Method of determining precoding and combining parameters for beamforming in MU-MIMO RSMA communication systems, and apparatus implementing the method

Abstract

A method of generating precoding and / or combining parameters for wireless interfaces of a first and a second communication device, respectively, is presented. The first wireless communication device is configured for wireless communication with a plurality of second communication devices (UEs) in a MU-MIMO RSMA communication system. The method comprises, for determining the precoding and / or combining parameters of the common part, performing a first decomposition of the estimated channel tensor comprising the channel matrices for all second communication devices into the product of a matrix common to all UEs, a rectangular unitary matrix for each individual UE, and a diagonal matrix representing channel spaces occupied by each individual UE. A similar second decomposition is performed for determining the precoding and / or combining parameters of the private part. The first and the second decomposition differ in at least the diagonal matrices. A subsequent beamforming phase design process is targeted to optimise the common and private message parts of signals to be transmitted over multiple antennas in accordance with a previously selected objective.

Description

[0001] METHOD OF DETERMINING PRECODING AND COMBINING PARAMETERS FOR BEAMFORMING IN MU-MIMO RSMA COMMUNICATION SYSTEMS, AND APPARATUS IMPLEMENTING THE METHOD

[0002] FIELD OF THE INVENTION

[0003] The invention relates to the field of wireless communication, in particular to wireless communication using rate splitting multiple access (RSMA) in a multi-user multipleinput multiple-output (MU-MIMO) communication system.

[0004] NOTATIONS

[0005] Real-valued column vectors and matrices are denoted in bold face and capitalized bold face letters, respectively, while their complex-valued counterparts are represented in corresponding italic boldface, respectively. The1( 2and Frobenius norms are denoted by ll-lli, ll-ll2and ||-||F, respectively. The element-wise absolute value, transpose, conjugate transpose, inverse, trace, vectorize, diagonalize and block diagonalize operations are represented as | ■ |, (-)T, (-)H, (-)-1,Tr[-]], vec(-), diag(-),blkdiag(-), respectively. The imaginary unit, the N x N identity matrix, the N x 1 all-1 column vector, and the Khatri-Rao product are respectively denoted by j,\N, 1N, and o. The k-th column and the (i, / c)-th element of the matrix X are denoted as (X)k, and respectively. The complex Gaussian distributions with mean vnand variance denoted by

[0006] BACKGROUND

[0007] The current fifth (5G) and upcoming sixth generation (6G) wireless communications and beyond are designed to serve a large number of high-mobility users, e.g., vehicles, subways, highways, trains, drones, low earth orbit (LEO) satellites, etc.

[0008] The core requirements for 5G communications include serving data-driven use cases with a data rate requirement of up to 20 Gbps in the downlink (DL), i.e., enhanced mobile broadband (eMBB), providing ultra-reliable low latency communications (URLLC) with block error rates (BLER) of 10'5or less and latencies of 1 ms or lower, and providing grant-free access in the uplink (UL) to a large number of low- complexity and low-power devices, inter alia for enabling massive machine type communications (mMTC). These requirements may not necessarily be met simultaneously. The core requirements for 6G communications go beyond those of 5G, including simultaneously meeting eMBB and URLLC, simultaneously meeting enhanced eMBB and mMTC, enhanced URLLC and mMTC, and simultaneously meeting enhanced eMBB, URLLC and mMTC, although trade-off-based, i.e., accepting compromises in any one or more of the three.

[0009] Various methods of ensuring proper access of multiple user equipment (UE) units to a base station (BS) using the shared wireless resource are known. The initially deployed communication systems typically used so-called orthogonal multiple access (OMA) schemes, which may be considered as serving a single user per resource. When sufficient numbers of orthogonal resources, i.e. time, frequency, code, and space, are available in a system, OMA can realize highly reliable communications avoiding multi-user interference (MUI). However, with increasing number of users and evolving use-cases of wireless communication, it is increasingly difficult to provide sufficient numbers of orthogonal resources due to the limitation of wireless resources and the system spectral efficiency (SE) can be degraded.

[0010] More recent developments lead to the advent of non-orthogonal multiple access (NOMA) methods, which break the traditional orthogonality of resource and signal use in MA. NOMA may be considered as serving multiple users in a single resource. This simple distinction does not fully reflect modern communication designs, in which OMA-based communication networks actually serve multiple users on orthogonal resources using time division multiple access (TDMA), frequency division multiple access (FDMA), code division multiple access (CDMA), or orthogonal frequency division multiple access (OFDMA). In addition, these modern communication systems often are equipped with multiple antennas and can further extend the multi user access through spatial domain processing in the form of multiuser linear precoding (MU-LP), space division multiple access (SDMA), multiuser multiple-input multipleoutput (MU-MIMO), and massive MIMO. MU-LP, SDMA, MU-MIMO serve users in a nonorthogonal manner since multiple users are allocated different precoders, resulting in different “beams" directed to the respective different users, in the same time-frequency grid and interfere with each other in the same cell. All these multi user access schemes require a proper interference management, either on the transmit side or the receive side, for proper interference cancellation (IC). In order to mitigate MUI caused by the non-orthogonality, NOMA systems employ various techniques such as superposition coding, successive interference cancelation (SIC), and various other optimisations, and rely heavily on optimised message passing algorithms. These techniques permit achieving high spectral efficiency, massive connectivity, and low latency.

