Method of decoding symbols transmitted via spatial modulation and apparatus implementing the method

Abstract

A method of decoding information coded in respective activation patterns of activated antenna subsets of a MIMO transmitter transmitting quadrature-modulated signals comprises decoupling real and imaginary parts of the signal components of the received signal vector, receiving, determining or estimating respective channel matrices for the real and imaginary channels, and representing the respective real and imaginary signal components as respective products of a transmitted symbol component and an activation unit vector. The respective activation unit vectors of the decoupled real and imaginary parts are then represented by corresponding random variable vectors dependent on a probability mass function of the activation patterns available at the transmitter. A Gaussian belief propagation-based message passing process is applied on the random variables, for jointly estimating the activation unit vectors for the respective real and imaginary parts of the received signal vector, which are finally decoded for retrieving the information.

Description

[0001] METHOD OF DECODING SYMBOLS TRANSMITTED VIA SPATIAL MODULATION AND APPARATUS IMPLEMENTING THE METHOD

[0002] FIELD OF THE INVENTION

[0003] The present invention relates wireless communication via spatial modulation (SM), in particular to a method of decoding information transmitted via SM, and targets to enable or facilitate integrated sensing and communications (ISAC), also referred to as joint communication and sensing (JCAS) or joint radar and communication (JRC), where wireless signals are simultaneously used for communication and environment perception, i.e. , generating information about the environment and objects therein.

[0004] NOTATIONS

[0005] Throughout this specification, bold symbols represent vectors or matrices. Scalar values are denoted herein by lowercase letters in italics, as in x. SuperscriptsTandH, respectively denote the transpose and complex conjugate transpose of a vector or matrix.

[0006] BACKGROUND

[0007] Integrated sensing and communications (ISAC) has recently been recognised as a new key technology for beyond fifth generation (B5G) and sixth generation (6G) wireless communications systems. While ISAC is expected to enable new applications, the fundamental trade-off between sensing and communication functionalities is also certain to put pressure on the equally important objective of curbing the power consumption of B5G and 6G systems. In fact, B5G and 6G systems are required to significantly improve over existing systems not only in terms of energy and spectral efficiencies, but also on data throughput, reliability, latency, coverage, and user capacity, motivating the investigation of novel technologies such as millimetre-wave (mmWave) / Terahertz (THz) communications, massive multiple- input multiple-output (mMIMO) and cell-free MIMO (CF-MIMO), reconfigurable intelligent surfaces (RISs), and index modulation (IM).

[0008] In IM, which is a special case of SM, a transmitter with multiple transmit antennas activates only a subset out of the available antennas for each transmission instance for transmitting information symbols and beamforming. To compensate for the loss in information due to a lower number of transmitted symbols, information is also encoded in the selection pattern of the respectively activated transmit antennas. If the decoder can determine which antennas are activated, the corresponding information can be decoded.

[0009] Among the alternatives mentioned above, IM is attractive for future wireless communication systems since the frugal utilization of resources at the transmitter and the encoding of information in the respective activated subsets of the totally available resources enables high-efficiency operation while at the same time exploiting the information that is combinatorially encoded "energy-less" or “energy-free" in the resource activation patterns to achieve high spectral-efficiency. The sparse utilization of radio frequency (RF) chains enabled by IM is highly appealing to millimetre-wave (mmWave) and Terahertz (THz) systems, in particular for reducing the required total transmit energy. The characteristic of IM also lends great flexibility since the symbols actually transmitted are not directly relevant to the antenna subset activation scheme itself, making it transparent to other promising technologies, as demonstrated by a quickly expanding literature on the integration of IM in connection with mMIMO, CFMIMO, RISs and ISAC.

[0010] Generally, an IM scheme activating P selected patterns for transmitting out of a total of 2V resource allocation patterns can convey up to [log2additional information bits on top of those conveyed over the selected P resources themselves. Therefore, even with sufficiently large N and an adequate P, very large amounts of information can be encoded in the pattern or index domain, such that IM has shown the potential to outperform fully dense, i.e. , P = N, systems in certain scenarios, with the added bonus of improving the energy- and spectral efficiency, freeing the unused resources to other functionalities, such as opportunistic communications and radar / sensing, etc.

[0011] Figure 1 shows a simplified schematic representation of IM. Among the multiple antennas, at each transmit instance, respectively delimited by the dashed vertical lines distributed across the time domain, only a subset of antennas is used for transmitting, each of the subsets being unique and thus carrying information in itself. Within IM beamforming is still possible by appropriately controlling the phase and amplitude of the analogue transmit signals transmitted by each antenna, and / or appropriate precoding.

[0012] Motivated by the advantages of IM, a rapid development of enhanced SM designs aiming to maximise energy and spectral-efficiencies, and minimise error rates and decoding complexities can be found in recent literature. An excellent example is the quadrature spatial modulation (QSM) scheme found in in "Quadrature spatial modulation," IEEE Trans. Veh. Technol., vol. 64, no. 6, pp. 2738-2742, Jun. 2015, by R. Mesleh, S. S. Ikki, and H. M. Aggoune, in which the SM technique is applied independently to each in-phase and quadrature (IQ) component of the transmit symbols, such that P real-parts and P imaginary-parts of the symbols are independently transmitted from the corresponding selected P transmit antennas from a total of NTtransmit antennas. The total number of antenna pattern combinations in QSM can be expressed by the combinatorics binomial coefficient. QSM results not only in a two-fold increase in the rate of the spatially-modulated information, but also in improved bit error rate (BER) performance compared to the original SM scheme discussed by R. Y. Mesleh, H. Haas, S. Sinanovic, C. W. Ahn, and S. Yun, in "Spatial modulation," IEEE Trans. Veh. Technol., vol. 57, no. 4, pp. 2228-2241 , Jul. 2008. In addition to virtually doubling the codebook size and hence the spectral efficiency in the spatial domain, QSM is also well suited for use in ISAC applications, since the actual transmit symbols need not all be used for carrying information, leaving some or even all symbols for configuration exclusively for sensing purposes, e.g., using them as pilot signals whose properties are known at the receiver.

