Method of modulating and demodulating, respectively, wireless signals for high mobility communications, and apparatus implementing the methods

Abstract

A signal for wireless transmission is modulated by converting a serial sequence of symbols in the time domain into parallel symbol streams, transforming the parallel symbol streams into the frequency domain, mapping the resulting frequency domain signals onto subcarriers, converting the mapped signals into the time domain and converting the parallel time-domain signals into a serial signal. The serial signal is subjected to chirping and is transmitted to a receiver after adding a cyclic prefix (CP). The receiver removes the CP from the signal and, after de-chirping the prefix-less signal, converts the signal into parallel signals. The parallel signals are converted into the frequency domain for channel estimation, equalisation, and subcarrier mapping of detected symbols. The mapped symbols are transformed into the time domain before converting them into a serial stream of symbols.

Description

[0001] METHOD OF MODULATING AND DEMODULATING, RESPECTIVELY, WIRELESS SIGNALS FOR HIGH MOBILITY COMMUNICATIONS, AND APPARATUS IMPLEMENTING THE METHODS

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to mobile wireless communication, in particular to wireless communication in accordance with 6thgeneration (6G) standards and beyond.

[0004] NOTATIONS

[0005] Scalar values are denoted herein by lowercase or uppercase letters in italics, as in x or N, while vectors and matrices in the frequency domain are denoted by boldface lowercase and uppercase letters, as in x and X, respectively. The transpose and Hermitian transpose of a matrix are denoted by superscript letters (-)Tand (-)H, respectively. diag{a} denotes a square diagonal matrix with a’s elements in its main diagonal. ® is the Kronecker product, Tr{-} is the trace operation, and E{-} indicates the expectation operation.

[0006] BACKGROUND

[0007] Modulation, sometimes also referred to as transmission waveform or simply waveform, has been regarded as one of important components in every generation of communications, enabling increased capacity and data rates, improved spectral and power efficiency, new applications, etc. The 6G waveform candidates currently discussed can be classified into three categories: multi-carrier, single-carrier, and multi-carrier chirping.

[0008] Mobile wireless communication in accordance with current 4thgeneration (4G, LTE), 5thgeneration (5G) and future 6thgeneration (6G) communication standards may generally use OFDM as a common modulation technique for downlink connections, i.e. , connections transmitting data from a base station (BS) to a user equipment (UE). 6G in particular is expected to use different flavours of OFDM or different modulation techniques altogether, with different modulation techniques possibly being used for uplink, i.e., from a mobile UE to a BS, and downlink communication connections. Amongst the possible modulation techniques for downlink in 6G, Affine Frequency Division Multiplexing (AFDM) and Orthogonal Time Frequency Space (OTFS) are promising candidates, while Discrete Fourier Transform spread OFDM (DFT-s- OFDM) is a promising modulation technique for uplink communication connections due to its low peak-to-average power ratio (PAPR). However, the presently envisaged modulation techniques may not be suitable for high-mobility communication in the 6G wireless networks, which will be an important use case.

[0009] Multi-carrier waveforms include orthogonal time frequency space (OTFS), discrete Zak transform based OTFS, orthogonal delay-Doppler division multiplexing (ODDM), interleaved frequency division multiplexing (IFDM), constant-envelope OFDM (CE- OFDM), etc. However, similar to OFDM, OTFS, ODDM and IFDM based on multicarrier exhibit a high PAPR, making it unsuited for low-power devices. While FM- OFDM could reduce the PAPR by modulating the OFDM signal with a frequency modulator, its frequency spectrum utilization is inefficient sue to a high number of inactive subcarriers. Also, performance advantages of FM-OFDM over OTFS have not been observed. By modulating an OFDM signal with the phase modulator, CE- OFDM can also achieve a low PAPR. However, the performance of CE-OFDM is degraded in high-mobility communications.

[0010] The single-carrier category comprises orthogonal time sequence multiplexing (OTSM), whose PAPR, however, is as high as that of OTFS.

[0011] Orthogonal chirping division multiplexing (OCDM) and affine frequency division multiplexing (AFDM) belong to the multi-carrier chirping category. AFDM is an enhanced version of OCDM catering for high-mobility communications. However, both are based on multi-carrier and exhibit high PAPR.

[0012] In terms of computational complexity, i.e. , the number of operations that must be carried out to complete the modulation of symbols to be transmitted, varies largely between the conventional modulation techniques discussed above. Figure 1 shows a schematic comparison of the core operations required for obtaining the transmit signals from a selection of the conventional modulation schemes discussed above. The core operation of OFDM is an M-point Inverse Fast Fourier Transform (IFFT) that has a complexity of / Wlog2M with M being the number of subcarriers used. It is noted that the number of subcarriers M increases with the bandwidth of the channel. The core operations of AFDM add an diagonal matrix multiplication upstream of the Appoint IFFT that is required here, too, and a further diagonal matrix multiplication downstream of the Af-point IFFT, resulting in a complexity of M log2Af+ 2Af. OTFS requires an Inverse Symplectic Fast Fourier Transform (ISFFT) and, due to the 2- dimensional frame structure, an AfOTFS-point IFFT, resulting in an overall complexity of M log2Af +M log2AfOTFS. The core operations of DFT-s-OFDM comprise an Af-point DFT, followed by subcarrier mapping, and an JV-point IFFT, with an overall complexity of M log2Af +JVlog2N. Finally, the core operations of circularly shifted chirps with DFT-s-OFDM comprise all core operations of DFT-s-OFDM plus an FDSS filter for the chirp. The complexity of the filter is not exactly known, but it definitely adds to the overall complexity.

[0013] OFDM provides an acceptable reliability for wireless communications at the cost of a high PAPR, which may cause distortion and spectral spreading when the signal power peaks lead to operating the transmitter in the nonlinear region. Designing the radio frequency (RF) amplifier for high peaks is costly and reduces the average efficiency of the RF stage. While the reliability of AFDM and OTFS is higher than that of OFDM, the downside of high PAPR remains present. DFT-s-OFDM as well as circularly shifted chirps with DFT-s-OFDM provide similar reliability as AFDM and OTFS at lower PAPR. However, the latter two, like AFDM and OTFS, may not provide a desired ultra-high reliability required in some 6G use cases, e.g., communication for autonomous driving (AD) and other use cases, in which a repeating of messages and the delay incurred thereby is undesirable or unacceptable.

[0014] It is, therefore, desirable to provide a method of modulating symbols to be transmitted that exhibits low PAPR, low bit error rate (BER) and ultra-high reliability.

[0015] SUMMARY OF THE INVENTION

[0016] This object is achieved by the method of modulating symbols representing binary data for transmission over a wireless communication channel presented in claim 1 , the method of demodulating so-modulated symbols presented in claim 6, and the transmitter and receiver presented in claims 11 and 12, respectively. A computer program product and a computer-readable medium are provided in claims 13 and 14, respectively. Embodiments and developments are described in respective dependent claims.

[0017] The present invention combines aspects from the concepts of AFDM and DFT-s-OFDM as introduced in the background section of this specification. As will be shown hereafter, adding chirping after converting the DFT-processed signal into the time domain provides the desired properties.

[0018] Figure 2 shows a schematic block diagram of a chirped DFT-s-OFDM communication system in accordance with the invention, comprising a transmitter 500 and a receiver 600. Also shown in figure 2 are representations of the signals at various stages of the processing, as well as the respective domain, i.e., time domain or frequency domain, in which the signals are present.