[0011] RSMA has more recently emerged as a powerful multiple access, interference management, and multi-user strategy for next generation communication systems. RSMA refers to a broad class of multi-user schemes and represents a generalized idea of NOMA that integrates OMA and NOMA. Rate splitting (RS) involves splitting each user's message into respective common and private parts. Each user’s split message is encoded and precoded independently, and the common parts are combined into a common stream. The private parts remain individual private streams. The common stream is superposed, in a non-orthogonal manner, on top of all private streams, i.e. , the common and private streams are simultaneously transmitted as one signal by a transmitter (TX).

[0012] In the downlink, RSMA uses linearly or non-linearly precoded RS at the transmitter, i.e., at the base station, to split each user message into one or multiple common messages and a private message. The common messages are combined and encoded into common streams for the intended users. The common stream is decodable by all receivers (RX), while the private streams are to be decoded by their corresponding intended RX only. An RX would have to retrieve both the common stream and the private stream to reconstruct the original message. After decoding the common stream from the received signal the RX applies successive interference cancellation (SIC) - or any other form of joint decoding - to the common stream, for enabling proper decoding of the private stream. The decoded common and private streams are combined for retrieving the originally transmitted messages.

[0013] At each RX user equipment (UE), when decoding a signal of the common message, any interference is treated as noise. The private message is subsequently decoded by making use of SIC to eliminate interference from a signal of the common message. Finally, the common message part and the private message part are combined.

[0014] A key benefit of RS and its message splitting capability is to flexibly manage interuser interference. In fact, RS can be seen as a combination of transmit-side and receive-side interference cancellation where the contribution of the common stream can be adjusted according to the level of interference that needs to be cancelled by the receiver. This departs from the transmit transmit-side only and receive-side only interference cancellation strategies of SDMA, OMA and NOMA, respectively, and yields efficiency, flexibility, and robustness on communication.

[0015] Using RSMA in MU-MIMO systems, i.e., systems in which the BSs and UEs have multiple antennas configured for beamforming (BF), also referred to as spatial multiplexing, requires proper precoding in the transmitter for proper beamforming and proper combining in the receiver to make the best use of the signals of all antennas. The spatial multiplexing introduces additional multi-user interference, inter alia due to imperfect beamforming that inevitably “leaks” a part of the signal to other UEs not targeted by the beam, that needs to be dealt with in the receiver. While the common channel part of RSMA may still provide useful information for those UEs that are not targeted by a beam for performing CE and IC, currently available precoders and combiners that take into account, on the transmission side, uncertain CSI and the resulting imperfect SIC in receivers of a MU-MIMO RSMA system, have a complexity that is prohibitively high and thus prevents their widespread adoption. This leaves MU-MIMO RSMA systems with suboptimal precoders and combiners that are prone to performance degradation in the presence of uncertain CSI and strong MUI. This challenge is particularly difficult to address in heterogeneous systems, where different UEs have different numbers of antennas, and the known methods cannot be used in such situations or have a severely degraded performance.

[0016] SUMMARY OF THE INVENTION

[0017] In view of the limitations of known designs for precoder and combiner of downlink MU-MIMO RSMA communication systems it is desirable to propose a precoder and combiner design that is robust against CSI uncertainty and strong MUI while providing low latency and having a reasonably low complexity. It is, therefore, desirable to provide an improved low-complexity method of determining precoding and combining parameters for wireless devices of MU-MIMO RSMA communication systems, and to provide a corresponding transmitter that is adapted to cope with situations in which the transmitter and / or the receiver do not have perfect knowledge of the CSI, as well as a method of operating the transmitter. It is further desirable to provide methods and apparatus that can be used in communication systems having UEs with different numbers of antennas without suffering from severe performance degradation.

[0018] This need is addressed by the method of claim 1, the method of claim 5, the wireless communication device of claim 8, and the computer program product of claim 9. A corresponding computer-readable storage medium is presented in claim 10.

[0019] Embodiments and developments of the methods and apparatus, respectively, are provided in the respective dependent claims.

[0020] The invention will be described in the following assuming a multi-user downlink RSMA system composed of a base station (BS) equipped with N TX antennas and K users, or UEs, with MkRX antennas. An exemplary illustration of the system showing the main components of a corresponding transmitter, e.g., in a base station 300, and receiver, e.g., in a UE 400, respectively, is presented in figure 1 . It is noted that, when the estimated CSI is determined in the UE, the UE provides the CSI to the BS via the same ideal feedback.

