts into a new category of codes that transmit information / bits modulated on groups of at least two symbols while retaining the ZCZ property. This makes it possible to use the same code to determine a CIR at the receiver and to verify the security or information transmitted with the same code. When such a code is applied to secure ranging, the number of available attack vectors for secure ranging is significantly reduced.However, this new code may have many applications, such as multi-user specific code / message detection.

[0017] The dependent claims relate to further embodiments of the invention.

[0018] In one embodiment, each first group is constructed based on a single Golay element of at least one Golay pair of length N, each Golay pair comprising a first Golay element and a second Golay element.

[0019] In one embodiment, the at least one Golay pair comprises two Golay pairs of length N that are counterparts to each other.

[0020] In one embodiment, the at least one Golay pair comprises only a single Golay pair.

[0021] In one embodiment, the M first groups may be divided into a first set of first groups and a second set of first groups, wherein each first group of the first set corresponds to a first Golay element of one of the at least one Golay pair and has a related first group in the second set based on the second Golay element of the one of the at least one Golay pair.

[0022] In one embodiment, the second groups all have the same length.

[0023] In one embodiment, at least one of the second groups has a different length than the other second groups.

[0024] In one embodiment, the second groups have a length equal to or longer than N.

[0025] In one embodiment, the autocorrelation of the transmission code has the zero correlation zone property.

[0026] In one embodiment, the cross-correlation of the transmission code with a complementary code has the zero-correlation zone property.

[0027] In one embodiment, the transmission code is a code that is detected at the receiver in the received signal by performing a correlation of the received signal. Preferably, the transmission code is detected by performing a correlation of the transmitted transmission code itself with the received signal, i.e., an autocorrelation while neglecting noise. If the autocorrelation of the transmission code has the ZCZ property, the CIR can be determined with high quality despite the transmitted information. If the transmission code is constructed such that the cross-correlation of the transmission code with the complementary code has the zero-correlation zone property, the transmission code is detected by performing the correlation of the complementary code with the received signal.

[0028] In one embodiment, the transmission code can be determined by the equation explained below or variations of this formula: G(z)=∑i=1p[B2i−1z∑m=1iwmcπi(z)+Bp+2i−1zpN+∑f=1p+iwf∗sπi(z)]∗z(i−1)N where the first component value is represented by one, where the second component value is represented by minus one, where B is a random sequence of length M, where B i is the i-th component of the random binary sequence of length M with the first component value or the second component value for i=1, ..., M, where p is M divided by two, where (c0(z),s0(z)) and (c1(z), s1(z)) are Golay pairs, where πi is the i -te Bit of the binary representation π of an integer random number in the set [0,2 p - 1], where w iis the length of the i-th second group or the number of zeros inserted after the i-th first group, where variations of the above equation cover any other ordering of the first groups defined by this equation, and the use of Golay pairs other than those in the equation may be arbitrary.

[0029] In one embodiment, the variations of the above equation cover Z zeros inserted between two adjacent non-idle values ​​of the same first group, where Z is less than W, preferably less than three, where Z is preferably equal to one.

[0030] In one embodiment, the transmission channel is a UWB radio channel.

[0031] In one embodiment, the transmission channel is a pulsed transmission channel, wherein the first transmission symbol is a first pulse, wherein the second transmission symbol is a second pulse.

[0032] In one embodiment, the transmission code is a modulated transmission code carrying information modulated on the first groups, the information having a bit length equal to or less than M, each bit of the information being modulated on a different first group of the predefined transmission code. Preferably, the information is a random number.

[0033] In one embodiment, the transmission code carries information, the information having a bit length equal to or less than M, which corresponds to the number M of first groups of the transmission code.

[0034] In one embodiment, the transmission code carrying the information is obtained by modulating the information on a predefined transmission code as defined above, wherein each bit of the information is modulated on a different first group of the predefined transmission code to obtain the modulated transmission code.

[0035] In one embodiment, the first component value and the second component value are non-idle values, wherein the first group contains only non-idle values.

[0036] In one embodiment, the first component value and the second component value are non-idle values, wherein each first group contains N non-idle values ​​and at least one idle value, wherein a number Z is a minimum number of idle values ​​between two adjacent non-idle values ​​in the same first group or a minimum distance between two adjacent non-idle values ​​in the same first group, wherein Z is less than W. Preferably, Z is less than 3, preferably less than 2. Most preferably, Z is equal to one. In a preferred embodiment, adjacent non-idle values ​​of the first groups are separated by the same number of Z idle values, most preferably by Z = 1 idle value.

[0037] In one embodiment, the transmission code transmits binary symbols, wherein each transmitted binary symbol may only be the transmission of the first transmission symbol or the second transmission symbol.

[0038] In one embodiment, the first groups are designed such that the transmission code has a main peak for zero delay in the autocorrelation function.

[0039] In one embodiment, a pair of a first transmission code, as described above, and a second transmission code, as described above, is constructed, wherein the first and second transmission codes are constructed such that the first-order sidelobes of their correlation functions vanish in the sum of the correlation functions of the first and second transmission codes. Preferably, the first and second transmission codes are different from each other, preferably carrying different information.

[0040] In one embodiment, the transmission code modulated with the information is transmitted in the transmission channel to a receiving device.

[0041] In one embodiment, additional information outside the transmission code is transmitted to the receiving device, either within or outside the transmission channel, allowing the receiving device to detect the modulated transmission code in the received signal. Preferably, the receiving device is enabled to receive the modulated transmission code or a complementary code whose cross-correlation with the transmission code exhibits the zero-correlation zone property.

[0042] In one embodiment, the device generates a plurality of different transmission codes described above and transmits the different transmission codes sequentially in the transmission channel. Preferably, the plurality of different transmission codes comprises one or more pairs of transmission codes as defined above.

[0043] In one embodiment, the device receives a signal in the transmission channel, wherein the device calculates a correlation of the modulated transmission code in the received signal.

[0044] In one embodiment, a correlation code is determined based on further information received outside the transmission code, either within or outside the transmission channel, which allows the modulated transmission code to be identified by correlating the correlation code with the received signal. The correlation code is preferably the transmission code itself or a complementary code.

[0045] In one embodiment, a received signal comprises a plurality of different transmission codes, wherein the device calculates different correlation functions for the different transmission codes in the received signal, summing the plurality of correlation functions. Preferably, the plurality of different transmission codes comprises at least one pair of transmission codes as defined above, such that the sum of the correlation functions has an extended ZCZ.