[0019] The transmitter 500 performs two main processing functions, DFT-s-OFDM modulation comprising function blocks 510 to 550, and chirping in function block 560. In detail:

[0020] At the transmitter 500 a serial sequence of data symbols is first received at serial-to- parallel (S2P) converter 510 and converted into an unmodulated time-domain data vector of length M, denoted herein as x = [x[0],x[l], ••• ,x[M - 1]]T, of parallel data symbols. The parallel data symbols are input to block 520 which transforms the data symbols from the time domain into corresponding representations in the frequency domain, e.g., through an AT- point DFT, for obtaining M data symbols in the frequency domain. The resulting frequency-domain data vector of length M is given by X = FMx, with FMbeing the M-point DFT matrix used in this example. Block 530 receives the M frequency-domain data symbols and pads them with a second number, N-M, of padding symbols, e.g., zeros, yielding a third number, N, of frequency-domain transmit symbols. Also in block 530, the N frequency-domain transmit symbols are mapped to respective subcarriers in accordance with a specified subcarrier mapping scheme. Typically, there are two subcarrier mapping schemes to select from, subband scheme and interleaved scheme, although other schemes may be conceivable. Of the two typical mapping schemes, sub-band scheme mapping with consecutive subcarriers for data transmission is more likely to suffer a deep fade and exhibit high PAPR than interleaved mapping. Mapping in accordance with the interleaved scheme is thus considered in the remainder of this specification, unless stated otherwise, with the subcarrier mapping matrix P = of size

[0021] N x M(N > M), where IMis an identity matrix of size M x M. The integer-number DFT spreading factor (SF) is defined as SF = — . After the subcarrier mapping the data vector of length N is written as

[0022] S = PX. Note that it is possible to choose a fractional value for SF, and to define the subcarrier mapping matrix in other ways, although this comes at the expense of an increased PAPR.

[0023] The N frequency-domain transmit symbols are input to block 540, which transforms the transmit signals back into the time domain, e.g., through an JV-point IFFT, for obtaining N time-domain transmit symbols, represented by the time-domain signal s = F^s, with Fwbeing an / V-point FFT matrix. The time-domain transmit signal is input to parallel-to-serial (P2S) converter 550 that converts the N parallel timedomain transmit symbols into a serial time-domain signal of a first length, corresponding to the length of the concatenated parallel transmit symbols.

[0024] Note that the time-domain signal after DFT precoding differs from the unmodulated time-domain signal input to the process, as shown in the illustrative example provided at the top of figure 2. Here, M = 4, N = 8, SF = 2 and cr= - are exemplarily used. Af represents the subcarrier spacing, while B designates the bandwidth, t and / designate the time and frequency, respectively. The DFT precoding results in the bandwidth being broadened a factor of two from - to B, including the assigned subbands shown in the different pattern and the patternless, white unassigned subbands arranged in between. This bandwidth expansion is also referred to as DFT

[0025] 2 1 spread. Further, each data symbol transmission duration is halved from - to -, in B B accordance with SF = 2, with reduced amplitude, and then repeated after

[0026] Denoting the channel length as L, the coherence bandwidth corresponds to -. Each symbol extends over a frequency band of B - Af , which is typically bigger than the coherence bandwidth and, thus, frequency diversity can be achieved, as will be discussed in greater detail further below.

[0027] The serial time-domain signal s of the first length NTSis fed to chirping block 560, with N denoting the number of symbols and Tsdenoting the symbol duration. Tsis defined as -, with B corresponding to the bandwidth. Chirping block 560 further receives a corresponding chirp signal c of length NTSwith a chirp rate crand outputs the so-obtained chirped DFT-s-OFDM signal to block 570 that is configured for inserting a cyclic prefix (CP) into the time-domain chirped DFT-s-OFDM signal.

[0028] In the example the chirp signal is linear with and the chirp rate is set to c = in this example c = -, indicating that the frequency is increased by one f , or subcarrier spacing, per time instant corresponding to -, extending over the full bandwidth, as represented by the single-carrier chirping waveform shown between the pre-chirping and post-chirping symbol representations. The chirp signal may, however, also be non-linear. As a result, after chirping, data symbols represented by the different pattern, can “hop” to unassigned subcarrier bands. In other words, both assigned subbands and unassigned subbands are used for data transmission over time, i.e. , the full band, thus providing more observations than unknowns and leading to enhanced noise suppression in the frequency domain. Also, the impact of channel fading is mitigated. Such frequency band expansion is also referred to as chirp spread. In the figure, the arrows in the right-most symbol representation indicate the frequency increase due to chirping. The combined DFT spread and chirp spread preceding and succeeding the OFDM signal, respectively, gives rise to the moniker chirped DFT-s-OFDM for the proposed waveform. The chirped DFT-s-OFDM signal is denoted as sc: The CP appended to scbefore transmission preferably has a length of Lcp(Lcp with L being the channel order. h[n, Z] is defined as the channel gain of the Z-th channel path at the n-th time instant, with I = O,1, --- ,L and n = 0,1, — ,N - 1.

[0029] It is noted that increasing the SF to 4 as opposed to SF=2 as used in the present example would result in each symbol being repeated 4 times in the time domain, yielding additional noise suppression.

[0030] The modulated signal output from block 570 is then transmitted via antenna 580 over a wireless channel subject to doubly-selective fading. The expression doubly- selective fading channel refers to a wireless communication channel subject to speed-dependent Doppler shifts or spreads and quickly varying multipath reception caused by fast-moving transmitters and / or receivers, which results in severe time and frequency dispersiveness. Time and frequency dispersiveness due to different path lengths and difference velocity between transmitter and receiver, respectively, each cause signal fading at the receiver, thus the moniker doubly-selective channel fading. Doubly selective channel fading significantly impairs the performance of wireless communication systems. The communication channel is represented in the figure by the lightning and cloud symbols.

[0031] The channel matrix Htof the communication channel is derived as follows: Define fc

[0032] / max =asthe normalized maximum Doppler frequency with respect to the subcarrier spacing, with fc, v, c, and f being the carrier frequency, velocity, speed of light, and the subcarrier spacing, respectively. The maximum Doppler frequency should lie within one subcarrier spacing, yielding fmaxe (-0.5, 0.5], h[n, Z] is given by with hpand vp(pe [- / max, nax]) being the channel gain and the normalized Doppler shift of the p-th path. The time-domain channel matrix is expressed as and n is the forward cyclic-shift matrix, i.e., a matrix where each row is a cyclic right-shift of the row above it, also referred to as circulant matrix, as presented in the example below.

[0033] 0 ••• 0 1 n = l : ° ?]

[0034] 0 : 1 0

[0035] Note that in this specification a channel model with a random Doppler shift for each channel path is considered. Nevertheless, the proposed method can easily be extended to Doppler-spread channel models with multiple Doppler shifts for each channel path.

[0036] At the receiver 600 the transmitted time-domain signal is received at antenna 610 and provided to block 620 configured for removing the CP from the signal, yielding a prefix-less time-domain signal.

[0037] The received time-domain signal vector of length N after the removal of cyclic prefix is expressed as with w being an additive white Gaussian noise vector of variance a2. Define z = FWCHW. After dechirping and N point FFT, the frequency-domain received signal vector is

[0038] The prefix-less time-domain signal is then input to de-chirping block 630, which also receives a copy of the chirp signal used in transmitter 500. De-chirping block 630 reverses the chirping carried out in the transmitter and yields a signal carrying the third number N of DFT-s-OFDM-modulated transmit symbols that were transmitted from the transmitter. The de-chirped prefix-less received signal is then fed to S2P block 640, which outputs a number of parallel segments, the totality of which represents the de-chirped prefix-less received signal. The parallel segments are provided to block 650, which transforms the parallel segments into the frequency domain, e.g., through an JV-point FFT. The so-transformed segments are provided to block 660, which is configured for channel estimation (CE) and equalisation (EQ), for recovering the transmitted frequency-domain symbols. Various conventional OFDM channel estimation and equalization schemes can be exploited for this purpose. Any frequency-domain symbols that may have been recovered on any of the unassigned subbands, i.e. , subbands that were not assigned by the DFT at the transmitter and that are padded with padding symbols, may be discarded, indicated by the arrows pointing away into empty space from block 670. The remaining M recovered data symbols on the assigned subbands are then re-mapped to the corresponding subcarriers in re-mapping block 670 and transformed to time-domain symbols in block 680, e.g., by carrying out an M-point inverse discrete Fourier transform (IDFT). Finally, the parallel time-domain symbols are converted back to a serial stream of time-domain symbols in P2S block 690, which serial stream may be output for decoding.