[0013] Further examples in this line of work are the improved generalised quadrature spatial modulation (GQSM) designs incorporating space-time coding (STC) and other techniques to optimise the antenna activation patterns, e.g., as discussed in “Spacetime block coded spatial modulation," IEEE Transactions on Communications, vol. 59, no. 3, pp. 823-832, 2011 , by . Ba§ar, U. Aygdlu, E. Panayirci, and H. V. Poor, and in "Scalable quadrature spatial modulation," IEEE Trans, on Wireless Commun., vol. 21 , no. 11 , pp. 9293-9311 , 2022, by H. S. Rou, G. T. F. Abreu, H. limori, D. Gonzalez G., and O. Gonsa. To summarise, (G)QSM schemes achieve high bit error rate (BER)-performance as well as high energy- and spectral- efficiencies by modulating information both in transmitted symbols and in coded combinatorial activations of subsets of multiple transmit antennas, exceeding the performance of conventional SM methods on all parameters.

[0014] The price of the aforementioned advantages of IM, and of SM in general, is, however, the burden cast onto the receiver in terms of the computational complexity required to detect the activated resources at each given transmission instance, given all possible resource activation patterns in the codebook of size

[0015] Naive decoding of GQSM requires searching over a combinatorial space of size

[0016] ■ Mp, where NTis the number of transmit antennas, a is the codebook amplification factor (a = 1 for the classic GQSM), P is the number of symbols transmitted, and M is the size of the complex symbol constellation. Due to the nature of the binomial coefficient scaling factorially, as NTand P grows in the regime of B5G mMIMO systems with _ZVr>16, the number of total combinations grows super- exponentially in QSM systems. In other words, the codebook size becomes extremely large for massive MIMO scenarios with a large number NTof transmit antennas and with high data rate with large P.

[0017] This challenge has therefore motivated work on low-complexity decoders for IM, in its many variations. On the other hand, as the number of transmit antennas increases, the amount of information that can be encoded in the “spatial domain”, i.e. , in the antenna activation patterns, significantly increases in comparison to the information that can be encoded in the digital symbol constellation domain. This suggests that the transmit information may ultimately solely be encoded in the antenna domain, while the transmit symbols themselves can be fixed pilot symbols or specific waveforms for other functionalities, such as radar and sensing.

[0018] This means that the detector needs only to detect the antenna patterns, in hand of the known transmitted symbols. However, this still poses a hard problem for the decoder, since the knowledge of symbols only reduces the search space in the relatively smaller digital domain, but not on the true problematic antenna combinatoric domain. For larger antenna array sizes this turns out to be infeasible using conventional maximum likelihood (ML) decoding methods.

[0019] To cite some examples, improvements over the brute-force ML approach detection methods based on reduced-search methods such as lattice and sphere decoders, as discussed by I. Al-Nahhal, E. Basar, 0. A. Dobre, and S. Ikki, in "Optimum Low- Complexity Decoder for Spatial Modulation," IEEE Journal on Selected Areas in Communications, vol. 37, no. 9, pp. 2001-2013, 2019, by Z. Hu, F. Chen, Y. Liu, S. Liu, H. Yu, and F. Ji, in "Low-Complexity Detection for Multiple-Mode OFDM with Index Modulation," Physical Communication, vol. 34, pp. 38-47, 2019 or by

[0020] M. Simarro et al., in "Low Complexity Near-ML Sphere Decoding based on a MMSE ordering for Generalized Spatial Modulation," IEEE 31st Annual International Symposium on Personal, Indoor and Mobile Radio Communications, 2020, pp. 1-6, are able to decrease the total decoding complexity in proportion to the total codebook size, but their cost are still dependent on the combinatorial factor.

[0021] More recently, methods aiming to directly reduce the order of the binomial coefficient have also been proposed. For instance, in "The achievable rate analysis of generalized quadrature spatial modulation and a pair of low-complexity detectors," IEEE Trans, on Veh. Technol., vol. 71 , no. 5, pp. 5203-5215, 2022, J. An, C. Xu,

[0022] Y. Liu, L. Gan, and L. Hanzo, achieve a reduction of the complexity order from to < a < 1, by leveraging the orthogonal matching pursuit (OMP) algorithm to operate over the probable non-zero indices of the sparse signal of the generalised quadrature spatial modulation (GQSM), of which IM is a specific type. It was shown thereby that a trade-off between computational complexity and optimal performance can be achieved by adjusting the value of a.

[0023] In "An efficient vector-valued belief propagation decoder for quadrature spatial modulation," 2022 56th Asilomar Conference on Signals, Systems, and Computers, 2022, pp. 27-31 , H. S. Rou, G. T. F. de Abreu, and T. Takahashi proposed a GQSM detector leveraging the message passing (MP) algorithm with vector-valued variables under the Gaussian belief propagation (GaBP) framework, which was shown to eliminate the quadratic exponent in the combinatorial factor by employing a novel decomposition of the GQSM signal into two independent vectors. This reduces the

[0024] 1 decoding cost to the order of the square root of the binomial coefficient, while approaching the performance of a ML solution with fixed complexity gain of a quadratic order.