[0046] In one embodiment, an arrival time of the transmission code is determined based on the correlation function. The correlation function could also be the sum of the correlation functions, as described in the previous paragraph.

[0047] In one embodiment, the information is decoded from the received signal at the determined arrival time. Preferably, the arrival time of the first group of the transmission symbol is determined based on the arrival time of the determined transmission code, and the bit modulated on each first group is decoded from the signal received at the determined arrival time of the respective first group.

[0048] In one embodiment, the decoded information is used to verify the security of the input time measurement.

[0049] In one embodiment, the decoded information is compared bit-by-bit with a target information that counts decoding errors. The information is considered verified if the decoding errors are below a certain threshold. Preferably, the threshold is greater than zero errors.

[0050] In one embodiment, the determined and finally verified entry time is used for a (secure) distance measurement or (secure) entry time measurement.

[0051] In the embodiment of summing the different correlation functions of different transmission codes, each transmission code carries different information, the information carried by each transmission code is decoded (as described above), the input time measurement is determined based on the sum of correlation functions, the input time measurement is verified based on the decoded information of all transmission codes.

[0052] The concept of actually decoding information (already present at the receiver) to verify an input time measurement is actually new and not used in the prior art. In particular, the concept of accepting a certain number of errors in the decoded information while still verifying the input time measurement. This enables robust verification, even if the decoding is based only on the early path of the CIR and not on the full CIR, as is normally used to decode data. In a secure distance measurement, the transmitted verification information is usually not even decoded bit by bit, but only decoded via cross-correlation. By using the same transmission code to transmit the information and to detect the input time, the resources at the receiver can be reduced.

[0053] Other embodiments according to the present invention are set forth in the appended claims and the following description of an embodiment of the invention. Short description of the drawings Fig. 1 shows the nomenclature for the codes used here. Fig. 2 shows a calculation of an exemplary transmission code according to the invention based on equation 7. Fig. 3 shows the autocorrelation function of the exemplary transmission code of Fig. 2. Fig. Figure 4 shows the autocorrelation function for an example of a state-of-the-art LS code. Fig. Figure 5 shows how information is modulated on an LS code and how a code according to the invention is obtained from such a modulated LS code. Fig. Figure 6 shows the autocorrelation of the modulated LS code of Fig. 5, who loses his ZCZ. Fig. Figure 7 shows the autocorrelation function of the modulated LS code modified according to the present invention, as shown in Fig. 5 to maintain the ZCZ. Fig. 8 shows an embodiment of a system according to the invention using the transmission code according to the invention. Fig. Figure 9 shows the correlation functions of an example of a pair of transmission codes according to an improved embodiment of the invention.

[0054] In the drawings, the same reference numerals have been assigned to the same or analogous elements. Detailed description of an embodiment of the invention

[0055] Further features and advantages of the present invention will become apparent from the non-limiting description below and with reference to the drawings and examples.

[0056] The present invention relates to a sequence of transmission symbols of a transmission channel. The transmission channel is preferably a wireless transmission channel, preferably a radio transmission channel. The radio transmission channel is preferably an ultra-wideband (UWB) transmission channel. However, the invention could equally be applied to other transmission channels, such as a wired transmission channel, a (wired or wireless) optical transmission channel, etc.

[0057] The transmission symbols are preferably binary symbols, i.e., symbols that can transmit two bits, i.e., the symbol can have a first symbol value and a second symbol value (but no more). This is often also referred to as binary shift keying, e.g., binary frequency shift keying (BFSK), binary phase shift keying (BPSK), binary amplitude shift keying (or on-off shift keying), or others. Thus, the transmission symbol can be a first symbol carrying a first symbol value (e.g., bit 0) and a second symbol carrying a second symbol value (e.g., bit 1). However, the invention could also be applied to symbols that transmit a different number of bits, e.g., four bits, eight bits. In this case, the symbol can also be a third symbol carrying a third symbol value, etc.

[0058] The sequence of transmission symbols is transmitted in a sequence of transmission slots (defined by the transmission protocol), where each transmission slot can transmit a transmission symbol (with one of the possible symbol values) or, as is possible with some transmission protocols, can interrupt transmission and not send any transmission symbol in that particular transmission slot. The transmission symbols are preferably transmitted one after the other, i.e., sequentially. This means that the transmission slots are arranged one after the other in time (and not in parallel). The time between two transmission slots is called the inter-symbol or inter-slot time. The transmission slots are preferably arranged periodically so that the time between any two adjacent transmission slots is the same, or so that the inter-symbol or inter-slot time is always the same.However, it is also possible that the inter-symbol time is variable.

[0059] Preferably, each symbol is transmitted as a pulse and / or the transmission channel is a pulsed transmission channel. The inter-symbol, inter-slot, or inter-pulse time is preferably similar to the transmit pulse itself (at least for the first groups, so that the pulses of the first group can be transmitted in a short pulse burst). Preferably, the inter-pulse time is less than 5 times the duration of the transmit pulse, preferably less than 4 times the duration of the transmit pulse, preferably less than 3 times the duration of the transmit pulse, preferably less than 2 times the duration of the transmit pulse, preferably less than 1.5 times the duration of the transmit pulse. The pulses are preferably UWB pulses. UWB pulses are typically 2 nanoseconds (ns) long.For example, the interpulse time could be chosen to be 2 ns, so that one pulse is transmitted immediately after the other. The invention is explained for a pulsed UWB transmission, but can also be applied to non-pulsed transmission and other radio and non-radio transmissions.

[0060] The invention relates to a transmission code, i.e. a sequence of transmission symbols, preferably transmission pulses. The transmission code C of length L is subsequently represented by a sequence of L components or coefficients C = (c(1), c(2), ..., c(L)). Each component represents a transmission slot of the transmission channel. The sequence of components corresponds to the sequence of transmission slots in the same temporal order. Thus, the i-th component c(i) represents the i-th transmission slot. The components c(i) are indexed to define the respective component, where the index i (or another letter) can start from 0 (up to L-1) or from 1 (up to L) without distinction. If the index starts from 0, the i-th component would be component c(i-1).

[0061] The value of each component can have P+1 different component values, the P values ​​corresponding to the P possible symbol values ​​of the transmission symbol, and a value corresponding to not transmitting a symbol at the transmission slot, hereinafter referred to as the idle value. Preferably, the transmission symbols are binary symbols with P=2. Thus, each component can assume a first component value, a second component value, or the idle value. Hereinafter, the first component value is represented by 1, the second component value by -1, and the idle value by 0. If the i-th component has the first component value, the first symbol or pulse is transmitted in the i-th transmission slot. If the i-th component has the second component value, the second symbol or pulse is transmitted in the i-th transmission slot.If the i-th component has the idle value, no symbol or pulse is transmitted in the i-th transmission slot.