[0021] In the transmitter, i.e., the base station 300, after splitting the signals to be transmitted to the multiple UEs into a common part and multiple corresponding private parts, and after encoding the common and private signals, the resulting signal s is supplied to a precoder 302. An estimated channel state information (CSI) is input to a beamformer (BF) 304, which supplies a precoding matrix V to the precoder 302, which outputs a signal x that is ultimately transmitted via the multiple antennas 306 of the base station 300. Sending the respective precoded signals over the multiple antennas effectively results in an electronic beamforming of the private parts of the transmission towards the respective receiver. Beamformer 304 jointly determines the precoding matrix V and the combiner matrix U in accordance with estimated channel coefficients provided in channel coefficient matrix H, determined by a channel estimator 308. As mentioned before, the matrix H carrying the estimated channel coefficients, the precoding matrix V, as well as a combiner matrix U for use at the respective receiver is transmitted to the UE 400 via an ideal feedback link 399, i.e., can be assumed to be fully available at the UE 400 at the time of decoding the transmitted signal.

[0022] At the UE 400 the transmitted signal is received via the multiple antennas 402, and the received signal y is provided to combiners 404a, 404b. Combiner 404a combines the common message part of yk, using the combiner matrix Uc.k, and outputs a combined received signal a decoder 408 configured for decoding the common signal. Combiner 404b combines the private message part of yk, using the combiner matrix U*, and outputs a combined received signal to an interference cancellation (IC) unit 410, of a detector 406. The combiners use the previously received combiner matrices U for electronic beamforming towards the transmitter. Based on the common signal output from decoder 408 and the combined received signal the IC unit 410 determines a version of the received signal having a largely reduced interference, which is provided to a decoder 412 configured for decoding the private signal. Detector 406 outputs an estimated signal s representing the transmitted common and private signal.

[0023] The received signal at the can be modelled as

[0024] (1) where x G denote the transmit signal including TX BF, and the additive white Gaussian noise (AWGN) vector at the k-th user, respectively. HkG cMk*Nis the channel matrix between the BS and k-th user. With the idea of RSMA, the transmit signal x can be composed of the individually precoded common signal and the private signal skG CQkX1with corresponding TX BF matrices for the common signal and for the private signa

[0025] At the k-th receiving UE’s side, initially the messages of interest are the common signal scwhich is directly detected from the sc-component carried in the received signal yk, and the k-th private signal Sk is obtained by applying successive interference cancellation (SIC) to the received signal with the knowledge of estimated common signal sc.

[0026] For detecting the intended common signal, each fc-th user tries to recover the common signal with the matrix where sc>kis the estimated common signal at the k-th user. After the SIC with the detected common message, each k-th user tries to estimate the private signal of the k-th user as where skG C<3feX1and Up kG C<2feXMfedenotes the estimated private signal at the k-th user and the RX BF matrix for detecting the private signal, respectively. With the above detection, the achievable sum rate of a RSMA 7?sumcan be defined as with

[0027] (6a, 6b, 6c, 6d)

[0028] Before further describing embodiments of the proposed invention in greater detail, the signal or message flow in the exemplarily assumed communication protocols of the downlink RSMA system, time division duplex (TDD) and frequency division duplex (FDD), respectively, are illustrated in figures 2 and 3.

[0029] Figure 2 shows a swim-lane diagram of the messages exchanged between a BS and a target UE in a TDD communication system in the DL direction, and the respective processing invoked at the respective end. First, the target UE transmits a pilot signal to the BS. The pilot signal may be part of a regular communication transmission from the target UE to the BS. The BS uses the pilot signal for performing CE, i.e., estimating a channel coefficient matrix H, and determines, in the beamformer, a precoder matrix V, for electronic beamforming towards the target UE by accordingly transmitting appropriate signals via the Nt> 1 transmit antennas and the combiner matrix U. The estimated channel coefficient matrix H, the precoding matrix V and the combiner matrix U output from the BF are fed back to the UE, which stores the matrices for use in decoding received messages. Next, the BS splits the message to be sent into a common part intended for multiple UEs and a private part intended only for the target UE, i.e., produces an RSMA signal. The RSMA signal is then precoded using the precoding matrix V, yielding transmit signals for each of the Nt> 1 transmit antennas of the BS, and transmits the transmit signals, which will effectively result in electronic beamforming towards the target UE. The target UE receives the signals transmitted by the Nt> 1 transmit antennas of the BS at its Mk> 1 antennas and combines the signals, using the precoding matrix V and the combiner matrix U previously received from the BS. After the common and private messages are decoded, they can be combined into the originally sent message. Figure 3 shows a swim-lane diagram of the messages exchanged between a BS and a target UE in a FDD communication system in the DL direction, and the respective processing invoked at the respective end. Here, the BS first transmits a pilot signal to the target UE. Similar to the previous protocol discussed with reference to figure 2 the pilot signal may be part of a regular communication transmission from the BS to the target UE. The target UE uses the pilot signal for performing CE, i.e., estimating a channel coefficient matrix H and transmits the estimated channel coefficient matrix H to the BS. The BS uses the channel coefficient matrix H for determining, in the beamformer, a precoder matrix V for electronic beamforming towards the target UE by accordingly transmitting appropriate signals via the Nt> 1 transmit antennas and the combiner matrix U. The precoding matrix V and the combiner matrix U output from the BF are fed back to the UE, which stores the matrices for use in decoding received messages. Next, the BS splits the message to be sent into a common part intended for multiple UEs and a private part intended only for the target UE, i.e., produces an RSMA signal. The RSMA signal is then precoded using the precoding matrix V, yielding transmit signals for each of the Nt> 1 transmit antennas of the BS, and transmits the transmit signals, which will effectively result in electronic beamforming towards the target UE. The target UE receives the signals transmitted by the Nt> 1 transmit antennas of the BS at its Mk > 1 antennas and combines the signals, using the precoding matrix V and the combiner matrix U previously received from the BS. After the common and private messages are decoded, they can be combined into the originally sent message.