[0025] Finally, non-classical approaches also exist that are independent of the binomial coefficient, including techniques based on machine learning and quantum computing. Such alternatives have, nevertheless, their own limitations, such as the need for exhaustive offline training or expensive and not widely-available quantum computers, respectively.

[0026] Still, the complexity of all known detectors is dependent on the parameters of the combinatorial space, i.e., from the factorial relationship between the number of P activatable patterns out of a total of 2V resources.

[0027] It is, therefore, desirable to provide an improved method of decoding symbols in spatial index modulated wireless transmissions that provides a low complexity while maximising the spectral and energy efficiency, and that permits optimising both the communication and sensing performance in ISAC applications.

[0028] SUMMARY OF THE INVENTION

[0029] This object is attained by the method of claim 1 , the apparatus of claim 4. A communication system, a vehicle equipped with an apparatus in accordance with the invention, a computer program product and a corresponding computer-readable medium are provided in claims 7 to 11 , respectively. Advantageous embodiments and developments are provided in respective dependent claims.

[0030] A particular object of the present invention lies in addressing ISAC through SM in large scale systems, e.g., B5G massive MIMO. Embodiments of the present invention exploit piloted SM signals which, at the targeted large-scale systems, cannot be handled by known receivers due to the enormous computational complexity. A novel decoding method presented herein enjoys a complexity order that is independent of the combinatorial factor.

[0031] As mentioned above, many IM techniques can be found in the literature which address various issues such as the integration with other functionalities, e.g., radar and / or sensing, achievable data rates, decoding complexity and, of course, which resource domains to exploit and under which architecture. Without loss of generality, in this specification the GQSM approach is exemplarily considered, and its system and signal models will be leveraged in the following derivation and analysis.

[0032] Prior to describing the invention in greater detail the underlying GQSM system model and transmitter structure will be discussed.

[0033] Consider a point-to-point (P2P) MIMO wireless communications system where the transmitter and the receiver are equipped with NTand NRantennas, respectively, such that the received signal vector y e (CWRX1corresponding to the transmission of the information vector x e CWTX1through the flat-fading MIMO channel H e £NRXNT jsdescribed by where is a complex-valued additive white Gaussian noise (AWGN) vector with element-wise variance No, such that

[0034] In a GSQM transmitter, the in-phase and quadrature (IQ) components of P transmit symbols p p ptaken from a complex- valued constellation are sparsely mapped into the respective transmit vector componentsoftheform yielding the transmit signal vector

[0035] Note that the superscripts R and I, respectively, denote the real and imaginary counterparts of the corresponding parameters in a general spatial modulation (GSM) signal model, and the superscript c in equations represents either of the real and imaginary part whenever the two are treated identically in the equation. Further note that the classic quadrature spatial modulation (QSM) is a particular case of GQSM with P = 1.

[0036] The real and imaginary parts of the transmit symbols are independent, i.e., they can be transmitted from different antennas in (G)QSM. Consequently, the positions of the IQ vector components in equation (2) are described by two independent index vectors kR= from the set of possible index vectors K of size 0 = |K|. Specifically, 0 = 21M7)] implies that only binary- encodable subsets of the possible activation pattern combinations are utilised, such that the size of the GQSM IQ activation vectors codebook A is given by | A| = 0. Note also that the position of a symbol component in the vector corresponds directly to the activated antenna element at the transmitter.

[0037] By exploiting the possible combinatorial patterns of the symbol component positions, the GQSM scheme conveys information not only from the encoding of P symbols from S, but also from the selection of P positions out of NTpossible positions, respectively for both xRand x1.

[0038] In light of the above, the total information conveyed by the GQSM signal x is given by where BSpis the number of bits spatially encoded by the antenna position selection of P symbol parts, and BDgis the number of bits digitally encoded by the transmit symbols. In the following a codebook Example is given. For the sake of clarity, a small system with NT= 5, P = 3 is considered, such that a total of (^) = 10 activation vectors are

[0039] A valid codebook for such a system is a subset A of the above, containing which can be also represented by a corresponding set of index vectors, each of which contains the indices of the non-zero elements in the corresponding activation vector a„, that is

[0040] It can be understood that obtaining a given codebook A out of the larger set of possible activation vectors is a subject of optimization, and has been addressed, for instance, under a channel diversity criterion in "Scalable Quadrature Spatial Modulation" (ibid.), and under a decoding complexity criterion via QC by N. Ishikawa, in "Quantum Speedup for Index Modulation," IEEE Access, vol. 9, pp. 111114- 111124,2021.

[0041] In view of the formulation of GQSM transmit signals described in equation (2), the received signal model in equation (1 ) can be rewritten in the IQ-decoupled form as where y denote the IQ-decoupled counterparts of y,x, and w, respectively, and the IQ-decoupled channel matrix H e ]&2NRX2NT isfurther decomposed into two submatrices as with HRe ]R2WRXWT and Hle ]R2WRXWT denoting the effective channel components for xRand x1, respectively.

[0042] The real domain IQ-decoupled form y = Hx + iv presented in equation (5) is the basis of most known QSM / GQSM detection algorithms, which generally seek to estimate the effective transmit signal x, in knowledge of y and H, i.e. , seek to solve the recovery problem

[0043] XML = argmin || y - Hx \\j (7) where E is the discrete domain of the effective signal x, of cardinality

[0044] While the linear recovery problem appears trivial, the challenge lies in the infeasible size of the discrete domain with cardinality Q where is the flooring operation to the nearest power of 2.