[0062] Fig. 1 shows an example of a transmission code C with length L = 8. The first, third, seventh, and eighth components c(1), c(3), c(7), c(8) have the first component value 1 and are transmitted in the corresponding first, third, seventh, and eighth transmission slots 3 with the first pulse 1. The second and sixth components c(2), c(6) have the second component value -1 and are transmitted with the second pulse 2 in the corresponding second and sixth transmission slots 3. The fourth and fifth components c(4), c(5) have the value 0, and the transmission code C does not transmit a pulse in the corresponding fourth and fifth transmission slots 3.

[0063] The transmission code may not correspond to a complete transmission message, but could correspond to a specific section of the transmission message, e.g., the preamble of the transmission message or another section of the transmission message.

[0064] Mathematically, the code C can be equivalently represented by a polynomial function of order L-1, where the L coefficients for the polynomials, the L components of the code C of length L, can also be represented by the polynomial function: C(z)=∑i=0L−1c(i)∗zi where the coefficient of the polynomial z i represents the value of the component at the i+1th position of the code. Fig. 1 also shows the polynomial representation of the example code C.

[0065] The autocorrelation function of a code C is defined as Rc(d)=∑i=1L−dc(i)c(i+d) where d is the shift or lag of the autocorrelation between the code and itself.

[0066] The cross-correlation between two codes C1 and C2 is defined as RC1,C2(d)=∑i=1L−dc1(i)c2(i+d) assuming that both codes C1, C2 have the same length L.

[0067] The invention provides a new transmission code that allows information to be carried and has a ZCZ. The new transmission code is based on the theory of Golay pairs. The definition of Golay pairs is well known but will be briefly reviewed here.

[0068] A Golay pair (c0, s0) is the pair of a first Golay element c0 of length N and a second Golay element s0 of length N that satisfies the perfect autocorrelation property (equation 1): Rc0(d)+Rs0(d)=2Nδ(d) where δ(d) is the Dirac delta function, which is 1 for d=0 and 0 elsewhere. In other words, the sum of the autocorrelation R c0 (d) the first Golay element c0(z) of the autocorrelation R s0 (d) of the second Golay element 2N for a zero delay or displacement d=0 and is zero otherwise. The Golay elements of a Golay pair have the same length. The length N of a Golay pair shall be related to the length N of its Golay elements. A Golay element is a code or a sequence of components whose component value can be (only) the first component value or the second component value. The Golay element cannot have a component with an idle value. The Golay elements are expressed in their polynomial representation as c0(z) and s0(z). Another Golay pair (c1(z), s1(z)) can be derived from the first Golay pair (c0(z), s0(z)) using Equations 2: c1(z)=z(n−1)∗s0(z−1)&s1(z)=−z(n−1)∗c0(z−1) These two Golay pairs (c0(z),s0(z)) and (c1(z),s1(z)) are counterparts of each other. Golay pairs are said to be counterparts or equivalent to each other if the sum of the cross-correlation of the first Golay elements of the counterpart pairs and the cross-correlation of the second Golay elements of the counterpart pairs is zero everywhere (Equation 3): Rc0,c1(d)+Rs0,s1(d)=0. The pairs (c0, c1) and (s0, s1) are also counterparts. (c0, c1) and (s0, s1) each form a Golay pair with the above-mentioned property of their autocorrelation functions.

[0069] A simple Golay pair of length N = 2 is c0=[1,1]&s0=[1,−1].

[0070] Or in its polynomial representation (c0(z),s0(z))=(1+z,1-z)

[0071] Using equation 2, the second counterpart Golay pair can be calculated: c1(z)=z1s0(1z)=−1+z; s1(z)=−z1c0(1z)=−1=−1−z; or in its vector representation c1=[−1,1]&s1=[−1,−1].

[0072] Longer Golay pairs could be constructed starting from the basic pair c 0,2 = [1,1] & s 0,2 = [1, -1]) using recursions, which allows to define a first Golay pair (c 0,2n ,s 0,2n ) of length 2n based on a first Golay pair (c 0,n , s 0,n ) of length n by equation 4: (c0,2n,s0,2n)=(c0,n(z)+zns0,n(z),c0,n(z)−zns0,n(z))

[0073] And equally, the second Golay pair (c 1,2n ,s 1,2n ) of length 2n based on a second Golay pair (c 1,n , s 1,n ) of length n can be calculated by equation 5: (c1,2n,s1,2n)=(z2n−1s0.2n(z−1),−z2n-1c0.2n(z−1)).

[0074] The above Golay pairs and equations are only exemplary Golay pairs and any other Golay pair can be used for the invention that satisfies the definition of Golay pair.

[0075] The present invention proposes a novel code based on at least one Golay pair capable of carrying information without losing the ZCZ property. The proposed transmission code comprises M first groups and O second groups. Where M is the number of first groups and O is the number of second groups. The transmission code has at least two first groups (M >= 2). The transmission code comprises a single second group between every two consecutive first groups. Thus, the first and second groups alternate in the transmission code. Consequently, the number O of second groups can be M-1, M, or M+1. In a preferred embodiment, O = M, or the number M of first groups equals the number O of second groups.

[0076] While the second groups contain only idle values ​​or zeros, the first group contains only non-idle values, i.e., component values ​​associated with an actually transmitted symbol. Therefore, the first groups contain components that can assume the first component value and the second component value (but not the idle value). Preferably, the first groups contain only components with the first component values ​​and / or the second component values.

[0077] The first groups all have the same length N. The length of the second groups can be the same for all second groups or could be different for one or more second groups. The number w i be the length of the i-th second group. If all second groups have the same length W, then w i= W for all i=1, ...,O. The length of the second groups can also be different. In this case, the minimum length of the second groups is min (w i) = W as W. The minimum length W corresponds to the minimum number of idle values ​​in the second groups. The minimum length of the second groups W is actually an important parameter because it defines the length or width of the ZCZ = W. A ZCZ of W means that the ZCZ is equal to or greater than W. The minimum length W can be arbitrarily chosen as one or more. However, the larger W, the larger the ZCZ. Preferably, the minimum length W of the second groups is chosen as N or more. If the lengths of the second groups are different, it may be that only a single second group has a different length and all the others have the same length, or it may be that all the second groups each have a different length, or some other case in between.In an embodiment with different lengths of the second groups, the length of each group may be chosen randomly for each second group (possibly within a range of possible lengths).