[0039] Note that conventional elements of a transmitter or a receiver, e.g., oscillators, mixers, amplifiers, equalisers, etc., are not shown in the figure for clarity reasons.

[0040] Figure 3 shows the schematic comparison of the core operations required for obtaining the transmit signals from the conventional modulation schemes discussed herein as found in figure 1 , complemented by the method in accordance with the present invention as presented above. It is readily apparent that an inverse FFT is present in all modulation schemes, and that the subcarrier mapping is present in all modulation schemes involving DFT. Similar to the AFDM modulation the proposed method adds a chirping operation subsequent to the inverse FFT operation. The similarity or equivalence of the post-IFFT operation is indicated in the figure through the identical shading of the respective boxes.

[0041] The chirped DFT-s-OFDM modulation and the resulting waveform proposed herein exploit frequency diversity and introduce coding gain, while maintaining the good PAPR of the conventional DFT-s-OFDM. The benefits of the proposed DFT-chirp-s- OFDM modulation and waveform will be further elucidated in comparison to OFDM, AFDM and DFT-s-OFDM with reference to the illustrative time-frequency diagrams shown in figure 4. In the figure, Af represents the width of a subchannel, centred around a subchannel’s carrier frequency, corresponding to the subcarrier spacing, t and f represent time and frequency, respectively. Like in the illustrative example used in connection with the discussion of figure 2, the number of subcarriers is N = 8 and c = is used for chirping.

[0042] To achieve frequency diversity, the same symbol is transmitted at different frequencies. The frequency separation Bsshould be greater than the coherence bandwidth. An example is provided in figure 4, in which a 3-path channel, i.e. , L = 3 is assumed, yielding a delay spread of -, with B being the bandwidth, and t and / designating the time and frequency, respectively. The coherence bandwidth Bcis the inverse of the delay spread and thus obtained as Bc= As shown in figure 4 a), OFDM transmits N symbols, represented by the different filling pattern, over the total bandwidth B, with one symbol using one subcarrier band only, and thus its frequency separation is Bs= f. Since is typically greater than 1, Bsis smaller than Bcand OFDM cannot exploit frequency diversity.

[0043] AFDM, as shown in figure 4 b), thanks to the frequency sweeping over the full band using chirping, has a frequency separation for each AFDM symbol of Bs= B, which is clearly larger than - for the assumed 3-path channel. Thus, AFDM is able to achieve frequency diversity. The arrows across the subchannels indicate how the frequency for symbols transmitted in each respective subchannel increases due to the chirping.

[0044] Next, with reference to figure 4 c) through f), as single-carrier transmission, each symbol of DFT-s-OFDM and DFT-chirp-s-OFDM, respectively, is transmitted using the frequency spanning over a large band, such as, Bs= B - 2Af for a spreading factor SF = 2 as shown in figure 4 c) and d), respectively, and Bs= B - 4Af for SF = 4 as shown in figure 4 e) and f), respectively. Bsis normally larger than Bc, and thus, DFT-s-OFDM can exploit some frequency diversity, while DFT-chirp-s-OFDM can exploit full frequency diversity, similar to AFDM.

[0045] The chirped DFT-s-OFDM modulation presented herein not only achieves frequency diversity, but also brings additional coding gain, compared to a pure DFT-aided waveform, e.g., DFT-s-OFDM, or a pure chirping-aided waveform, e.g., AFDM. As can be seen in figure 4 d) the DFT-chirp-s-OFDM presented herein allows for a fullband transmission, i.e. , making active use of all subcarriers, compared to DFT-s- OFDM with fixed assigned frequency bands and unused bands in between. This exploitation of the full bandwidth B avoids deep fade due to channel fading and leads to extra coding gain. While both AFDM and DFT-chirp-s-OFDM allow full band transmission, DFT-chirp-s-OFDM has symbols spreading over multiple time slots, which brings additional coding gain compared with AFDM.

[0046] Moreover, as is apparent from the comparison of figure 4 d) and f), the proposed DFT-chirp-s-OFDM can bring enhanced coding gain as the DFT spreading factor SF increases from 2 to 4. For DFT-s-OFDM, as is apparent from the comparison of figure 4 c) and e), an increase of the spreading factor reduces the number of assigned frequency bands, and more frequency bands, or subcarriers, remain unused. This makes DFT-s-OFDM susceptible to channel fading, resulting in a performance degradation, while DFT-chirp-s-OFDM, thanks to the frequency sweeping with a chirp signal, can always maintain full-band transmission and each symbol is spreading over more frequency bands and time slots, contributing to enhanced coding gain.

[0047] Note that for the sake of full-band transmission, the chirp rate of proposed DFT-chirp- s-OFDM must be properly selected. It is readily apparent that the chirp rate value depends on the DFT spreading factor. The frequency increase per time instant is

[0048] SF given by c = a + b x — , with a = 1, 3, 5, ••• , SF - 1 and b being zero or positive integer values. For example, at SF = 2 in figure 3, the frequency increase per time instant should be c = 1 + 2b. Otherwise, the time-frequency diagram of DFT-chirp-s-OFDM would be identical to that of DFT-s-OFDM, without bringing additional coding gain. It is known that DFT precoding allows single-carrier transmission with low PAPR especially when interleaved subcarrier mapping is considered. On the other hand, the chirping subsequent to the OFDM as proposed herein uses a constant-amplitude chirp signal to sweep frequency only, without impacting the data signal's amplitude. Therefore, the proposed DFT-chirp-s-OFDM preserves the good PAPR of DFT-s-OFDM.

[0049] Using exemplary values of N = 256, M = 128, / VQTFS = 16, MOTFS = 16, and 16-quadrature amplitude modulation (16-QAM), the complementary cumulative distribution function (CCDF) of PAPR for the proposed chirped DFT-s-OFDM is plotted in figure 5 against those of OFDM, AFDM, OTFS, and DFT-s-OFDM. The CCDF of PAPR is defined as the probability that the PAPR exceeds a certain value, i.e. , CCDF = Pr(PAPR > A). As can be seen in the figure, the PAPR of DFT-s-OFDM modulation and the proposed chirped DFT-s-OFDM modulation with phase shift keying (PSK) for achieving a CCDF value of 10-4is approximately A = 0 dB, while A > 10 dB is required for OFDM, AFDM, and OTFS.

[0050] Referring back to the discussion of the computational complexity further above, in the following a comparison between OFDM, AFDM, DFT-s-OFDM, OTFS and chirped DFT-s-OFDM using N = 256, M = 128, / VQTFS = 16, MOTFS = 16 as exemplary system values is provided. Among the different modulation schemes, OFDM has the lowest complexity at A' log2N. Normalising this base value to 1 , the values for the other modulation schemes discussed herein will be respectively provided for comparison.

[0051] The complexity of AFDM follows A' log2A' + 2N, which translates into an increase of 25% over OFDM, yielding a normalised value of 1.25.

[0052] The complexity of DFT-s-OFDM follows A' log2A' + Mlog2M, which translates into a further 15.2% increase over AFDM, yielding a normalised value of 1.44.

[0053] OTFS’ complexity follows JVlog2V+JV / og2A / OTFS, translating into a further 4.2% increase over DFT-s-OFDM to a normalised value of 1.5. Finally, the complexity of DFT-chirp-s-OFDM follows A' (log2A' + l) +Mlog2M, representing an increase over OTFS of 4% and yielding a normalised value of 1.56.

[0054] It is readily apparent that DFT-chirp-s-OFDM, OTFS, and DFT-s-OFDM have comparable complexity, lying within less than 5% around OTFS.

[0055] Compared to multi-carrier based waveforms, e.g., OFDM and AFDM, some frequency bands of DFT-s-OFDM and DFT-chirp-s-OFDM shown in figure 4 are unused, with fewer data symbols transmitted. Note that the time-frequency diagrams in figure 4 are provided for a single user. The remaining frequency bands in the diagrams shown in figure 4 may be used by other users for data transmission.