[0045] As can been seen from the latter expression, the codebook size Q scales at a geometric rate on P, and at a squared factorial rate on NT, such that complexity becomes prohibitive even for moderately large MIMO scenarios, which is why simulation results in the known literature exist only up to NT≤ 10, P ≤ 3, even with lowest-complexity methods. The problem described by equation (7) is NP-hard due to the discrete solution domain E, which prevents classical convex optimization approaches, requiring instead a combinatorial search over a high-dimensional space for optimal solution. To circumvent this challenge, conventional low-complexity solutions leveraging various characteristics of the GQSM signal have been proposed. For example, the inherent sparsity of x can be exploited by compressive sensing (CS)-based methods, and the discrete codebook structure can be utilised to design search-based methods such as sphere decoders and pruned-search decoders. Further, a vector-valued MP method was recently proposed by H. S. Rou et al., in "An Efficient Vector-valued Belief Propagation Decoder for Quadrature Spatial Modulation" (ibid.), where the two variables xRand x1are concurrently estimated by leveraging the independent and identically distributed (i.i.d.) bivariate property of the decoupled vectors in equation (6). The bivariate vector-valued MP method in "An Efficient Vector-valued Belief Propagation Decoder for Quadrature Spatial Modulation" (ibid.) was shown to reduce the search space from

[0046] Building on the above, the present invention proposes a novel low-complexity decoder, which leverages a new unit vector decomposition (UVD)-based GQSM system model integrated into the GaBP framework, which achieves a remarkably low decoding complexity order that is entirely independent of the combinatorial factor (w / ).

[0047] In the following description a piloted GQSM scenario is considered, where some or all symbol component values are known at the receiver. The pilot symbols are assumed to be arbitrary and can be utilised for other functionalities such as authentication, radar, channel estimation, etc. However, even with the known pilot symbols, the challenge remains in estimating the unknown indices of the symbols in the combinatorial space, as seen in equation (2).

[0048] Exploiting the fact that each IQ symbol component occupies only a single position in the GQSM transmit vector x described in equation (2), i.e., is only transmitted from a single antenna element, the transmit signal can be rewritten as a superposition of the symbol components multiplied by elementary activation vectors et, yielding where the activation vector ete {0,1}WT, with t E T = {1, — ,NT}, is the t-th column of an NTx NTidentity matrix which defines the set 8 of orthonormal unit vectors on {0,1}WTas

[0049] In light of the reformulation in equation (8), the IQ-decoupled received signal vector in equation (5) becomes where the linear recovery of x has been transformed into the joint estimation problem of 2P activation (unit) vectors. The reformulation in equation (9) better highlights the construct of the GQSM signals with inherently independent spatial and digital encoding.

[0050] Figures 2 and 3 show factor graphs of the prior art GQSM systems based on the non-decoupled univariate model of equation (5) and of the fully-decoupled 2P- multivariate UVD model of a GSQM system as presented in equation (9), respectively, illustrating the difference between the conventional solutions and the solution proposed herein.

[0051] In light of the above, the random vector variable a is introduced to model the unit vectors, where the discrete uniform prior probability mass function (PMF) is given by where a denotes an instance of a, A = is the event set of a, and <?(•) denotes the unit impulse function where <5(x) = 1 if |x|0= 0, and <5(x) = 0 otherwise.

[0052] Since the 2P vector variables are instances of the variable a, the estimation problem is rewritten into the UVD form as where the random variables a?, ••• , a£ respectively model the unit vectors ekR, ••• , ekR and likewise for a(, which has been illustrated as a factor graph in figure 3.

[0053] Using the above, purpose-fit vector-valued MP rules operating on the factor graph of figure 3 can be derived, based on the well-known Gaussian belief propagation (GaBP) framework. This enables the joint estimation of the 2P activation vector variables (unit vectors) entirely within their respective signal domains of size NTeach.

[0054] First, the soft-replica vectors for the activation vector variables a£ and a^ for p e {1, •••, / ’} are defined as a£.nand ap.n, respectively, for the n-th factor node with n e {1, — ,2NR}. The corresponding expected error covariance matrix of the soft- replica ap.nis defined as In the following the derivations are provided only for the real components, i.e. , for aRas the expressions for the respective imaginary components are identical, except for the change of superscripts (-)Rto (-)1and vice-versa.

[0055] In hand of the soft-replicas, the factor nodes perform soft-interference cancellation (IC) on the received signals ynas where hRTe UVXWT e UVXWTrespectively denote the n-th rows of the channel components HRe ]R2WTXNT E^2NTXNT whjCh are defined from H [HR,H1].

[0056] The sum of the latter error terms and AWGN term wn, excluding the true symbol part, is approximated as a Gaussian scalar via the central limit theorem (CLT), which yield the conditional probability density functions (PDFs) of the soft-IC symbols with respect to a given activation vector aRas where the conditional variance vRnis obtained by Then, each variable node aggregates the conditional PDFs from the connected factor nodes to compute the extrinsic belief b^.nwith self-interference cancellation, following where jjRnand ARnare the information vector and the precision matrix of the extrinsic belief b*n, given by

[0057] In turn, the posterior Bayes-optimal soft-replicas are computed from the extrinsic beliefs via while the corresponding error covariance matrix is given by

[0058] Equations (13)-(19) describe the steps of one MP iteration to estimate the 2P activation vectors of the GQSM reformulated as equation (11 ), which yields the refined posterior soft-replica vectors and the corresponding error covariance matrices. In addition, at the end of such r-th MP iteration, the soft-replica vectors and the error covariance matrices are updated with damping to prevent a premature convergence to a local optimum, following where p e [0,1] is the damping factor, and T is the iteration number.