[0078] The first groups are constructed in such a way that the transmission code as a whole has a ZCZ property (of W), which is maintained when the first groups are modulated by bits.

[0079] An example of such a class of codes that fulfill this property are Golay pairs. Each first group of the transmission code is constructed based on a Golay element of at least one Golay pair of length N. A first group can be equal to the Golay element of the pair or could be multiplied by +1 or -1. In particular, it is possible for a first group to be based on the first Golay element of the Golay pair multiplied by +1 and a second group to be based on the second Golay element of the Golay pair multiplied by -1, without the transmission code losing its ZCZ properties. This property allows a single bit per first group to be modulated on the transmission code.Preferably, the M first groups can be divided into a first set of first groups and a second set of first groups, each first group of the first set corresponding to a first Golay element of one of the at least one Golay pair and having a related first group in the second set based on the second Golay element of one of the at least one Golay pair. In other words, in the transmission code, there are always two first groups based on two Golay elements of the same Golay pair. Due to the property of Golay pairs shown in Equation 1, the effect of the two first groups of a Golay pair is canceled out in the autocorrelation of the transmission code. This guarantees that the ZCZ property can be maintained even though the first groups have a length greater than 1. The transmission code could be constructed using Golay elements of only a single Golay pair.The transmission code could also be constructed using the Golay elements of (only) two counterpart Golay pairs.

[0080] The transmission codes G(z) could, for example, be constructed by equation 7: G(z)=∑i=1p[B2i−1z∑m=1iwmcπi(z)+Bp+2i−1zpN+∑f=1p+iwf∗sπi(z)]∗z(i−1)N where B is a random sequence of length M and B iis the i-th component of the random binary sequence B of length M with the first component value or the second component value for i=1, ..., M. In other words, B is any sequence of ones and minus ones of length M. The binary sequence B of length M actually corresponds to the information modulated on the transmission code (or the first groups of the transmission code). However, the derived "modulated" transmission code according to equation 7 could also be used as a base code, which is then modulated by another binary sequence B' of length M to modulate the information on the transmission code. Where P is the number M of the first groups divided by two. The two Golay pairs (c0(z),s0(z)) and (c1(z),s1(z)) are counterpart Golay pairs. πi where the i -te Bit of the binary representation π of a random or arbitrary integer in the set [0,2 p- 1]. In other words, π = (π1,...,πi,..., πp) is the sequence of p random / arbitrary bits. The i-th bit πi defines whether the i-th and i+1-th first groups are constructed based on the first Golay pair or the second Golay pair. w iis the length of the i-th second group, i.e., the number of zeros inserted into the second group. While the equation defines the position of the Golay elements of the same Golay pair (as consecutive first groups), they could be arbitrarily positioned within the transmission code at the position of any first group without consequences for the ZCZ. Other Golay pairs can also be used. For example, the Golay element s0(z) could be replaced by the Golay element c1(z), since they also form a Golay pair (c0(z),c1(z)) (or vice versa). Also, the Golay element c0(z) could be replaced by the Golay element s1(z), since they also form a Golay pair (s1(z),s0(z)).

[0081] Below, an exemplary transmission code is constructed using equation 7 given above. The two counterpart Golay pairs of length N = 2 defined above are used. c0(z)=1+z; s0(z)=1−z c1(z)=−1+z; s1(z)=−1−z where the other parameters are selected as follows: B=(−1, 1, 1, 1)→v=4, p=2 π=(0, 1) w1=3, w2=4, w3=3, w4=2

[0082] The transmission code is then calculated using equation 7 as follows: G(z)=−1*zw1c0(z)+1*z(2N+w1+w2+w3)s0(z)+1*z(N+w1+w2)c1(z)+1*z(3N+w1+w2+w3+w4)s1(z) G(z)=−z3c0(z)+1*z14s0(z)+1*z9c1(z)+1*z18s1(z)

[0083] Fig. Figure 2 shows the calculation of the Golay elements with the respective polynomials that lead to the exemplary transmission code according to the invention: G=(0, 0, 0−1, −1, 0, 0, 0, 0, −1, 1, 0, 0, 0, 1, −1, 0, 0, −1, −1)

[0084] Fig. Figure 3 shows that this transmission code actually has a ZCZ = W = 2 corresponding to the minimum length of the second group, and that this ZCZ is not destroyed by grouping the symbols into the first groups and by modulating the first groups with information. As can be seen from Formula 7, the transmission code G could be written with any of the 2 M possible information vectors B can be modulated without changing the ZCZ property. This new transmission code is thus the first transmission code to combine a ZCZ property, a grouping of symbols carrying code components (also called bursts), and a modulation of this code with information. It is clear that if all elements of π are equal (either all 0 or all 1), the transmission code is constructed based on only a single Golay pair.

[0085] Considering the exemplary transmission code G = [ a3, c0, a4, c1, a3, s0, a2, s1] of Fig. 2 where a w is a second group of length w according to equation 7, the transmission code can be further modified as described above. For example, the order of the Golay elements could be changed arbitrarily without consequences for the ZCZ, e.g., G'=[a3, s0, a4, c1, a3, c0, a2, s1]. As mentioned, it is also possible to replace a Golay element with its counterpart Golay element in one or more first groups, e.g., the Golay element s0(z) could be replaced by the Golay element c1(z) without consequences for the ZCZ, which for the exemplary transmission code G above would result in G'' = [a3, c0, a4, c1, a3, c1, a2, s1]. Alternatively or additionally, the Golay element c0(z) could be replaced by the Golay element s1(z), obtaining, for example, G'''=[a3, s1, a4, c1, a3, c1, a2, s1].

[0086] When comparing the inventive code with the solution of an STS, which is a code with a random bit / pulse at every eighth transmission position, i.e., a code in which each random bit is separated by seven zeros, an STS code with 512 transmission slots carries 64 random bits / pulses, and the remaining transmission slots are zero or idle. This STS has a ZCZ of 7. The STS can therefore carry information and has a ZCZ property, but does not allow the random bits to be grouped into bursts without destroying the ZCZ property. When using the inventive transmission code, the same 64 pulses are transmitted in (initial) groups (bursts) of N = 8, separated by 56 zeros each (W = 56). Therefore, the same number of pulses can be transmitted, but with a ZCZ of 56 instead of 7.This allows such a transmission code to be used for CIR or early path detection or input timing. In addition to this extended ZCZ, the code allows for the transmission of 8 bits of information by modulating the 8 bursts / first groups with 8 bits. The transmitted information can be reduced compared to STS, but with the benefit of a significant increase in ZCZ. The properties of bursts based on Golay pairs allow the ZCZ obtained by the zero groups to be maintained, even though the bursts contain more than one pulse.