[0056] Therefore, DFT-s-OFDM and DFT-chirp-s-OFDM can achieve the same spectral efficiency of OFDM and AFDM.

[0057] In the following section a performance comparison of the proposed chirped DFT-s- OFDM against OFDM, AFDM, OTFS, and DFT-s-OFDM based simulations is presented.

[0058] Following the simulation setting that is used by A. Bemani, N. Ksairi, and

[0059] M. Kountouris, in “Affine frequency division multiplexing for next generation wireless communications,” IEEE Transactions on Wireless Communications, vol. 22, no. 11, pp. 8214-8229, 2023, the IFFT size of OFDM, AFDM, DFT-s-OFDM, and chirped DFT-s-OFDM is TV = 256. The numbers of OTFS delay and Dopier bins are MOTFS = 16 and NOTFS = 16. For chirped DFT-s-OFDM and DFT-s-OFDM, the size of DFT is M = 128, resulting in a DFT spreading factor of SF = 2, unless otherwise stated. The carrier frequency and subcarrier spacing are set to fc= 4GHz and Af = 15KHz. A 3- path equal-gain channel with a velocity of v =50°hkmis considered. The modulation scheme is 4-quadrature amplitude modulation (4-QAM). The chirp rate of the proposed chirped DFT-s-OFDM is c = Linear minimum mean square error (LMMSE) equalization technique is used for all waveforms. The error performance of the proposed chirped DFT-s-OFDM modulation is investigated using pairwise error probability (PEP) analysis using a maximum likelihood (ML) equalizer as optimal reference implementation.

[0060] The BER upper bound for the proposed chirped DFT-s-OFDM modulation is achieved with a maximum likelihood (ML) equaliser, which is considered optimal. The system model represented by equation (5) can be rewritten as

[0061] Denote E;(x) = FwCHD(n(CFJvPFMx. The received frequency-domain signal vector y is re-expressed as y = E(x)h + z, (7) with E = [Eo, E ••• , EL] and h = , / rT. The data symbol vector x can be estimated by using the ML equalizer: x = min||y - E(x)h||, X6K (8) where x denotes the candidate vector of the data symbol and is chosen from a certain modulation alphabet IK. Note that the ML equalizer incurs high computational complexity, making it less suitable for big data vector sizes (M) and big symbol alphabet sizes (Q). However, per-survivor processing (PSP) can be used to approximate the ML equaliser with low complexity.

[0062] Denote {x -> x} as the pairwise error event, where x represents the transmitted signal vector and x the erroneously detected signal vector using the ML equalizer, x and x are chosen from a certain modulation alphabet, i.e. , x e IK and x e IK, but with x x. Define 0(x,x) = (E(x) - E(x))H(E(x) - E(x)). The rank of 0(x,x) and its non-zero eigenvalues are denoted as R and {A1,A2, --- ,AR}. Assume each entry in h is an independent identically distributed complex Gaussian random variable, i.e., The SNR for each data symbol is denoted as y, i.e., y = Following the derivation provided by Y. Ge, Q. Deng, D. Gonzalez G., Y. L. Guan, and Z. Ding, in "OTFS signaling for SCMA with coordinated multi-point vehicle communications," IEEE Trans. Veh. Technol., vol. 72, no. 7, pp. 9044-9057, 2023, and Z. Sui, H. Zhang, S. Sun, L.-L. Yang, and L. Hanzo, in "Spacetime shift keying aided OTFS modulation for orthogonal multiple access," IEEE Trans. Commun., vol. 71, no. 12, pp. 73937408, 2023, the PEP can be expressed as

[0063] At high SNR equation (9) can be approximated as

[0064] The average BER can then be obtained by using the union bound technique discussed in "OTFS signaling for SCMA with coordinated multi-point vehicle communications" (full citation above) as follows: with d(x,x) being the number of bits in difference between x and x.

[0065] The diversity order of chirped DFT-s-OFDM modulation is given by

[0066] GD = rank(0(x,x)) (12) x61K,x61K,x*x

[0067] By calculating GDusing equation (12), the diversity order is found to be equal to the number of channel paths for the chirped DFT-s-OFDM modulation.

[0068] Table I shows the values of GDof conventional DFT-s-OFDM and the proposed chirped DFT-s-OFDM for different values of Doppler shifts with the number of channel paths L = 3, calculated using equation (12). The parameters underlying the values v0, vltand v2.are provided in the left-most column. The diversity order for the parameters randomly generated from - / MAX to fMM. ■ is calculated and averaged over 100k realisations.

[0069] The value of GDfor DFT-s-OFDM is calculated by setting the chirp rate to cr= 0. It can be seen that DFT-s-OFDM cannot achieve full frequency diversity and its diversity order varies with varying Doppler shifts. In contrast, the proposed chirped DFT-s-OFDM can exploit full frequency diversity and shows high resilience to varying Doppler shifts.

[0070] Fig. 6 a) shows the BER upper bounds derived using equation (11) and the simulated BER of the DFT-s-OFDM and the chirped DFT-s-OFDM using the optimal ML equalizer. The DFT size and IFFT size are M = 2 and N = 8. The maximum Doppler frequency, velocity, and subcarrier spacing are fmax= 2KHz, v = 500 km / h, and f = 15KHz. For each Monte Carlo simulation, the values of Doppler shifts are randomly generated from -fmaxto fmax. Binary phase shift keying (BPSK) modulation is adopted. As is apparent from the figure 6 a), in which L = 3 is assumed, at high SNRs the simulated BER is close to the derived BER upper bound. The slope of the BER curves for the DFT-s-OFDM is flatter than that for the chirped DFT-s-OFDM, indicating a smaller diversity order of the DFT-s-OFDM over the chirped DFT-s- OFDM, which is consistent with the results shown in table I. Regarding the chirped DFT-s-OFDM, its diversity order calculated from its BER curves is found to correspond with the number of channel paths and is consistent with equation (12), as is apparent from figure 6 b). In figure 6 b) curves for values of L ranging from 1 to 4 are shown.

[0071] In the following section the output SNR of the proposed chirped DFT-s-OFDM modulation is analysed in comparison to other waveform candidates, using an LMMSE equalizer. By letting Heff= FwCHHtCF^PFFM, equation (5) is rewritten as y = Heffx + z. (13)

[0072] Using the LMMSE equalizer x can be estimated as

[0073] Note that the intersymbol interference (I SI) has been mitigated to some extent through the use of an LMMSE equalizer. According to equation (14), without considering the impact of noise, the signal estimate is expressed as

[0074] GHeffx with G = The impact of ISI can be viewed from the non-diagonal elements of GHeff, which are found to be small and negligible.

[0075] As has been shown by Y. Jiang, M. K. Varanasi, and J. Li, in "Performance analysis of ZF and MMSE equalizers for Ml MO systems: An in-depth study of the high SNR regime," IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 2008-2026, 2011, the output SNR of chirped DFT-s-OFDM modulation using the LMMSE equalizer can be expressed as

[0076] E[xHHpffGHGHeffx]

[0077] Output SNR = -i — (15) H E{zHGHGz}v 7where E{-} indicates the expectation operation. Due to the properties of the trace operation, the following can be obtained: xHHgffGHGHeffx = Tr{xHHgffGHGHeffx} = Tr{xxHHgffGHGHeff} and zHGHGz = Tr{zHGHGz} = Tr{zzHGHG}. Equation (15) can thus be rewritten as with E{XXH} = IM, E{ZZH} = a2Iw, and Tr{GHG} = Tr{GGH}.

[0078] As a result, the output signal power and output noise power corresponds to the sum of the diagonal elements of H^f GHGHeffand o-2GGH, respectively. The m-th diagonal element of HgffGHGHeffand o-2GGHcorresponds to the output signal power and output noise power at the m-th symbol, respectively. The output signal power and output noise power with respect to the symbol index m for the chirped DFT-s-OFDM are depicted in figures 7 and 8. The output SNR with respect to the symbol index m is shown in figure 9. Following the similar derivations, the output signal power, output noise power, and output SNR for DFT-s-OFDM, AFDM, OTFS, and OFDM are likewise depicted in figures 7 to 9 for comparison purposes.