[0059] Next, to obtain the hard-decisions on the 2P activation vectors a, the information is aggregated between all 2NRfactor nodes to compute the consensus beliefs, i.e. , equation (14) without the self-interference cancellation, which yields the extrinsic consensus PDFs of the belief bR.

[0060] Finally, the optimal activation vector estimate is selected by evaluating the PDFs for the NTvalid states of a e A, i.e. , aeA

[0061] The proposed method of decoding via a novel UVD-GaBP decoder for piloted GQSM, described by equations (12)-(20), is summarised below. The reference numbers refer to the flow diagram shown in figure 4.

[0062] Inputs to the method 100 are the received signal y, the effective channels HRand H\ pilot symbols sRand spfor all p, and the noise variance No. The corresponding outputs are the estimated activation vectors and aj, for all p.

[0063] After receiving the aforementioned inputs in step 110, the soft-replicas of the activation vectors a£.nand ap.nare initialised, for all n and p, in step 120. In step 130 the corresponding error covariance matrices TRnand Tp.nare calculated via equation

[0064] (12). In the subsequent loop MP iterations for all n and p are carried out for both real and imaginary components until a termination criterion is met, e.g., until a predetermined number rmaxof iterations has been carried out or until a desired convergence of the soft-replicas is reached, whichever criterion is met first. In step 140 of the iterative loop, a soft-IC is carried out on the received signals via equation

[0065] (13). In step 150 the conditional variances vRnand v^.nare computed via equation (15), and in step 160 the information vectors rjR.nand i]p.n, as well as the precision matrices ARnand Axp.n, of the extrinsic belief bRnare computed via equation (17). Next, in step 170, the posterior Bayes-optimal soft-replicas aR,nand ap.nare computed from the extrinsic beliefs via equation (18), and in step 180 the corresponding error covariance matrices rp\ and T^.nare computed via equation (19). Then, in step 190, the Bayes-optimal soft-replicas aR,nand ap.nare updated via damping. Step 200 checks if a termination criterion is met. In the negative case, “no”- branch of step 200, the next iteration is carried out using the results obtained in step 190 as input to step 140. In the positive case, “yes”-branch of step 200, the iteration loop is terminated and the optimal activation vector estimates and a?1is selected, in step 210, by evaluating the PDFs for the NTvalid states of a e A as per equation (20). Finally, the selected optimal activation vector estimates and a? are available for outputting in step 220, e.g., to an overarching method 10 invoking the method 100.

[0066] Figure 5 depicts a further illustration of the method in a self-explaining block-flow- type diagram.

[0067] Simulations illustrate the performance of the proposed method. Figure 6 shows GQSM simulation results for mMIMO systems with NT= 16 and 32, and varying values of P, where the performance is evaluated in terms of the BER against the SNR per bit Eb / N0. Fixed MP parametrization have been used for all scenarios, with damping factor p = 0.5 and max. number of MP iterations T = 100. The proposed method is referenced “Prop.” in the figure.

[0068] Since the computational complexity of the brute-force ML and other conventional decoders are prohibitive in the considered system scales, a Genie-aided matched filter bound (MFB), e.g., as discussed by T. Takahashi, S. Ibi, and S. Sampei, in "Design of adaptively scaled belief in multi-dimensional signal detection for higher- order modulation," IEEE Trans. Commun., vol. 67, no. 3, pp. 1986-2001 , 20192019, is introduced instead as an absolute performance bound, which is obtained by providing the UVD-GaBP method with perfect prior knowledge of the activation vectors and pilot symbols.

[0069] The simulations demonstrate the efficient demodulation capability of the proposed UVD-GaBP decoder for high-rate GQSM signals in unprecedented 16 x 16 and 32 x 32 mMIMO setups, even with the affordable computational power of an average personal computer. It can be observed that optimal performance is achieved by the UVD-GaBP for P = 1 in both scenarios, and a slight performance loss of about 1 ~ 2 dB and an error-floor is exhibited at high Eb / N0, for increasing P > 1. Note the extremely low Eb / N0ranges of the GQSM, which benefits from the fact that most information is encoded without using any transmission power, corroborating the original motivation of enabling energy- and spectral-efficient mMIMO. However, notice that the negative effect in both the BER performance and the error-floor is reduced in the larger system with NT= 32, which benefits from the increased sparsity in the system and the consequently increased orthogonality in the unit vector random variables.

[0070] The proposed method exhibits a low complexity, as will be discussed in the following. Table I compares the decoding complexity of the proposed UVD-GaBP method against exemplary conventional methods. For fairness, the complexity of the symbol- level detection has been disregarded for the conventional methods, since a fully piloted scenario is considered.

[0071] TABLE I: Complexity orders of various GQSM decoders.