[0087] Comparing the prior art LS codes with the transmission code according to the invention, the LS codes exhibit a ZCZ property and group the symbols with a reduced number of zeros. However, the LS code does not allow arbitrary information to be modulated onto the LS code without destroying its ZCZ property. Let's take the example of the LS code, which is based on Golay pairs of length N=4: LS=[1, 1, 1, −1, 1, −1, 1, 1, 0, 0, 0, 0, 1, 1, −1, 1, 1, −1, −1, −1] with a ZCZ of 3, as in Fig. 4. However, if we modulate the following groups LS1=[1, 1, 1, −1] LS2=[1, −1, 1, 1] LS3=[1, 1, −1, 1] LS4=[1,−1,−1,−1]. with B = [-1,1,1,1], where the modulated groups are obtained: LS1,m=[−1,−1,−1,1] LS2,m=[1,−1,1,1] LS3,m=[1,1,−1,1] LS4,m=[1,−1,−1,−1]. which leads to the modulated LS code: LSmod=[−1,−1,−1,1,1,−1,1,1,0,0,0,0,1,1,−1,1,1−1,−1,−1] as in the third line of Fig. 5. However, the modulation destroys the ZCZ, as shown in Fig. 5. The LS code is also constructed based on Golay pairs. When inserting second groups Z of zero into the LS code between each group LS i a transmission code according to the invention is obtained which can be modulated without destroying the ZCZ, as in Fig. 6 is evident.

[0088] As explained, the transmission code is designed to carry information. The transmission code can modulate a single bit per first group. The transmission code can therefore carry information of M bits (or less). This information is preferably a random number, often called a nonce. However, depending on the application, other types of information can also be carried by the transmission code. Instead of a random number, the information could be an address code identifying the recipient. The information carried is therefore not for security purposes, but solely to ensure that only the recipient recognizes the message in the communication channel.

[0089] The transmission code according to the invention is a transmission code that is used (in its entirety) to calculate the cross-correlation with a received signal in order to detect the transmission code in the received signal. This cross-correlation can be used for various purposes, such as detecting the arrival time of the transmission code in the transmission channel, determining the channel impulse response (CIR) of the transmission channel, detecting a message in the transmission channel, etc. When the cross-correlation of the transmission code is used to detect the arrival time, this preferably refers to the arrival time of the early path 4, i.e., the shortest path 4 between the transmitter TX and the receiver RX and non-reflected longer paths 5 that arrive with the same message containing G[I] later than the direct / early path 4.

[0090] The transmission code according to the invention is processed in a device. The device can be a transmitter or a receiver, or a transceiver with the function of both a transmitter and a receiver. The device is, for example, a transmitter, receiver, or transceiver chip, or any device that includes such a transmitter, receiver, or transceiver function.

[0091] The transmission code G[I] with the modulated information I must be prepared before transmission in the transmitter TX and / or the receiver RX to detect the transmission code G[I] in the received signal. The preparation of the transmission code based on the information I is described only once, although the description applies equally to the transmitter and the receiver.

[0092] Preferably, the receiver RX / transmitter TX stores a reference transmission code G[0] with a reference set of M first groups S0. The information I is modulated on the set of M first groups S0. Thus, each of the M bits of the information I is modulated on a different one of the first groups. Preferably, bit 1 is modulated by multiplying the first group by +1 and bit 0 is modulated by multiplying the first group by -1, i.e., by inverting the first group. However, this can be done the other way around (0 -> +1, 1 -> -1). A modulated transmission code G[I] is obtained. If the second groups have variable lengths determined by the second group I w are defined, the second groups of the transmission code G[I, I w ] based on this information I w However, it is also possible to use the transmission code G[I] or G[I, I w] not from a reference transmission code G[0], but to generate a completely new transmission code according to some or all of the parameters of equation 7. It is also possible to have different reference transmission codes G[0] depending on a transmission mode, e.g., of different length L, with different number M of first groups, with different length N of the first groups, and with different (minimal) length W of the second groups. Hereinafter, the generated transmission code is simply referred to as G[I], without any restriction that the transmission code G[I] may be based on more information such as I w, L, M, N, W, etc. Each of these parameters could be changed from transmission code to transmission code or determined by the selected transmission protocol. Preferably, at least the I modulated on the first group changes from one transmission code to the next transmitted by the same transmitter Tx.

[0093] The transmitter TX sends the generated transmission code G[I] to the receiver RX. It is clear that the transmission code G[I] is processed in the physical layer of the transmission channel to transmit the transmission code G[I], such as by modulating the code components with the respective transmission symbols at the respective transmission slots 3 and / or modulating this signal on a carrier frequency. However, these details of the physical layer are clear to those skilled in the art, and the term transmission code G[I] does not change for the data layer and the physical layer of the OSI model. The transmission code G[I] is typically sent within a transmission message defined by the transmission protocol of the transmission channel. The transmission code G[I] could be used as the preamble of the transmission message.

[0094] The transmission code G[I] is transmitted. The transmission code G[I] reaches the receiver RX via at least one transmission path 4, 5 of the transmission channel. Depending on the transmission channel, the at least one transmission path 4, 5 could comprise a plurality of transmission paths 4 and 5 to the receiver RX.

[0095] The receiver RX receives a signal in the transmission channel carrying the transmission code G[I] of each of the at least one path 4, 5. The temporal relationship between the different paths (if more than one) and their relative strength is defined by the CIR. The CIR can be obtained by cross-correlating the received signal with a code known to the receiver RX and to be included in the received signal, e.g., the transmitted transmission code G[I].

[0096] The receiver RX generates the same transmission code G[I] as the transmitter TX, as explained above. The transmission code G[I] is preferably generated based on parameters defined by the transmission protocol and / or received by the transmitter TX. Preferably, the transmitter TX transmits at least one parameter of the transmission code G[I], preferably the modulated information I and optionally also the variable-length information I. wto the receiver RX so that the receiver RX can generate the same transmission code G[I] as that transmitted by the receiver RX. This one or more parameters can be sent from the sender TX to the receiver RX encrypted or based on any transmission protocol (e.g., via seed information). These parameters can be sent in the same transmission channel or in an out-of-bound channel. For example, if the transmission channel is a UWB channel, the out-of-bound channel can be a narrowband channel, which is better suited for data transmission. The one or more parameters are preferably transmitted in such a way that third parties cannot intercept them. The one or more parameters can be transmitted before or after (or simultaneously with) the transmission code G[I].In another embodiment, the information for generating the transmission code G[I] can also be obtained other than by receiving from the transmitter TX.