[0079] As is easily seen in figures 7, 8, and 9, unlike in DFT-s-OFDM, chirped DFT-s-OFDM, AFDM, and OTFS, the output signal power, output noise power, and output SNR of OFDM differ significantly for some symbols. This is due to the OFDM symbols being modulated in the frequency domain, with different symbols experiencing different fading due to multipath channel. In the other modulation schemes each symbol is transmitted across nearly the entire frequency band, enhancing their resilience to frequency-selective fading. Specifically, each chirped DFT-s-OFDM symbol is modulated in the time domain and transmitted across a wide frequency band. In the case of AFDM, chirping allows each symbol on a specific subcarrier to hop to all other subcarrier bands. For OTFS, each symbol is modulated in the delay-Doppler domain and is spreading over the full frequency band after ISFFT. As a result, except for OFDM, the other modulation schemes shown in figures 7, 8, and 9 exhibit nearly identical output signal power, output noise power, and output SNR across all symbols.

[0080] As can further be seen in the figures, the proposed chirped DFT-s-OFDM modulation produces lower output noise power and higher output SNR than DFT-s-OFDM modulation. This is due to the inclusion of chirping in chirped DFT-s-OFDM, which facilitates full-band transmission. For example, when setting the DFT size and IFFT size of DFT-s-OFDM and chirped DFT-s-OFDM respectively to M=2 and N=8, without chirping-enabled full band transmission, two (2) unknown data symbols are mainly estimated from the received data symbols on two (2) subcarriers, as shown in figure 4 e). In contrast, by spreading the signal across the full band, two (2) unknown data symbols can be estimated from the received data symbols on eight (8) subcarriers, as shown in figure 4 f), i.e., from the received data symbols on all subcarriers. Hence, there are more observations than unknowns, and the redundant information from more observations can mitigate the impact of noise.

[0081] As can yet further be seen in the figures, the proposed chirped DFT-s-OFDM outperforms AFDM and OTFS in terms of output noise power and output SNR. This is because the introduction of DFT precoding in chirped DFT-s-OFDM spreads data symbols in the time domain. This is easily seen in figure 4 e) and f) where, due to the spreading factor being set to four (4), two data symbols are transmitted four times over the time. Such retransmission can significantly reduce the impact of noise.

[0082] In the following section the communication performance of the proposed chirped DFT-s-OFDM modulation is compared with that of existing waveforms, e.g., DFT-s-OFDM, AFDM, OTFS, and OFDM. To ensure a fair comparison, different waveforms are compared with identical bit to noise ratio Eb / NO. The energy per active subcarrier for DFT-s-OFDM and chirped DFT-s-OFDM remains the same as that of OFDM, AFDM, and OTFS. Unless otherwise stated, the values of the simulation parameters are set as follows: The IFFT size for chirped DFT-s-OFDM, DFT-s-OFDM, AFDM, and OFDM is set to N = 256. The DFT size for chirped DFT-s-OFDM and DFT-s-OFDM is set to M = 64, resulting in a DFT spreading factor of SF = 4. The chirp rate is set to cr= 1 / N. The carrier frequency and subcarrier spacing are set to fc= 4GHz and Af = 15KHz, respectively. A 3-path equal-gain channel is assumed. The velocity is set to v = 500 km / h, corresponding to a Doppler frequency of fmax= 2KHz. For each Monte Carlo simulation, the values of Doppler shifts are randomly generated from -fmaxto fmax. For OTFS, the numbers of delay grids and Doppler grids are set to MOTFS = 16 and / VOTFS = 16. Quadrature phase shift keying (QPSK) modulation and LMMSE equalizer are adopted.

[0083] Figures 10 and 11 present the BER and output SNR, respectively, of the proposed chirped DFT-s-OFDM, compared to DFT-s-OFDM, AFDM, OTFS, and OFDM. The proposed chirped DFT-s-OFDM benefits from an enhanced noise suppression, as discussed further above, and outperforms the existing waveforms in terms of BER and output SNR, with around 4 dB SNR gain over AFDM, OTFS, and DFT-s-OFDM. Although OFDM has an output SNR that is comparable to that of OTFS and AFDM, it has deep fades as shown in figure 9. Meanwhile, it cannot exploit frequency diversity, and thus, its BER is easily identified as worst in figure 10.

[0084] Figure 12 shows the impact of the DFT spreading factor on the BER of DFT-s-OFDM and the proposed chirped DFT-s-OFDM. The BER of DFT-s-OFDM does not benefit from enhancing the DFT spreading factor. In contrast, for the proposed chirped DFT- s-OFDM, there is a significant BER improvement, especially when the DFT spreading factor increases from 2 to 4. This is caused by the enhanced noise suppression resulting from the increase of the DFT spreading factor, as can be seen in figure 13. As discussed further above, the enhanced noise suppression results from full band transmission and symbols retransmission enabled by chirping and DFT precoding, respectively. Note that, increasing the SF beyond SF = 4, will not result in a noticeable performance enhancement, since increasing the SF leads to decreased signal amplitude of 1 / . — , as has been shown by H. G. Myung, J. Lim and D. J.

[0085] ' SF

[0086] Goodman, in “Single carrier FDMA for uplink wireless transmission," IEEE Veh.

[0087] Technol. Mag., vol. 1 , no. 3, pp. 30-38, Sept. 2006, by Y. Shao and S. C. Liew, in “Flexible subcarrier allocation for interleaved frequency division multiple access,” IEEE Trans. Wireless Commun., vol. 19, no. 11 , pp. 7139-7152, Nov. 2020, and by M. W. Chia, B. S. Thian and T. T. Tjhung, in “Distributed DFT-spread OFDM," Proc. 10th IEEE Singapore ICCS, Singapore, 2006, pp. 1-5, February, Singapore. For example, the amplitude reduction would be 0.35 and 0.25 for SF=8 and SF=16, respectively. This amplitude reduction would result in performance degradation, cancelling out the additional benefits gained from additional repeated transmission.

[0088] Note that, in the previous results, DFT-s-OFDM as well as chirped DFT-s-OFDM with SF>1 exhibit a different spectral efficiency compared to AFDM and OTFS using all subcarriers. Figure 14 shows the BER values of different modulation waveforms under the same bandwidth efficiency with SF=4. AFDM and OTFS use a similar data mapping scheme as DFT-s-OFDM and chirped DFT-s-OFDM, with one-fourth of the interleaved subcarriers (for AFDM) or delay grids (for OTFS) allocated to a specific user for data transmission. The unused subcarriers or delay grids can be assigned to other users for data transmission. Compared to figure 10, the BER values of AFDM and OTFS in figure 14 are lower and are nearly identical to that of chirped DFT-s- OFDM. This implies that the superior BER of chirped DFT-s-OFDM over AFDM and OTFS in figures 10 and 14 mainly results from DFT precoding. However, even though AFDM, OTFS, and chirped DFT-s-OFDM exhibit similar BER values in figure 14, AFDM and OTFS exhibit significantly higher PAPR than chirped DFT-s-OFDM.

[0089] In practical implementations, when the input signal is too high, the power amplifier's output would reach its upper limit and is unable to increase further, resulting in clipping and non-linear distortion. Considering a clipping ratio of 1 , the BER values of different waveforms under the same bandwidth efficiency are simulated and shown in figure 15. AFDM and OTFS are found to be more sensitive to clipping and their BER values are worse than those of DFT-s-OFDM and chirped DFT-s-OFDM. This is due to the signals with high PAPR values, as in AFDM and OTFS, being easily affected by clipping. Besides, considering the same bandwidth efficiency using SF=4, OTFS presents higher PAPR than AFDM, which is why its BER degrades more severely than that of AFDM in figure 15.