[0030] Each of the two exemplary communication protocols briefly discussed above ensure that the BS has all information necessary for determining, in the BF, the precoder matrix V for transmitting to the UEs and the combiner matrix U. Providing information about the precoding matrix V and the combiner matrix U output from the BS to the UEs enables improved signal recovery in the UEs.

[0031] As can be seen from the discussion of figures 1 to 3 determining the precoder and combiner matrices in the BF is an important element for the performance of the communication between the BS and the UEs. In accordance with embodiments of the invention the beamformer may be adaptable or configurable, enabling provision of the most suitable precoder and combiner matrices for changing communication requirements and environments.

[0032] Figure 4 shows an exemplary simplified block diagram of such an adaptable and configurable block in the BS that handles the BF design and configures a BF for determining a precoding matrix V and a combiner matrix U required for beamforming in the BS and combining the signals received at the Mk> 1 antennas in the UE. In other words, the adaptable and configurable block adaptably designs the BF prior to determining the precoding and combining matrices adapted for the respective communication requirement and environment.

[0033] The inputs to BF design block are an estimated channel coefficient matrix H and a corresponding matrix H representing the error statistics of H, the outputs are a precoder matrix V and a combiner matrix U that are optimised for one of various specific objectives discussed below. The actual block that generates the output from the input signals is shown as a “black box”, exemplary implementations of which will be discussed hereinafter in greater detail.

[0034] The following section discusses various aspects and stages of the BF design in accordance with embodiments of the invention. The various aspects and stages comprise denoising, channel decomposition for phase design, and optimisationbased resource allocation. Embodiments of the invention may comprise individual or combinations of the aforementioned aspects and stages.

[0035] Denoisinq of the estimated channel matrix

[0036] As discussed by H. Joudeh and B. Clerckx in “Sum-rate maximisation for linearly precoded downlink multiuser MISO systems with partial CSIT: A rate-splitting approach,” IEEE Trans. Commun., vol. 64, no. 11 , pp. 4847-4861 , 2016 and by A. Mishra, Y. Mao, O. Dizdar, and B. Clerckx in “Rate-splitting multiple access for downlink multiuser MIMO: Precoder optimisation and PHY-layer design,” IEEE Trans. Commun., vol. 70, no. 2, pp. 874-890, 2022, the channel matrix between the BS and the fc-th user Hkcan be modelled as the sum of the estimated channel matrix and the channel estimation error: where Hke denote the estimated channel matrix between the BS and the k-th user and its estimation error with a covariance matrix Re fcG CNxN, respectively. Within a coherent interval of channel fading, the ^-th realisation of the estimated channel matrix for the k-th user Hfe(O e CMfeX2Vis also expressed by the ^-th estimation error of the channel matrix Hk(f) G CMfcXW:

[0037] Note that the expression “realisation” refers to an estimation of the channel for the k-th UE. With a sufficient number of realisations for the estimated channel matrix L, the effects of the channel estimation error can be mitigated by sample averaging (SA), as likewise proposed in the aforementioned documents: G cAffeX7Vdenotes an available denoised channel matrix for the BF design between the BS and the k-th user. Alternatively, a median matrix of the sample interval may be determined, which may reduce the computational complexity.