[0097] The receiver RX receives the signal in the transmission channel. This typically involves receiving the signal in the physical layer (including, ultimately, some downconversion, filtering, amplification, etc.). Preferably, the analog signal is digitized by an analog-to-digital converter to digitally process the received signal. The receiver RX performs cross-correlation of the prepared transmission code G[I] (expected to be received in the transmission channel signal) with the received signal. The cross-correlation is preferably performed on the received digital signal. However, it could also be performed on the analog signal using appropriate analog elements. When we speak of correlating the transmission code G[I] with the signal, it is clear that the transmission code G[I] is used in physical layer form, i.e., in the same form as the correlated signal, for the correlation.For example, if the signal is used in baseband, the corresponding transmission code G[I] in the baseband must be used for correlation. This is well known to experts, and for simplicity, we will simply refer to a (cross-)correlation of the transmission code with the signal.

[0098] At the instant the signal contains the transmission code G[I], the cross-correlation of the signal with the transmission code G[I] generates a cross-correlation that corresponds to the autocorrelation of the transmission code G[I] with itself (neglecting noise and multipath interference). Thus, due to the ZCZ property of the transmission code G[I], a clear peak in the cross-correlation would be visible in the ZCZ without false sidelobes around this peak. This makes it possible to detect a clear peak for each transmission code G[I] received via each path 4, 5. If the ZCZ is chosen sufficiently large for the inter-path interference, i.e., the time between the first and the last (measurable) path, a clear CIR can be determined. This can be used to decode subsequent data transmitted with higher quality or simply to detect the earliest path and thus the earliest arrival time of the transmission code G[I].

[0099] For secure input time measurement, the information I carried by the transmission code G[I] is verified to verify the security or integrity of the input time measurement. In the simplest case, verification can be achieved by requiring the receiver to only recognize the transmission code G[I] in the signal if it knows the information used to generate the transmission code G[I]. Thus, the detection of the transmission code G[I] in the received signal is already a type of verification. However, a higher level of security can be achieved if the information I is actually decoded from the signal and verified with corresponding information I known to the receiver RX, preferably received from the transmitter TX. Preferably, decoding only occurs at the arrival time of the transmission symbols of the transmission code, which is determined from the arrival time of the early path determined from the previously described CIR or cross-correlation.Normal data decoding utilizes all received paths to maximize the power of the received signal to reduce the number of decoding errors. Preferably, the transmission slots of the symbols / pulses of the first groups are chosen close together, so that an attack that eavesdrops on the first pulses / symbols of the first group and spoofs a second half of the first group would only allow very short time manipulation. For example, the length of a first group of 4 pulses is 8 ns if the time between pulses of UWB pulses is reduced to the duration of the UWB pulses of 2 ns, so such an attack could only tamper with the signal by a few meters.However, in environments with high noise and / or complex multipath interference, verifying the received information using time-accurate decoding (of the early path) may be more error-prone than other state-of-the-art verification methods based on the full CIR. Therefore, a certain error rate of the decoded bits is typically allowed to achieve a robust verification method. Although time-accurate decoding is likely the most secure verification method, alternative verification methods are also possible.

[0100] An important application for secure input timing is secure ranging, also known as secure ranging. For secure ranging, the transmission code is also called an integrated ranging integrity sequence (IRIS) because it integrates the random number for range measurement integrity, previously transmitted separately with the STS, into the code used to establish cross-correlation or CIR (formerly the preamble). Secure input timing could also be used for other applications, such as radar applications, etc.By integrating the security information I into the same transmission code G[I] used to determine the early path, the security of the distance measurement or entry time is significantly increased, as it eliminates a large number of attacks that use precisely the fact that the time or entry is determined separately from the secure element.

[0101] A further advantage of the transmission codes G[I] according to the invention presented is that they are multi-user capable without additional processing. Since each transmission code G[I] transmitted by different users is based on the transmitted information I, only the receiver RX that expects the transmission code G[I] intended for it recognizes the transmission code G[I], while the other receivers RX that expect other transmission codes G[I'] do not recognize the transmission code G[I]. This is due to the fact that the correlation with the various transmission codes G[I'] from other transmitters TX is not recognized or is recognized to a lesser extent when correlating the signal with the transmission code G[I]. This multi-user property can be further improved by variable lengths of the second groups, since this increases the correlation between different transmission codes G[I, I w ] is further reduced and G[I', I w'] becomes even weaker. So if the receiver RX receives two transmission codes G[I, I w ] and G[I', I w '] from different transmitters TX and TX', the transmission code G[I', I w '] from the other transmitter TX', which is not intended for the receiver RX, the determination of the cross-correlation of the received signal with the transmission code G[I, I w ] less disruptive. The new code thus enables (secure) distance measurement that is very robust in multi-user environments. This also applies to applications that do not require security but rather robustness for multiple users.

[0102] While the main application is certainly secure distance measurement, the transmission code according to the invention could also be used for other applications.

[0103] One application could be a receiver-sensitive preamble. In such an application, each receiver would use a different transmission code G[I, Iw ], perhaps each with a different I or each with different I and Iw, so that the receiver RX would actually only recognize the messages or preambles addressed to the receiver RX, since the other receiver RX would interpret the received signal according to different transmission codes G[I', I w '] would scan.

[0104] Alternatively or additionally, the transmission code G[I, I w ] can be used to improve the quality of the CIR by reducing the interference of other transmission codes G[I', I w '] is reduced.

[0105] Although the transmission code has been explained using the example of Golay elements / pairs, other classes of codes with similar properties could also be used for the present invention.

[0106] The transmission code G described above exhibits autocorrelation with a ZCZ property. However, it would also be possible to have a transmission code G that exhibits (only or additionally) cross-correlation with a complementary code with the ZCZ property. In this case, the transmission code would be transmitted, and the receiver would correlate the complementary code with the received signal to determine the correlation function with the ZCZ property.