[0090] As 6G and beyond are expected to also implement sensing based on communication signals, also referred to as integrated sensing and communications (ISAC), the sensing capability of the proposed DFT-chirp-s-OFDM will be discussed in the following section. Adopting the simulation setting that is used by L. Giroto de Oliveira, B. Nuss, M. B. Alabd, A. Diewald, M. Pauli, and T. Zwick, in “Joint radar-communication systems: Modulation schemes and system design," IEEE Transactions on Microwave Theory and Techniques, vol. 70, no. 3, pp. 1521-1551, 2022, the IFFT size of the DFT-s-OFDM and the DFT-chirp-s-OFDM is set to N = 2048. The carrier frequency and bandwidth are set to fc= 79GHz and B = 1GHz, respectively. Each data frame consists of Nf= 512 symbols. The chirp rate of the DFT-chirp-s-OFDM is c = 1 / N. The DFT size of the DFT-s-OFDM and DFT-chirp-s-OFDM is M = 1024. The range and velocity of the target are 150 m and 180 m / s, respectively. The value of Eb / NO is -33 dB.

[0091] Communication-assisted sensing is considered. The data frame is transmitted and reflected by a target. The reflected data frame is processed to sense the range and velocity of the target by a sensing unit which is co-located with the transmitter. The reflected signal has wo dimensions, e.g., N x Nf. The first dimension N and second dimension Nfcorrespond to fast-time axis and slow-time axis, respectively. The sensing unit produces an ambiguity function by applying a matched filter, i.e., correlating the received signal with the time reverse and complex conjugate of the transmitted signal, implementing IFFTs along the fast-time axis, and FFT along the slow-time axis.

[0092] Fig. 16 shows the ambiguity function of DFT-chirp-s-OFDM. There is a distinct peak, which means one target is detected. The coordinates of the peak are used for estimating the range and velocity of the target, which are close to their true values. However, if a DFT-s-OFDM data frame is used for sensing, as shown in figure 17, there are two peaks, one of which is a false peak caused by the repetition of data symbols. The number of false peaks tends to increase with the DFT spreading factor, which false peaks may be mistakenly detected as the number of targets. In contrast, thanks to chirping, the data symbols of DFT-chirp-s-OFDM are not repetitive, and thus, false peaks can be prevented and the number of targets can be correctly detected.

[0093] In light of the foregoing discussion, in accordance with a first aspect of the invention a method of modulating data symbols representing binary data for transmission over a wireless communication channel is presented. The wireless channel may suffer from doubly-selective fading, interfering signals and / or multipath reception. The method comprises converting a serial sequence comprising a first number, M, of data symbols into a first number of M parallel data symbols, and transforming the M parallel data symbols from the time domain into the frequency domain. The method further comprises padding the M parallel data symbols in the time domain with a second number, N-M, of padding symbols, yielding a third number, N, of parallel frequency-domain transmit symbols. The padding may be zero-padding, although other symbols may be used, e.g., symbols that are designed for channel estimation while causing no or a minimised interference with data symbols. In a further step of the method the N frequency-domain transmit symbols are mapped onto respective subcarriers prior to being transformed into the time domain. The time-domain transmit signals obtained in the previous step are converted into a serial time-domain signal of a first length, N, which is chirped with a chirping signal of a corresponding length N. Finally, a CP is added to the chirped signal before it is output for transmission.

[0094] In one or more embodiments of the method transforming the first number, M, of parallel data symbols from the time domain into the frequency domain comprises subjecting the symbols to an A / -point DFT.

[0095] In one or more embodiments of the method mapping the third number, N, parallel frequency-domain transmit symbols to respective subcarriers comprises applying an interleaved mapping scheme.

[0096] In one or more embodiments of the method transforming the mapped third number, N, frequency-domain transmit symbols into the time domain comprises subjecting the symbols to an JV-point I DFT.

[0097] In accordance with a second aspect of the invention, a method of de-modulating symbols received over a wireless communication channel is presented. The method of de-modulating comprises receiving a time-domain signal carrying symbols that are modulated using the method in accordance with the first aspect of the invention, and removing the CP, yielding a prefix-less representation of the received signal. The prefix-less representation of the received signal is de-chirped in a subsequent step, yielding a signal carrying a third number, N, of transmit symbols, and the de-chirped prefix-less representation of the received signal is converted into a number of parallel segments, the totality of which representing the de-chirped prefix-less received signal. The parallel segments are transformed from the time domain into the frequency domain. A symbol detection is performed on the parallel segments in the frequency-domain, which carry representations of the transmitted symbols, yielding a representation of the third number, N, of transmitted symbols in the frequency domain. Symbols that are detected on transmitter-assigned subbands are re-mapped to the specified carriers. Symbols detected on non-assigned subbands may be discarded. The re-mapped symbols are transformed into the time domain, yielding a first number (A / ) of parallel received symbols in the time domain, which are converted into a serial stream of received data symbols in the time domain that are output for further processing. The first number (A / ) of parallel received symbols corresponds to the third number, N, of transmitted symbols minus the discarded symbols.

[0098] In one or more embodiments of the method in accordance with the second aspect of the invention transforming the parallel segments from the time domain into the frequency-domain comprises subjecting the parallel time-domain signals to an N- point fast Fourier transform.

[0099] In one or more embodiments of the method in accordance with the second aspect of the invention performing the symbol detection further comprises performing a channel estimation.

[0100] In one or more embodiments of the method in accordance with the second aspect of the invention performing the symbol detection comprises applying an equalisation.

[0101] In one or more embodiments of the method in accordance with the second aspect of the invention transforming the re-mapped symbols into the time domain comprises applying an inverse M- point discrete Fourier transform on the transmitter-assigned subbands and the symbols mapped thereon. In accordance with a third aspect of the invention, a transmitter implementing the method presented in the first aspect of the invention is presented. The transmitter comprises an antenna and circuitry for processing radio frequency signals, e.g., oscillators, mixers, amplifiers, filters and the like. The transmitter further comprises one or more microprocessors as well as volatile and non-volatile memory. The aforementioned elements and components are connected via one or more data and / or signal lines or buses. The non-volatile memory stores computer program instructions which, when executed by the one or more microprocessors, configure components of the wireless transmitter to implement or carry out a method in accordance with the first aspect of the invention, for obtaining a modulated signal, or to receive a signal modulated in accordance with the first aspect of the invention, and to transmit the modulated signal via the circuitry for processing radio frequency signals and the antenna.

[0102] In accordance with a fourth aspect of the invention, a receiver implementing the method presented in the second aspect of the invention is presented. The receiver comprises an antenna and circuitry for processing radio frequency signals, e.g., oscillators, mixers, amplifiers, filters and the like. The receiver further comprises one or more microprocessors as well as volatile and non-volatile memory. The aforementioned elements and components are connected via one or more data and / or signal lines or buses. The non-volatile memory stores computer program instructions which, when executed by the one or more microprocessors, configure components of the wireless receiver to implement or carry out a method in accordance with the second aspect of the invention.

[0103] As will be appreciated by one skilled in the art, aspects of the embodiments may be embodied as a system, apparatus, method, or program product. Accordingly, embodiments may take the form of an entirely hardware embodiment, an entirely software-implemented embodiment, including firmware, resident software, microcode, etc., or an embodiment combining software and hardware aspects.

[0104] For example, the disclosed embodiments may be implemented as a hardware circuit comprising custom very-large-scale integration (VLSI) circuits or gate arrays, off-the- shelf semiconductors such as logic chips, transistors, or other discrete components. The disclosed embodiments may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices, or the like. As another example, the disclosed embodiments may include one or more physical or logical blocks of executable code which may, for instance, be organised as an object, procedure, or function.

[0105] The method presented hereinbefore may be represented by computer program instructions. Accordingly, in accordance with a further aspect of the invention, a computer program product comprises computer program instructions which, when executed by a microprocessor of a wireless transmitter in accordance with the third aspect of the invention, cause the microprocessor to execute the method in accordance with the first aspect of the present invention, and to accordingly control hardware and / or software blocks or modules of the wireless transmitter or, when executed by a microprocessor of a wireless receiver in accordance with the fourth aspect of the invention, cause the microprocessor to execute the method in accordance with the second aspect of the present invention, and to accordingly control hardware and / or software blocks or modules of the wireless receiver.