[0038] Figure 5 illustrates the general concept of a channel decomposition that can be used in determining the precoder and combiner parameters V and U, respectively, in a MU-MIMO RSMA communication system. The decomposition is derived from the idea of multi-linear generalized singular value decomposition (ML-GSVD), e.g., as proposed by L. Khamidullina, A. L. F. de Almeida, and M. Haardt in “Multilinear generalized singular value decomposition (ML-GSVD) with application to coordinated beamforming in multi-user MIMO systems,” Proc. IEEE ICASSP, Barcelona, Spain, 2020, pp. 4587-4591. Applying the general principles of ML-GSVD the matrix H* representing the channel coefficients for the £-th UE can be decomposed into the product of the matrices BA, C* and AT, as shown in figure 5. Figure 5 shows multiple so-called “slices”, each slice dimension exemplarily representing a channel coefficient matrix and the decomposed factors, respectively, for one of the k UEs. ATis a square matrix similar to the right singular vectors of a conventional singular value decomposition (SVD) except for the fundamental difference that it is common to all slices of H*. It is, therefore, represented only once. B* is a rectangular unitary matrix for each individual slice, akin to the left singular vectors in a conventional SVD. Ct is a diagonal matrix for each individual slice, representing channel spaces occupied by each UE. The channel spaces represented by the diagonal matrix C* may comprise information about the dimensions of the antennas.

[0039] The most important aspect in designing the BF in space division multiple access (SDMA) systems is the structure of the decomposed channel, especially the diagonal matrices Ct, and exclusive dimension allocation, i.e., space allocation. However, the known ML-GSVD method is not designed to promote the separation of the subspaces of the common interface matrix AT, a drawback that clearly does not facilitate the construction of TX beamformers.

[0040] The present invention addresses this issue by, inter alia, performing a novel decomposition of the channel tensor comprising the channel matrices HA, more specifically by performing different decompositions for the common message part and the private message part. This novel decomposition permits a BF that broadcasts the common message to all UEs, while concentrating the transmission for individual UEs to those respective UEs. The novel decomposition results in two separate and different sets of factors B, C and A for the common and private message parts.

[0041] Channel decomposition for the common message part

[0042] Based on the idea of higher-order generalised singular value decomposition (HO- GSVD) as presented by S. P. Ponnapalli, M. A. Saunders, C. F. V. Loan, and O. Alter in “A higher-order generalized singular value decomposition for comparison of global mRNA expression from multiple organisms,” PLoS ONE, vol. 6, no. 12, 2011 , for the common message part the denoised channel matrices can be ideally decomposed into three factors as,

[0043] For the decomposition, the common matrix for the common message AcG CNXNcan be computed as

[0044] Once the common matrix is obtained, the channel matrix can be diagonalized from the right hand side as HkAcG cMkXNand can be decomposed into two factors as

[0045] Channel decomposition for the private message part

[0046] In order to mitigate interference caused by the private message communication, a block diagonalisation of a channel tensor for the private message part can be considered as where Bp kG CMfcXjV, Cp fcG IRAfxjV, and ApG cNxN. Following a known consideration for spatial division multiple access (SDMA), e.g., as discussed by K. Ando, H. limori, G. T. F. de Abreu, and K. Ishibashi in “User-heterogeneous cell-free massive MIMO downlink and uplink beamforming via tensor decomposition,” IEEE Open J. Commun Society, vol. 3, pp. 740-758, 2022 or by K. Ando, K. Ishibashi, and G. T. F. de Abreu in “Robust tensor decomposition for heterogeneous beamforming under imperfect channel state information,” IEEE Open J. Signal Process., pp. 1-10, 2023, the decomposition enforced the diagonal factor Ck,V / c into an exclusive structure for the sake of MUI mitigation. With the idea of spatial separation, the middle factor CP)fcis defined as of stream index allocated k th user. For the update of Bk, a following unitary constrained optimisation problem can be formulate as

[0047] From the above optimisation, the Lagrangian is calculated as where Lme cMkXMkdenotes the Lagrange multiplier matrix. The solution to equation

[0048] (16) derived via Wirtinger calculus is where Dke cMkXNdenotes a temporal matrix that is given by the initial common factor 4Cused in channel decomposition for common message as

[0049] Finally, the refinement of the right-hand side matrix -4pis given as+

[0050] From the block diagonalized linear expression

[0051] (20b, 20c)

[0052] Figure 6 shows a schematic exemplary flow diagram of the steps of the procedure of channel decomposition for common and private message part, respectively, as used for generating precoding and / or combining parameters Vc, V*, Uc.*, U* for wireless interfaces of a first and a second communication device, respectively in accordance with the invention.

[0053] Inputs to the method are HkG cMkXNand The steps for the channel decomposition for the common message are:

[0054] 110 Initialise Acfrom Hkas per equation (11 )

[0055] 120 Compute Cc k, Wk from Acand Hkas per equation (12)

[0056] 130 Compute Bc k, Wk from Acand Hkas per equation (13)

[0057] The steps for the channel decomposition for the private message are:

[0058] 140 Initialise Cp kfrom N and Mkas per equation (15)

[0059] 150 Compute Bp kfrom Ac, Cp kand Hkas per equation (19)

[0060] 160 Compute i4pfrom Bp k, CP)feand Hkas per equation (20)

[0061] Note that the steps 110 to 130 and 140 to 160 may be executed sequentially or in parallel, as indicated by the dashed boxes and arrows in the figure. Step 102 represents a check for a trigger event that triggers execution of the process. Figure 7 graphically illustrates the novel decomposition. The property of the respective tensor decomposition can be characterised by the structure of the middle diagonal factor C. The decomposition for the common message part is targeted to make CC / feinto an inclusive structure to all UEs, while the decomposition for the private message part is targeted to make Cfcan exclusive structure that minimises MUI.