[0072] It can be seen that the conventional methods have reduced the squared- combinatorial term appearing in the brute-force ML search. Namely, the relaxed orthogonal matching pursuit-based ordered successive IC (ROMP-OSIC) decoder proposed in "The achievable rate analysis of generalized quadrature spatial modulation and a pair of low-complexity detectors" relaxes the upper index of the binomial coefficient by a factor Nvwith P < Nv< NT, whereas the IQ-decoupled GaBP decoder proposed presented in “An efficient vector-valued belief propagation decoder for quadrature spatial modulation" (ibid.) eliminates the quadratic factor on the binomial coefficient, and rmaxis the number of MP iterations. However, the conventional methods still retain the binomial coefficient which is not realistically scalable to the mMIMO system of consideration. On the other hand, the proposed UVD-GaBP decoder enjoys a significantly reduced complexity, which is completely independent of the binomial coefficient. This is due to the variables apbeing unit vectors, which results in the corresponding soft-replicas and covariance matrices reaching high sparsity at convergence, such that the practical computational complexity is further reduced with each MP iteration. The low complexity enables the decodability of GQSM schemes in significantly larger mMIMO systems than with conventional methods, as verified in the performance evaluation results.

[0073] In light of the foregoing description, in accordance with a first aspect of the present invention a method of decoding information coded in respective activation patterns of activated subsets out of a first plurality of activatable transmit antennas of a multiple- input multiple-output (MIMO) transmitter is presented. Each of the activated antennas transmits quadrature-modulated signal components of transmit symbols. The method comprises receiving the quadrature-modulated signals at a second plurality of receive antennas, represented by a received signal vector y. Further, a copy of at least a subset of the transmitted quadrature-modulated signal components, represented by a transmit signal vector x, is received. Receiving of at least the subset may comprise obtaining it from a memory. The subset of the transmitted quadrature-modulated signals may comprise pilot signals and / or signals optimised for non-communication purposes, including signals optimised for radar-like purposes. The method further comprises decoupling real and imaginary parts of the signal components of the received signal vector y, and receiving, determining or estimating respective channel matrices HRand W1for the channels of the real and imaginary parts of the signal components of the received signal vector y. In further steps the method comprises representing the respective real and imaginary signal components of the decoupled real and imaginary parts of the received signal vector y as respective products of a transmitted symbol component spand an activation unit vector et, and modelling the respective activation unit vectors etof the decoupled real and imaginary parts of the received signal vector y by corresponding random variable vectors aPdependent on a probability mass function (PMF) of the activation patterns available at the transmitter. Then, a Gaussian belief propagation (GaBP)- based message passing (MP) process is applied on the random variables aP, for jointly estimating the activation unit vectors for the respective real and imaginary parts of the received signal vector y, and the activation vector estimates output by the GaBP process is decoded for retrieving the transmitted information.

[0074] In one or more embodiments of the method the GaBP-based MP process comprises receiving the respective decoupled real and imaginary parts of the signal components of the received signal vector y, the channel matrices HRand W1for the corresponding channels of the real and imaginary parts of the signal components of the received signal vector y, the random variable vectors aPfor the decoupled real and imaginary parts of the signal components of the received signal vector y at least the subset of the transmitted quadrature-modulated signal components, represented by the transmit signal vector x for all p subsets of activated transmit antennas, , and initialising soft-replicas of the activation vectors ap.nand apx,nfor all factor nodes and all variable nodes of a factor graph modelling the system. After calculating the corresponding error covariance matrices rp\ and r^.n, an iteration loop is respectively executed for the real and imaginary part of the signal until a termination criterion is met. The iteration loop comprises, after performing a soft interference cancellation (IC) on the received signal, computing (150) the conditional variances vp.nand vp.n, the information vectors ijRnand rfp.nand the precision matrices Ap.nand Ap.nof the extrinsic belief bp.n, the posterior Bayes-optimal soft-replicas ap.nand apx.nfrom the extrinsic beliefs bRn, and the corresponding error covariance matrices rp.nand Tp.n. The computed variables are then used for updating the Bayes-optimal soft-replicas ap.nand aj,.nvia damping. A check is performed to verify if the termination criterion is met and, in the negative, the iteration loop is repeated with the previously computed values as inputs. In the positive, the optimal activation vector estimates and apxare selected and output.

[0075] The termination criterion can include, for example, a predetermined number of iterations, or a convergence of the Bayes-optimal soft-replicas ap.nand aj,.nwithin a predetermined range or below a predetermined value. Such convergence criterion can be fulfilled, e.g., when the average change between consecutive post-iteration Bayes-optimal soft-replicas ap.nand aj,.nlies below the predetermined value. In accordance with a second aspect of the present invention a wireless apparatus configured for receiving quadrature-modulated signal components of transmit symbols is presented. The wireless apparatus comprise multiple antennas, associated circuitry for processing radio frequency signals, one or more microprocessors, and associated volatile and non-volatile memory. The elements or 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 elements or components of the receiver to implement or carry out one or more embodiments of the method in accordance with the first aspect of the present invention.

[0076] In one or more embodiments the wireless apparatus is further configured for sending quadrature-modulated signals.

[0077] In one or more embodiments the circuitry for processing radio frequency signals comprises a low noise amplifier and / or a mixer configured for providing a representation of a received signal at an intermediate frequency. The mixer preferably uses a same oscillator signal as a transmitter co-located with the receiver in the wireless apparatus. The latter may enable using signals transmitted by the entity comprising the receiver, which are reflected off objects, for environment perception.

[0078] Two or more wireless apparatus according to the second aspect of the invention, when configured for transmitting quadrature-modulated signals, may form a communication system.

[0079] The receiver in accordance with the third aspect of the invention may be arranged in a vehicle.

[0080] 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, micro- code, etc., or an embodiment combining software and hardware aspects. 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.

[0081] 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 apparatus in accordance with the second aspect of the invention, cause the microprocessor to execute methods in accordance with the first aspect of the present invention, and to accordingly control hardware and / or software blocks or modules of the wireless apparatus.