[0106] Computer program instructions, or code, for carrying out operations for embodiments may be any number of lines and may be written in any combination of one or more programming languages including an object- oriented programming language such as Python, Ruby, Java, Smalltalk, C++, or the like, and conventional procedural programming languages, such as the “C” programming language, or the like, and / or machine languages such as assembly languages. The code may execute entirely on the user’s computer, partly on the user’s computer, as a stand-alone software package, partly on the user’s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user’s computer through any type of network, including a local area network (LAN), wireless LAN (WLAN), or a wide area network (WAN), or the connection may be made to an external computer, for example, through the Internet using an Internet Service Provider (ISP).

[0107] The computer program instructions may be retrievably stored or transmitted on a computer-readable medium or data carrier. The medium or the data carrier may by tangibly or physically embodied, e.g., in the form of a hard disk, solid state disk, flash memory device or the like. However, the medium or the data carrier may also comprise a modulated electro-magnetic, electrical, or optical signal that is received by the computer by means of a corresponding receiver, and that is transferred to and stored in a memory of the computer.

[0108] A further aspect of the invention pertains to a wireless signal generated through execution of the method in accordance with the first aspect of the present invention.

[0109] The described features, structures, or characteristics of the embodiments may be combined in any suitable manner. In this description, numerous specific details are provided, such as examples of programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments. One skilled in the relevant art will recognize, however, that embodiments may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of an embodiment. Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment, but mean “one or more but not all embodiments” unless expressly specified otherwise. The terms “including,” “comprising,” “having,” and variations thereof mean “including but not limited to,” unless expressly specified otherwise. An enumerated listing of items does not imply that any or all of the items are mutually exclusive, unless expressly specified otherwise. The terms “a,” “an,” and “the” also refer to “one or more” unless expressly specified otherwise.

[0110] Where aspects of the embodiments are described in this specification with reference to schematic flowchart diagrams and / or schematic block diagrams of methods, apparatuses, systems, and program products according to embodiments it will be understood that each block of the schematic flowchart diagrams and / or schematic block diagrams, and combinations of blocks in the schematic flowchart diagrams and / or schematic block diagrams, can be implemented by code. This code may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart diagrams and / or block diagrams.

[0111] It should be noted that, in some implementations or embodiments, the functions noted in the exemplary embodiments shown in the figures may occur out of the order shown in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more blocks, or portions thereof, shown in the figures.

[0112] The new single-carrier DFT-chirp-s-OFDM modulation scheme presented herein, obtained by chirping DFT-s-OFDM in the time domain, maintains the low PAPR of DFT-s-OFDM that is superior over AFDM, OFDM and OTFS modulation schemes. The full band transmission and symbols retransmission enabled by chirping and DFT precoding provides enhanced noise suppression in LMMSE equalization. Further, the new DFT-chirp-s-OFDM presents higher output SNR and lower BER values than the conventional modulation schemes, including DFT-s-OFDM, AFDM, OTFS, and OFDM. In addition, the proposed waveform can achieve full frequency diversity and shows high resilience to Doppler shifts. Last but not least, the low PAPR of the chirped DFT-s-OFDM modulation presented herein provides greater resistance to clipping than multicarrier waveforms with high PAPR.

[0113] The present invention can be used in various contexts, notably in high-speed mobility communication scenarios and autonomous driving, e.g., in 6G communications and beyond.

[0114] BRIEF DESCRIPTION OF THE DRAWING In the following section the invention will be described with reference to the drawings, in which

[0115] Fig. 1 shows a schematic comparison of the core operations required for obtaining the transmit signals from the conventional modulation schemes discussed herein,

[0116] Fig. 2 shows a schematic block diagram of a DFT-chirp-s-OFDM communication system in accordance with the invention,

[0117] Fig. 3 shows the schematic comparison of the core operations required for obtaining the transmit signals from the conventional modulation schemes of figure 1 , complemented by the core operations of the method in accordance with the invention,

[0118] Fig. 4 exemplarily shows the use of the total bandwidth for conventional modulations schemes and the modulation scheme in accordance with the present invention,

[0119] Fig. 5 shows a comparison of the CCDF over the PAPR threshold for OFDM, AFDM, OTFS and DFT-based modulation schemes,

[0120] Fig. 6 shows the BER upper bounds and simulated BER of DFT-s-OFDM and chirped DFT-s-OFDM,

[0121] Fig. 7 shows the output signal power over the symbol index for the proposed chirped DFT-s-OFDM, DFT-s-OFDM, AFDM, OTFS, and OFDM,

[0122] Fig. 8 shows the output noise power over the symbol index for the proposed chirped DFT-s-OFDM, DFT-s-OFDM, AFDM, OTFS, and OFDM,

[0123] Fig. 9 shows the output SNR over the symbol index for the proposed chirped DFT- s-OFDM, DFT-s-OFDM, AFDM, OTFS, and OFDM,

[0124] Fig. 10 shows the BER over Eb / No for the proposed chirped DFT-s-OFDM, DFT-s- OFDM, AFDM, OTFS, and OFDM,

[0125] Fig. 11 shows the output SNR over Eb / No for the proposed chirped DFT-s-OFDM, DFT-s-OFDM, AFDM, OTFS, and OFDM,

[0126] Fig. 12 shows the impact of the DFT spreading factor on the BER of DFT s OFDM and the proposed chirped DFT-s-OFDM,

[0127] Fig. 13 shows impact of the DFT spreading factor on the output noise power of DFT-s-OFDM and the proposed chirped DFT-s-OFDM, Fig. 14 shows the BER values of various modulation waveforms over Eb / No under the same bandwidth efficiency without clipping,

[0128] Fig. 15 shows the BER values of various modulation waveforms over Eb / No under the same bandwidth efficiency with clipping,

[0129] Fig. 16 shows the ambiguity function of DFT-chirp-s-OFDM for an exemplary scenario,

[0130] Fig. 17 shows the ambiguity function of DFT--S-OFDM for the exemplary scenario of figure 16,

[0131] Fig. 18 shows an exemplary block diagram of a transmitter or a receiver, respectively, in accordance with the third or fourth aspects of the present invention,

[0132] Fig. 19 shows an exemplary flow diagram of a method of modulating symbols representing binary data for transmission over a wireless communication channel in accordance with the first aspect of the invention, and

[0133] Fig. 20 shows an exemplary flow diagram of a method of de-modulating symbols received over a wireless communication channel in accordance with the second aspect of the present invention.

[0134] In the figures identical or similar elements may be referenced using the same reference designators.

[0135] DETAILED DESCRIPTION OF EMBODIMENTS

[0136] Figures 1 to 17 have been described further above and will not be discussed again.

[0137] Figure 18 shows an exemplary block diagram of a transmitter 500 or a receiver 600 configured for carrying out the method in accordance with the first or the second aspect of the invention, respectively. The transmitter 500 or the receiver 600 comprises at least one antenna 580 or 610, respectively, as well as circuitry 501 for processing radio frequency signals, one or more microprocessors 502, volatile memory 503 and non-volatile memory 504. The aforementioned components or elements are connected via one or more data and / or signal lines or buses 505. The non-volatile memory 504 stores computer program instructions which, when executed by the one or more microprocessors 502, configure components of the transmitter 500 to implement or carry out the method in accordance with the first aspect of the invention, or configure components of the receiver 600 to implement or carry out the method in accordance with the second aspect of the invention, respectively.

[0138] Figure 19 shows an exemplary flow diagram of a method 100 of modulating symbols representing binary data for transmission over a wireless communication channel in accordance with the first aspect of the invention. After receiving a serial data sequence of data symbols in the time domain in step 105, the serial sequence is transformed into the frequency domain in step 110 and converted into a first number of A / parallel data symbols in step 120. In step 130 the first number of A7 parallel data symbols is padded with a second number N- -M of symbols, yielding a third number of A' of parallel frequency-domain symbols. The third number of N parallel frequencydomain symbols is mapped to respective subcarriers in step 140. Next, the mapped third number N of parallel frequency-domain symbols is transformed into the time domain in step 150 and converted into a serial time-domain signal of a first length NTSin step 160. The serial time-domain signal is chirped in step 170 before a CP is added in step 180. The so-modulated signal is output in step 190.