[0062] Figure 8 illustrates a schematic block diagram of a processing block performing the novel decomposition. The estimated CSI and error is input to the overall process block and fed to the initialisation block for factor 4Cand to the process blocks for updating factor B and for updating factors Bcand Cc. The process block for updating factor B further receives the initialised factor C , and its output is used for updating factor .4. The overall processing block outputs decomposed factors Bc, Ccand Acfor the common message part and decomposed factors B, C and A for the private message part.

[0063] Figure 9 illustrates the arrangement of the decomposition process described before in an exemplary overall process of generating precoding and combining parameters.

[0064] Phase design of the BF matrices

[0065] Thanks to the above channel decomposition, the phase of TX BF, RX BF, and the space separation matrix can be respectively designed as

[0066] (21a - 22h) where the operator P[-] punctures out all zero column vectors of a matrix. pc and pPjfedenote resource allocation vectors for common message and private message of fc-th user, respectively.

[0067] Considering that the signals for all UEs share the same resource, the allocation of respective shares for the available resource is critical for the operation of the system.

[0068] In "Precoding and Decoding Schemes for Downlink MIMO-RSMA with Simultaneous Diagonalisation and User Exclusion," 2022 IEEE International Conference on Communications Workshops (ICC Workshops), Seoul, Korea, R. Diab,

[0069] A. Krishnamoorthy and R. Schober discuss precoder and combiner designs for an RSMA communication system, and also address the resource allocation. More specifically, the authors consider a successive convex approximation (SCA) based convex approximation for the resource allocation, which targets to maximize the total achievable data rate by solving the convex optimisation problem. However, the known SCA process for resource allocation is optimised for lower data rates and does not meet the performance requirements for higher data rates.

[0070] To address this shortcoming, a fractional programming (FP) process for the resource allocation may be used. FP refers to a family of optimization problems that involve ratio terms, e.g., a ratio of two functions that are in general nonlinear. The ratio to be optimized often describes some kind of efficiency of a system.

[0071] Resource Allocation via Fractional Programming (FP)

[0072] Thanks to the decomposition and the corresponding BF design described above, the channel matrices can be diagonalized. Then, the achievable total SE defined in equation (5) can be approximated as (22a, 22b, 22c) with

[0073] (23a, 23b) and

[0074] (24a, 24b, 24c) where pc>q, and pp>kiqdenote q-th element of pc, and pPjfcrespectively.

[0075] With the above approximation, the optimisation problem for the sum-rate maximisation (SRM) can be formulated as

[0076] (25a, 25b, 25c)

[0077] Since the objective function of the above optimisation problem is not convex, the efficient convex optimisation technique cannot be applied. In order to solve the above optimisation problem in an efficient way, the optimisation problem can be convexised by applying the FP technique discussed by K. Shen, W. Yu, L. Zhao, and D. P.

[0078] Palomar in “Optimisation of MIMO device-to-device networks via matrix fractional programming: A minorisation-maximisation approach," IEEE / ACM Trans.

[0079] Networking, vol. 27, no. 5, pp. 2164-2177, 2019 and by K. Shen and W. Yu in “Fractional programming for communication systems - Part I: Power control and beamforming,” IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2616-2630, May 2018. The corresponding optimisation problem is reformulated as with where TC / (fc / q)and TP / (fc ( / ) are auxiliary variables, which are updated as

[0080] Since focusing solely on SRM can sacrifice fairness of SE among users to maximize system achievable sum rate, some of the users can be in outage. In order to avoid such outage, in contrast to the SRM-only objective, a fairness-aware max-min optimisation problem can be formulated as maximize v

[0081] Pc>Pp,fc subject to

[0082] (29a, 29b, 29c, 29d) where v G HR1X1denotes a slack variable. Introducing the fairness aspect into the max-min optimisation and SRM comes at the cost of a trade-off in performance, i.e., the max-min optimisation may sacrifice achievable sum rate performance.