[0107] In one embodiment, instead of transmitting a very long transmission code, a plurality of smaller transmission codes are transmitted. The receiver determines a correlation function for each transmission code transmitted in the received signal and sums their correlation functions. The correlation functions to be calculated at the receiver are thus shorter, which is computationally better. It is better to calculate Q correlation functions of length L than to calculate a single correlation function of length QL. The first transmission symbol can thus be recognized in the received signal based on a much shorter correlation function, and the rough position of the other transmission symbols will be known from the first transmission symbol, so the computational load for subsequent transmission symbols is significantly lower.By summing the different correlation functions, the summed correlation function is as robust as a correlation function of a code of length QL. By transmitting different information with each transmission code, arrival time reliability can be improved by transmitting a longer information of Q*M (if each transmission code transmits the same number M of bits). In this embodiment, a plurality Q of transmission codes are transmitted sequentially in the same transmission channel, preferably also in the same transmission message. The receiver can then detect the different transmission codes in the received signal (of the same message) by their corresponding correlations with the received signal.

[0108] This embodiment can be further improved. In this improved embodiment, a pair of transmission codes G1(I1) and G2(I2) is generated. Therefore, at least 2 transmission codes are generated, transmitted, and / or received; more generally, P pairs of transmission codes are generated, transmitted, and / or received, so that 2P transmission codes are generated, transmitted, and / or generated. Since the correlation function of the 2P transmission codes is summed, their transmission order is arbitrary. Each transmission code G1(I1), G2(I2) of a pair differs from the other of the pair. Each transmission code G1(I1) and G2(I2) of the pair G1(I1) and G2(I2) preferably carries a different information I1 and I2.The first transmission code G1(I1) and the second transmission code G2(I2) preferably have the same parameters for one or more of the following parameters of the transmission codes of the pair: length L of the transmission code, length N of the first groups, lengths w. iof the second groups. However, they could also be chosen with different parameters. In particular, the first groups of the two transmission codes can be constructed based on different Golay pairs (counterparts or not). The first transmission code G1(I1) exhibits the correlation property with a ZCZ of W1 (minimum length of the second groups of the first transmission code), and the second transmission code G2(I2) exhibits the correlation property with a ZCZ of W2 (minimum length of the second groups of the second transmission code). For simplicity, it is assumed below that W1 = W2 = W. More specifically, the codes described above have a correlation function that has a main peak for zero delay (d = 0), which has the ZCZ of W for d = 1,...,W, and exhibits a first-order sidelobe and then again a second-order zero-correlation zone up to the second-order sidelobes.Depending on the code, especially with varying second group lengths, the arrangement of the sidelobes can vary slightly. First-order sidelobes are defined as the group of non-zero components of the correlation function closest to the main peak (spaced at a distance of W). In general, the nth sidelobes are defined as the nth group of non-zero components of the correlation function from the main peak. A group of non-zero components is defined as a set of neighboring components of the correlation function that are all non-zero.

[0109] According to the present improvement, the two transmission codes G1(I1) and G2(I2) are constructed in such a way that first-order side lobes of the correlation function R G1 (d) of the first transmission code G1(I1) the inverted first-order side lobes of the correlation function R G2(d) of the second transmission code G2(I2). In other words, the two transmission codes G1(I1) and G2(I2) are constructed such that the sum of the first-order side lobes of the correlation function R G1 (d) of the first transmission code G1(I1) and the first-order side lobes of the correlation function R G2 (d) of the second transmission code G2(I2) are zero. Since the first sidelobes and the second sidelobes are again separated by W zeros (second-order ZCZ), the sum of the correlation function of the pair of transmission codes G1(I1) and G2(I2) would have a ZCZ consisting of the sum of the first-order ZCZ, the second-order ZCZ, and the length of the first-order sidelobes, i.e., approximately 2W+N. Therefore, the sum of the correlation function R G1 (d) the first transmission code G1(I1) and the correlation function R G2(d) of the second transmission code G2(I2), an extended ZCZ. In most cases, the ZCZ of this sum is more than doubled. The first transmission code G1(I1) is generated arbitrarily. The second transmission code G2(I2) of the pair is then chosen so that the explained property is satisfied. It is also possible to construct both with the aim of satisfying this property. Such a property-conforming construction of one or both of the transmission codes of the pair can be realized through a simulation with systematic trial and error. In an alternative embodiment, the one or more transmission codes of the pair are constructed based on a formula. Since the pairs with this property must be recalculated for each information pair I1,I2, the pair of transmission codes must be recalculated each time.However, due to the high degree of freedom in constructing the transmission codes, there are many alternative pairs of transmission codes for the information pair I1, I2. The different transmission codes of a pair can be varied, for example, in the order of the first groups or in the Golay pairs used. If the transmitted information I1 and I2 is random information, it is also possible (alternatively or additionally) to modify the transmitted random information so that the property is fulfilled. Since there are many possible pairs, this would not compromise the security of the transmitted random information.

[0110] In Fig. In Figure 9, this improvement will be explained using the example of a pair of transmission codes G1(I1) and G2(I2). The transmission symbols G1 and G2 are constructed based on the following two Golay pairs of length N = 4 with c0 = [1, 1, 1, -1]; s0 = [1, -1, 1, 1]; c1 = [1, 1, -1, 1]; s1 = [1, -1, -1, -1]; with M = 4 first groups. The transmitted information of the two transmission codes is I1 = [1, 1, 1, -1] and I2 = [1, 1, 1, 1], which results in the following two transmission codes, for example: G1(I1)=[s1,aw,s0,aw,c0,aw,−c1,aw] G2(I2)=[s1,aw,c1,aw,c0,aw,c1,aw] where a pair with the extended ZCZ property defined above is provided by the sum of their correlation functions. a w is the second group with length W. Fig. 9 now shows the correlation function R G1 of the first transmission code G1(I1) (first correlation function) and the correlation function R G2of the second transmission code G2(I2) (second correlation function), each with a ZCZ of W and the first-order side lobes 6, 7. The first-order side lobes 6 of the first correlation function and the first-order side lobes 7 of the second correlation function are such that they cancel each other out when summed. The sum of the first and second correlation functions (sum function) thus causes the first-order side lobes to vanish. Thus, the sum function has an extended ZCZ of at least 2 times W. Fig. 9 W was chosen as 8.