[0139] Figure 20 shows an exemplary flow diagram of a method 200 of de-modulating symbols received over a wireless communication channel in accordance with the second aspect of the present invention. After receiving a time-domain signal carrying symbols that are modulated in accordance with the method 100 discussed with reference to figure 10 in step 210, any CP is removed that may be present in the received time-domain signal is removed in step 220, yielding a prefix-less representation of the received signal. In step 230 the prefix-less representation of the received signal is de-chirped before it is converted into a third number of N parallel representations of received symbols in the frequency-domain in step 240. In step 250 the third number of N parallel representations of received symbols in the frequencydomain is transformed into the frequency domain, and a symbol detection is performed on the parallel signals in step 260. The symbol detection may comprise a channel estimation (not shown in the figure) and yields the transmitted frequencydomain symbols. In step 270 symbols detected on transmitter-assigned subbands are re-mapped to the specified carriers, and the resulting parallel signals are converted from the frequency domain into corresponding parallel signals in the time domain in step 280. The parallel signals in the time domain are then transformed into a serial signal in step 290 before the demodulated signal is output in step 295.

[0140] LIST OF REFERENCE NUMERALS (PART OF THE DESCRIPTION)

[0141] 100 method 500 transmitter

[0142] 105 receive serial sequence of data 501 RF circuitry symbols 502 microprocessor(s)

[0143] 110 t -^ / domain conversion 30 503 volatile memory

[0144] 120 S2P conversion 504 non-volatile memory

[0145] 130 padding 505 data / signal line(s) / bus(es)

[0146] 140 subcarrier mapping 510 S2P conversion

[0147] 150 f^> t domain conversion 520 t -^ / domain conversion

[0148] 160 P2S conversion 35 530 padding I subcarrier mapping

[0149] 170 chirping 540 domain conversion

[0150] 180 CP insertion 550 P2S conversion

[0151] 190 output modulated signal 560 chirping

[0152] 570 CP insertion

[0153] 200 method 40 580 antenna

[0154] 210 receive time-domain signal

[0155] 220 remove CP 600 receiver

[0156] 230 de-chirping 610 antenna

[0157] 240 S2P conversion 620 CP removal

[0158] 250 t -^ / domain conversion 45 630 de-chirping

[0159] 260 symbol detection 640 S2P conversion

[0160] 270 subcarrier re-mapping 650 t -^ / domain conversion

[0161] 280 f^> t domain conversion 660 symbol detection

[0162] 290 P2S conversion 670 subcarrier re-mapping

[0163] 295 output demodulated signal 50 680 t domain conversion

[0164] 690 P2S conversion

Claims

CLAIMS1. A method (100) of modulating data symbols representing binary data for transmission over a wireless communication channel, comprising:- converting (110) a serial sequence comprising a first number (M) of data symbols into a first number (M) of parallel data symbols,- transforming (120) the first number (M) of parallel data symbols from the time domain into the frequency domain,- padding (130) the first number (M) of parallel data symbols in the frequency domain with a second number (N-M) of padding symbols, yielding a third number (JV) of parallel frequency-domain transmit symbols,- mapping (140) the third number (JV) of parallel frequency-domain transmit symbols to respective subcarriers,- transforming (150) the mapped third number (JV) of parallel frequency-domain transmit symbols into the time domain,- converting (160) the third number (JV) of parallel time-domain transmit symbols into a serial time-domain signal of a first length,- chirping (170) the serial time-domain signal of the first length with a chirping signal of a corresponding length,- adding (180) a cyclic prefix to the chirped signal, and- outputting (190) the modulated signal for transmission.

2. The method (100) of claim 1 , wherein transforming (120) the first number (M) of parallel data symbols from the time domain into the frequency domain comprises subjecting the symbols to an AT- point discrete Fourier transform (DFT).

3. The method (100) of claim 1 or 2, wherein padding comprises zero-padding.

4. The method (100) of any one of the preceding claims, wherein mapping (140) the third number (JV) of parallel frequency-domain transmit symbols to respective subcarriers comprises applying an interleaved mapping scheme.

5. The method (100) of any one of the preceding claims, wherein transforming (150) the mapped third number (JV) of frequency-domain transmit symbols into the time domain comprises subjecting the symbols to an JV-point inverse discrete Fourier transform (IDFT).

6. A method (200) of de-modulating symbols received over a wireless communication channel, comprising:- receiving (210) a time-domain signal carrying symbols that are modulated in accordance with the method (100) of one or more of claims 1 to 5,- removing (220) any cyclic prefix that may be present in the received timedomain signal, yielding a prefix-less representation of the received signal,- de-chirping (230) the prefix-less representation of the received signal, yielding a signal carrying a third number (JV) of transmit symbols,- converting (240) the de-chirped prefix-less representation of the received signal into a number of parallel segments, the totality of which representing the de-chirped prefix-less received signal,- transforming (250) the parallel segments from the time domain into the frequency domain,- performing (260) a symbol detection on the parallel segments in the frequency-domain, yielding a representation of the third number (JV) of transmitted symbols in the frequency-domain,- re-mapping (270) symbols detected on transmitter-assigned subbands to corresponding carriers,- transforming (280) the re-mapped symbols into the time domain, yielding a first number (AT) of parallel received symbols in the time domain,- converting (290) the first number (M) of parallel received symbols in the time domain into a serial stream of data symbols in the time domain, and- outputting (295) the serial stream of data symbols in the time domain.

7. The method (200) of claim 6, wherein transforming (250) the parallel segments from the time domain into the frequency-domain comprises subjecting the parallel time-domain signals to an JV-point fast Fourier transform.

8. The method (200) of claim 6 or 7, wherein performing (260) the symbol detection further comprises performing a channel estimation.

9. The method (200) of one or more of claims 6 to 8, wherein performing (250) the symbol detection comprises applying an equalisation, including a maximum likelihood (ML) equalisation or a minimum mean squared error (MMSE) equaliser.10 The method (200) of one or more of claims 6 to 9, wherein transforming (280) the re-mapped symbols into the time domain comprises applying an inverse AT- point discrete Fourier transform on the transmitter-assigned subbands and the symbols mapped thereon.

11. A transmitter (500) comprising an antenna (502), circuitry (504) for processing radio frequency signals, one or more microprocessors (506), volatile (508) and non-volatile memory (510), connected via one or more data and / or signal lines or buses (512), wherein the non-volatile memory (510) stores computer program instructions which, when executed by the one or more microprocessors (506), configure components of the wireless transmitter (500) to implement or carry out a method in accordance with one or more of claims 1 to 5 for obtaining a modulated signal, or to receive a signal modulated in accordance with one or more of claims 1 to 5, and to transmit the modulated signal via the circuitry (504) for processing radio frequency signals and the antenna (502).

12. A receiver (600) comprising an antenna (502), circuitry (504) for processing radio frequency signals, one or more microprocessors (506), volatile (508) and non-volatile memory (510), connected via one or more data and / or signal lines or buses (512), wherein the non-volatile memory (510) stores computer program instructions which, when executed by the one or more microprocessors (506), configure components of the wireless receiver (600) to implement or carry out a method in accordance with one or more of claims 6 to10.

13. Computer program product comprising computer program instructions which,- when executed by a microprocessor of a wireless transmitter (500) according to claim 11 , cause the wireless transmitter (500) and / or control hardware blocks, modules or components of the wireless transmitter (500), respectively, to implement or carry out the method of one or more of claims 1 to 5, or- when executed by a microprocessor of a wireless receiver (600) according to claim 12, cause the wireless receiver (600) and / or control hardware blocks, modules or components of the wireless receiver (600), respectively, to implement or carry out the method of one or more of claims 6 to 10.

14. Computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 1315. Wireless communication signal carrying modulated symbols representing binary data, characterised in that the signal is generated using the method of one or more of claims 1 to 5.

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