[0083] Besides of the max-min optimisation problem, the geometric-mean (GMean) maximisation problem can be considered to naturally incorporate a fairness aspect into the SRM, as has been shown by S. Fukue, H. limori, G. T. F. De Abreu, and K. Ishibashi in “Joint access configuration and beamforming for cell-free massive MIMO systems with dynamic TDD,” IEEE Access, vol. 10, pp. 40 130-40 149, 2022, and the corresponding optimisation problem can be reformulated as

[0084] (30a, 30b, 30c)

[0085] In light of the above, an exemplary resource allocation useable with the proposed BF design method can be summarised as described below with reference to figure 10:

[0086] Inputs to the method, received in step 202, are Hk,H Vk and afr. The steps for the phase design of the BF are:

[0087] 210 Compute intermediate precoding and / or combining matrices for the common message part (V’c, U’c,jt) and the private message part (V’A, U’A), respectively, in which the phase of the BF is set, as per equation (21 )

[0088] 220 Initialise pcand pP;feas equal power allocation while the alternating optimisation converges (checking step 250) 230 Update Tc,( / c,q) and TPi(k,q) with fixed pcand pP;feas per equation (28) 240 Solve the convex optimisation for pcand pp>feas expressed in equation (26), (29) or (30)

[0089] 260 Once the convergence stops or falls below a predetermined threshold, output the optimised pcand pP)feto the combiner block

[0090] 270 combine the intermediate precoding and / or combining matrices and the optimised pcand pPjfcfor obtaining final precoding and / or combining matrices Vc, VP / fc, UCik, UPik

[0091] 280 output the final precoding and / or combining matrices Vc, VP)fe, UCik, UPik

[0092] Figure 11 illustrates an exemplary schematic block diagram of a processing block 10 performing the resource allocation. The input signals, including the estimated CSI, the factor decomposition of the common signal part and private signal part, respectively, are provided to an optimisation block 12, configured to optimise the power allocation to the common signal part and private signal part, and to blocks 14a, 14b configured for generating the intermediate precoding and / or combining matrices, respectively. The intermediate precoding and / or combining matrices, respectively, are further provided to the optimisation block 12, and further, along with an output signal of the optimisation block 12, to a combiner block 16 that is configured to generate optimised precoding and / or combining matrices V, U.

[0093] In the following section the performance of the proposed channel decompositionbased and power allocation optimised BF design will be evaluated and compared with known BF designs presented by A. Mishra, Y. Mao, O. Dizdar, and B. Clerckx in “Rate-splitting multiple access for downlink multiuser Ml MO: Precoder optimisation and PHY-layer design,” IEEE Trans. Commun., vol. 70, no. 2, pp. 874-890, 2022, and R. Diab, A. Krishnamoorthy, and R. Schober in “Precoding and decoding schemes for downlink mimo-rsma with simultaneous diagonalisation and user exclusion,” in 2022 IEEE International Conference on Communications Workshops (ICC Workshops), 2022, pp. 586-591 . The evaluation comprises numerical simulations of the worst-case complexity and achievable SE. The computational complexity of the proposed method can be estimated by determining the sum of the worst case complexity for the channel decomposition and the solving of the optimisation problem. The worst case complexity for the channel decomposition is estimated as O(KN3) caused by the K times matrix multiplication and the singular value decomposition (SVD). Since the optimisation problem presented in equations (26), (29), or (30) is a constrained convex optimisation problem, they can be solved by Newton's method of the interior-point method.

[0094] Applying Newton's method, the worst case complexity of the per-iteration worst case complexity of the BF design method can be estimated by the product of the number of Newton iteration and the complexity for each Newton iteration. The number of required Newton iterations L can be estimated as, where M denotes the number of inequality constraint for an optimisation problem. Since the parameters e, tS°\ fi,y, and c are constant for solving the optimisation problem, the number of required Newton iterations is proportional of Mlog(M). Regarding the per-Newton-iteration complexity, it is well known that an optimisation problem with N real domain optimisation variables requires at least O(1V3) floating point number operations (FLOPs). Thus, the per-iteration complexity order for solving the optimisation problem can be simplified as worst case complexity of O(N3• Mlog(M)). Specifically, from the optimisation problem as expressed in equations (26), (29), or (30), the corresponding parameters N and M of the proposed BF design are derived as

[0095] (32a, 32b) Since the complexity order for solving the optimisation problem is much larger than the complexity of the channel decomposition, the effective complexity order, i.e., the dominant complexity, for the proposed BF design is regarded as where Tpropdenotes the number of iterations for the convergence of the alternating optimisation in the BF design method.

[0096] For the BF designs of low complexity as presented by R. Diab, A. Krishnamoorthy, and R. Schober in “Precoding and decoding schemes for downlink mimo-rsma with simultaneous diagonalisation and user exclusion,” or of high complexity as presented by A. Mishra, Y. Mao, O. Dizdar, and B. Clerckx in “Rate-splitting multiple access for downlink multiuser MIMO: Precoder optimisation and PHY-layer design”, it is also required to iteratively solve a convex optimisation problem for obtaining sophisticated BF. Thus, the worst case complexity of both known designs are likewise dominated by the complexity for solving the optimisation problem. Since the formulation of the low complexity optimisation problem is similar to the proposed design as presented in equation (26), the corresponding complexity can be regarded as

[0097] 0(rSotA1 1 • NsotAI ’ ^SotAI l°g(MsotA1 ))

[0098] ^SotAI = Mprop. = 1 + QC+ ^ Qk + K fc

[0099] (34a, 34b, 34c) where IsotAi denotes the number of iterations for the convergence of the low- complexity alternating optimisation.