[0111] In the embodiments described above, the first groups were selected to consist only of non-idle values, e.g., for binary transmission symbols +1 or -1. However, it is also possible to insert at least one idle value within the first groups, preferably with the same number Z of idle values / zeros between two adjacent non-idle values ​​of the same first groups. This can be done for each adjacent tuple of each first group, or only for one adjacent tuple, or only for some. Even if Z is chosen to be smaller than W, due to the special shape of the selected first groups, the ZCZ property of any modulated transmission code is still W.If a different number of idle values ​​Zi is inserted between different tuples of non-idle values ​​of the same first group or different first groups, Z would correspond to the minimum number of idle values ​​inserted between two non-idle values ​​in all first groups. Z can be one, two, or more. If Z = 0, this would correspond to the case described above, where the first groups contain only non-idle values. This insertion of one or more idle values ​​between adjacent non-idle values ​​of the first groups might not destroy the property of the described LS code; however, the larger Z, the higher the risk of guessing the bit carried by a first group from the first pulse of the group and tampering with the transmission of the first group by anticipating the guessed remaining pulses of the first group.Therefore, the smaller Z, the more secure the code is against this type of manipulation. Inserting at least one idle value (Z equal to one or higher) between adjacent tuples of non-idle values ​​from the first groups could be beneficial for pulse processing in the transmitter and receiver. The optimal compromise between improved pulse processing and security would be Z = 1.

[0112] It is clear that the present invention is not limited to the embodiments described and that variations may be applied without departing from the scope of the claims. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] US 2007 / 168841A1

[0007] US 2020 / 014526A1

[0007]

Claims

[1] Transmission code for transmission in a transmission channel, wherein the transmission code comprises a sequence of components, wherein each component can assume a first component value, a second component value and an idle value, wherein each component represents a transmission slot (3), wherein the first component value in one of the components represents the transmission of a first transmission symbol (1) in the respective transmission slot (3), the second component value represents the transmission of a second transmission symbol (2) in the respective transmission slot (3), wherein the idle value represents the transmission of no transmission symbol in the respective transmission slot (3), wherein the transmission code comprises a number M of at least two first groups and a plurality of second groups, wherein each first group comprises a number N of at least two components,wherein each component of each first group can assume the first component value and the second component value, wherein all first groups have the same length, wherein each second group comprises only idle values, wherein each two consecutive first groups are separated by one of the second groups, wherein the first groups are designed such that each first group can carry one bit and that the transmission code has a zero correlation zone property of W for any M bits carried by the first groups, where W is the minimum number of idle values ​​of each of the second groups or the minimum length of each of the second groups. [2] A transmission code according to claim 1, wherein each first group is constructed based on a single Golay element of at least one Golay pair of length N, each Golay pair comprising a first Golay element and a second Golay element. [3] A transmission code according to claim 2, wherein the at least one Golay pair comprises two Golay pairs of length N which are counterparts to each other. [4] A transmission code according to claim 3, wherein the M first groups can be divided into a first set of first groups and a second set of first groups, each first group of the first set corresponding to a first Golay element of one of the at least one Golay pair and having a related first group in the second set based on the second Golay element of the one of the at least one Golay pair. [5] A transmission code according to any one of claims 1 to 4, wherein the transmission code is a code which is detected at the receiver in the received signal by performing a correlation of the received signal. [6] Transmission code according to one of claims 1 to 5, wherein the transmission code can be determined by the equation explained below or variations of this formula: G(z)=∑i=1p[B2i−1z∑m=1iwmcπi(z)+Bp+2i−1zpN+∑f=1p+iwf∗sπi(z)]∗Z(i−1)N where the first component value is represented by one, where the second component value is represented by minus one, where B is a random sequence of length M, where B i is the i-th component of the random binary sequence of length M with the first component value or the second component value for i=1, ..., M, where p is M divided by two, where (c0(z),s0(z)) and (c1(z), s1(z)) are Golay pairs, where πi is the i -te Bit of the binary representation π of an integer random number in the set [0, 2 p - 1], where w iis the length of the i-th second group or the number of zeros inserted after the i-th first group, where variations of the above equation cover any other ordering of the first groups defined by this equation, and the use of Golay pairs other than those in the equation may be arbitrary. [7] A transmission code according to claim 6, wherein the variations of the above equation Z cover zeros inserted between two adjacent non-idle values ​​of the same first group, where Z is less than W, preferably less than three, where Z is preferably equal to one. [8] A transmission code according to any one of claims 1 to 7, wherein the transmission channel is a pulsed UWB radio channel, wherein the first transmission symbol is a first UWB pulse, wherein the second transmission symbol is a second UWB pulse. [9] A transmission code according to any one of claims 1 to 8, wherein the first component value and the second component value are non-idle values, the first group containing only non-idle values. [10] Transmission code according to one of claims 1 to 8, wherein the first component value and the second component value are non-idle values, each first group containing N non-idle values ​​and at least one idle value, a number Z being a minimum number of idle values ​​between two adjacent non-idle values ​​in the same first group or a minimum distance between two adjacent non-idle values ​​in the same first group, Z being less than W, preferably less than three, Z preferably being one. [11] A transmission code according to any one of claims 1 to 10, wherein the transmission code transmits binary symbols, wherein each transmitted binary symbol can only be the transmission of the first transmission symbol or the second transmission symbol. [12] A transmission code according to any one of claims 1 to 11, wherein the first groups are designed such that the transmission code has a main peak for a zero delay in the autocorrelation function. [13] Method for processing a transmission code according to one of claims 1 to 12 in a device. [14] A method according to claim 13, wherein the transmission code carries information, the information having a bit length equal to or less than M corresponding to the number M of first groups of the transmission code. [15] A method according to claim 14, wherein the transmission code carrying the information is obtained by modulating the information on a predefined transmission code according to any one of claims 1 to 12, each bit of the information being modulated on a different first group of the predefined transmission code. [16] A method according to claim 15, wherein the transmission code modulated with the information is transmitted in the transmission channel to a receiving device. [17] The method of claim 15, wherein the device receives a signal in the transmission channel, the device calculating a correlation function of the modulated transmission code in the received signal. [18] A method according to claim 17, wherein a correlation code is determined on the basis of further information received outside the transmission code in or outside the transmission channel, which makes it possible to detect the modulated transmission code by correlating the correlation code with the received signal. [19] The method according to claim 17 or 18, wherein an arrival time of the transmission code is determined based on the correlation function. [20] The method of claim 19, wherein the arrival time of the first group of the transmission symbol is determined based on the arrival time of the determined transmission code, and the bit modulated on each first group is decoded from the signal received at the determined arrival time of the respective first group. [21] The method of claim 20, wherein the decoded information is used to verify the security of the input time measurement. [22] Apparatus designed to carry out a method according to any one of claims 13 to 21.

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