[0082] 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).

[0083] 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.

[0084] 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.

[0085] 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.

[0086] 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.

[0087] The method presented above is particularly advantageous in large antenna arrays, where the binomial coefficient quickly grows with the number of antennas. Further advantageous uses of the method include ISAC / JCAS systems, which benefit from a larger number of antennas. Here, the large number of antennas whose activation pattern can be efficiently detected by the method in accordance with the present invention, can be used for transmitting radar- or sensing-optimised symbols. The method in accordance with the present invention thus combines the advantages of massive IM and ISAC techniques.

[0088] The method and apparatus proposed herein can be used with great advantage in mobile communications such as vehicle-to-everything (V2X), high-speed railway communication systems, low earth orbit (LEO) satellite communications, communications with unmanned aerial vehicles (UAV), in particular in swarm settings, massive machine-type Internet-of-Things (loT) communications, e.g., in wireless factory and other industrial settings, extra-large scale MIMO and OFDM systems, and even in underwater acoustic communications.

[0089] While the invention has been described herein using an exemplary mMIMO IM QSM system it is obvious to the skilled person having read and understood this specification that the principles and methods developed and presented above also apply to general SM-based systems, including QSM, GSM, GQSM, STC-QSM, OS-QSM.

[0090] The detailed description set forth below with reference to annexed drawings is intended as a description of various configurations and is not intended to represent the only configurations in which the concepts described herein may be practiced. The detailed description includes specific details for the purpose of providing a thorough understanding of the various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In particular, although terminology from 3GPP 5G NR may be used in this disclosure to exemplify embodiments herein, this should not be seen as limiting the scope of the invention.

[0091] BRIEF DESCRIPTION OF THE DRAWING

[0092] The figures in the attached drawing are used for detailing aspects of the present invention. In the drawing

[0093] Fig. 1 shows a simplified schematic representation of a combination of IM, Fig. 2 shows a factor graph of a conventional GSQM system model, Fig. 3 shows a factor graph of a decoupled UVD GSQM system model in accordance with the invention,

[0094] Fig. 4 shows a flow diagram of a GaBP-based MP process in accordance with the invention,

[0095] Fig. 5 shows an illustration of the method in a block-flow-type diagram,

[0096] Fig. 6 shows GQSM performance simulation results for mMIMO systems with NT= 16 and 32, and varying values of P, evaluating the performance in terms of the BER against the SNR per bit Eb / N0,

[0097] Fig. 7 shows a flow diagram of an exemplary method of decoding in accordance with the invention comprising or invoking the method of figure 4, and

[0098] Fig. 8 shows an exemplary block diagram of an apparatus configured for implementing embodiments of the method in accordance with the invention.

[0099] In the figures, identical or similar elements may be referenced using the same reference designators. DETAILED DESCRIPTION OF EMBODIMENTS

[0100] Figures 1 to 6 have been discussed further above and will not be elucidated again.

[0101] Figure 7 shows a flow diagram of an exemplary method 10 of decoding in accordance with the invention comprising or invoking the method 100 discussed with reference to figure 4. The method decodes information coded in respective activation patterns of activated subsets out of a first plurality of activatable transmit antennas of a multiple-input multiple-output (MIMO) transmitter. Each of the activated antennas transmits quadrature-modulated signal components of transmit symbols. In step 12 the quadrature-modulated signals are received at a second plurality of receive antennas, represented by a received signal vector y. In step 14 a copy of at least a subset of the transmitted quadrature-modulated signal components is received, represented by a transmit signal vector x, and in step 16 real and imaginary parts of the signal components of the received signal vector y are decoupled. In step 18 respective channel matrices WRand W1for the channels of the real and imaginary parts of the signal components of the received signal vector y are received, determined or estimated. Next, in step 20, the respective real and imaginary signal components of the decoupled real and imaginary parts of the received signal vector y are represented as respective products of a transmitted symbol component spand an activation unit vector et. Subsequently, in step 22, the respective activation unit vectors etof the decoupled real and imaginary parts of the received signal vector y are modelled by corresponding random variable vectors aPdependent on a probability mass function (PMF) of the activation patterns available at the transmitter. In step 24 a Gaussian belief propagation (GaBP)-based message passing (MP) process 100 is applied on the random variables aP, for jointly estimating the activation unit vectors for the respective real and imaginary parts of the received signal vector y, and in step 26 activation vector estimates output by the GaBP process 100 are decoded for retrieving the transmitted information.

[0102] Figure 8 shows a schematic block diagram of an exemplary wireless apparatus 300 in accordance with the invention. The wireless apparatus 300 is configured for receiving quadrature-modulated signal components of transmit symbols and comprises two or more antennas 302, circuitry 304 for processing radio frequency signals, one or more microprocessors 306, and associated volatile 308 and non- volatile memory 310. The various components and elements of the apparatus 300 are communicatively connected via one or more data and / or signal lines or buses 312. The non-volatile memory 310 stores computer program instructions which, when executed by the one or more microprocessors 306, configure components of the wireless apparatus 300 to implement or carry out embodiments of the method in accordance with the first aspect pf the invention as described herein.

[0103] re-

[0104] LIST OF REFERENCE NUMERALS (PART OF THE DESCRIPTION)

[0105] 10 method of decoding 170 computing posterior Bayes-

[0106] 12 receiving optimal soft-replicas

[0107] 14 receiving 180 computing error covariance

[0108] 16 decoupling matrices

[0109] 18 receiving / determining / estimating 25 190 updating posterior Bayes-

[0110] 20 representing optimal soft-replicas

[0111] 22 modelling 200 check termination criterion

[0112] 24 applying GaBP-based process 210 select optimal activation vector

[0113] 26 decoding estimates

[0114] 30 220 output optimal activation vector

[0115] 100 GaBP-based process estimates

[0116] 110 receiving

[0117] 120 initialising 300 apparatus

[0118] 130 calculating error covariance 302 antennas matrices 35 304 RF circuitry

[0119] 140 performing soft-IC 306 microprocessor

[0120] 150 computing conditional variances 308 volatile memory

[0121] 160 computing information vectors 310 non-volatile memory and precision matrices 312 data / signal lines / buses

Claims

CLAIMS1. A method (10) of decoding information coded in respective activation patterns of activated subsets out of a first plurality of activatable transmit antennas of a multiple-input multiple-output (MIMO) transmitter, each of the activated antennas transmitting quadrature-modulated signal components of transmit symbols, the method comprising:- receiving (12) the quadrature-modulated signals at a second plurality of receive antennas, represented by a received signal vector (y),- receiving (14) a copy of at least a subset of the transmitted quadrature- modulated signal components, represented by a transmit signal vector (x),- decoupling (16) real and imaginary parts of the signal components of the received signal vector (y),- receiving, determining or estimating (18) respective channel matrices (HR, W1) for the channels of the real and imaginary parts of the signal components of the received signal vector (y),- representing (20) the respective real and imaginary signal components of the decoupled real and imaginary parts of the received signal vector (y) as respective products of a transmitted symbol component (sp) and an activation unit vector (et),- modelling (22) the respective activation unit vectors (et) of the decoupled real and imaginary parts of the received signal vector (y) by corresponding random variable vectors (aP) dependent on a probability mass function (PMF) of the activation patterns available at the transmitter,- applying (24) a Gaussian belief propagation (GaBP)-based message passing (MP) process (100) on the random variables (aP), for jointly estimating the activation unit vectors for the respective real and imaginary parts of the received signal vector (y), and- decoding (26) activation vector estimates output (220) by the GaBP process, for retrieving the information.

2. The method (10) of claim 1 , wherein the GaBP-based MP process (100) comprises:- receiving (110) the respective decoupled real and imaginary parts of thesignal components of the received signal vector (y), the channel matrices (HR, H1) for the corresponding channels of the real and imaginary parts of the signal components of the received signal vector (y), the random variable vectors (aP) for the decoupled real and imaginary parts of the signal components of the received signal vector (y), at least the subset of the transmitted quadrature-modulated signal components, represented by the transmit signal vector (x), for all p subsets of activated transmit antennas,- initialising (120) soft-replicas of the activation vectors (ap.n, ap:n) for all factor nodes and all variable nodes of a factor graph modelling the system, and- calculating (130) the corresponding error covariance matrices (TRn, rp.n), wherein the method further comprises an iteration loop, respectively executed for the real and the imaginary part of the signal, with- performing (140) a soft interference cancellation (IC) on the received signal,- computing (150) the conditional variances (vRn, Vp.n),- computing (160) the information vectors (r]Rn, rfp.n) and the precision matrices (Ap.n, Ap.n) of the extrinsic belief- computing (170) the posterior Bayes-optimal soft-replicas (a^.n, aj,.n) from the extrinsic beliefs (bRn),- computing (180) the corresponding error covariance matrices (rp\, r^:n),- updating (190) the Bayes-optimal soft-replicas (&£.„, aj,:n) via damping,- checking (200) if a termination criterion is met, and in the negative,- repeating the iteration loop with the previously computed values as inputs, or in the positive,- selecting (210) the optimal activation vector estimates (a£, ap, and- outputting (220) the selected activation vector estimates (§£, aj,).

3. In one or more embodiments of the method (10) the subset of the transmitted quadrature-modulated signals comprises pilot signals and / or signals optimised for non-communication purposes.

4. Wireless apparatus (300) configured for receiving quadrature-modulated signal components of transmit symbols, comprising two or more antennas(302), circuitry (304) for processing radio frequency signals, one or more microprocessors (306), volatile (308) and non-volatile memory (310), connected via one or more data and / or signal lines or buses (312), wherein the non-volatile memory (310) stores computer program instructions which, when executed by the one or more microprocessors (306), configure components of the wireless apparatus (300) to implement or carry out a method of any one of the preceding claims 1 to 3.

5. The wireless apparatus (300) of claim 4, wherein the apparatus (300) is further configured for transmitting quadrature-modulated signals.

6. The wireless apparatus (300) of claim 4 or 5, wherein the circuitry (304) for processing radio frequency signals comprises a low noise amplifier and / or a mixer configured for providing a representation of a received signal at an intermediate frequency.

7. A communication system (400) comprising two or more wireless apparatus (300) according to any one of the claims 5 to 6.

8. A vehicle comprising a wireless apparatus (300) according to any one of the claims 4 to 6.

9. Use of a wireless apparatus (300) according to any one of the claims 4 to 6 and / or a communication system according to claim 7, and / or of a method (10, 100) according to any one of claims 1 to 3.

10. Computer program product comprising computer program instructions which, when executed by a microprocessor of a wireless apparatus (300) according to one or more of claims 4 to 6, cause the wireless apparatus (300) and / or control hardware blocks, modules or components of the wireless apparatus (200), respectively, to execute the method (10, 100) of one or more of claims 111. Computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 10.

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