[0100] On the other hand, the high-complexity optimisation problem discussed by A. Mishra, Y. Mao, O. Dizdar, and B. Clerckx in “Rate-splitting multiple access for downlink multiuser MIMO: Precoder optimisation and PHY-layer design” is formulated in a different way so that the corresponding complexity order is derived as, 0 (^SotA2 ’ ^SotA2 ' ^SotA21°g(^SotA2)) #sotA2 = 2N (QC+ ^ Qfc j + 2K X fc /

[0101] ^SotA2 = 1 + 2K

[0102] (35a, 35b, 35c) where TSotA2denotes the number of iterations for the convergence of the alternating high-complexity optimisation.

[0103] Regarding the achievable SE performance evaluation, communication over a Rayleigh fading channel is considered so that the actual channel between the BS and k-th user is Hk with ak= l / K,Vk. In addition, the covariance matrix for channel estimation error is given as Re fc= okP~a\Nwith a = 0.6. The actual value of the other key parameters for the system are noted as in Table I below:

[0104] Simulation Parameters

[0105] Symbol Meaning Value

[0106] N Number of antennas at TX 36

[0107] K Number of users 18

[0108] MkNumber of antennas at k-th user 2

[0109] QkNumber of stream for k-th user's private message 2

[0110] QcNumber of stream for common message 2

[0111] L Number of channel realization for SA 1000

[0112] The achievable SE performance of each BF design is evaluated with complexity tradeoff. Figure 12 shows the convergence behaviour of the averaged total SE E[j?sum]. The known high complexity BF design, indicated by the dashed line with the filled dots, realized the best performance with TSotA2= 16 iterations. From the complexity analysis, the corresponding worst case complexity of the known high complexity BF design can be estimated as 0 (TSotA2 ■ Ws30tA2' ^sotA21og(MSotA2)) = 4.6 x 1013.

[0113] Since the low complexity BF design, indicated by the dashed line, and the proposed BF design have the same complexity order, a fair comparison can be made with the same number of iterations. At 7sotA1, Tprop= 6 iterations, the complexity orders of both designs are estimated as 7.6 x 107.

[0114] The figure shows that the proposed BF design, indicated by the solid line for the MaxMin optimisation and by the solid line with the upward-pointing filled triangles for SRM and with the downward-pointing filled triangles for the GMean optimisation, achieves better performance with the same complexity as the known low-complexity BF design and, at the same time, reduces the complexity for the BF design without catastrophic performance degradation compared to the known high-complexity BF design. However, the known high-complexity BF design provides poor scalability due to its complexity.

[0115] Figure 13 shows the averaged total SE over the SNR for the various embodiments of the proposed method and known reference methods. While the high-complexity known method performs best for all SNR values, the different variants of the proposed method come in second or third, performing significantly better than the low-complexity known method and the SDMA-MMSE access scheme used for further comparison.

[0116] Figure 14 shows the cumulative distribution function (CDF) over the total SE for the various embodiments of the proposed method and known reference methods. The CDF indicates the ability to scan in wide angles. Once again, the high-complexity known method performs best for all SNR values, while the different variants of the proposed method come in second or third, performing significantly better than the low-complexity known method and the SDMA-MMSE access scheme used for further comparison. Figure 15 shows the CDF over the minimum SE for the various embodiments of the proposed method and known reference methods. Here, the different variants of the proposed method provide the best CDF and high minimum SE, while the high- complexity known method comes in fourth, clearly beating the low-complexity known method and the SDMA-MMSE access scheme.

[0117] Figure 16 shows the CDF over the each user’s SE for the various embodiments of the proposed method and known reference methods. Here, the high-complexity known method performs slightly better than the different variants of the proposed method, which performs mostly better than the low-complexity method. The SDMA- MMSE access scheme shows the poorest performance.

[0118] In light of the above, in accordance with a first aspect of the present invention a method of generating precoding and / or combining parameters Vc, Vk, Uc,jt, wireless interfaces of a first and a second communication device, respectively, is presented. The first wireless communication device is configured for wireless communication with a plurality of second communication devices in a MU-MIMO RSMA communication system. The method comprises, for determining the precoding and / or combining parameters Vc, Ucjtof the common part, performing a first decomposition of the estimated channel tensor comprising the channel matrices HA for all second communication devices into the product of a matrix Accommon to all second communication devices, into a rectangular unitary matrix BC,A for each individual second communication device, and a diagonal matrix CC)* representing channel spaces occupied by each individual second communication device.

[0119] The method further comprises, for determining the precoding and / or combining parameters Vk, U* of the private part, performing a second decomposition of the estimated channel tensor comprising the channel matrices HA for all second communication devices into the product of a matrix Apcommon to all second communication devices, into a rectangular unitary matrix BP,A for each individual second communication device, and a diagonal matrix Cp>* representing channel spaces occupied by each individual second communication device. In accordance with the present invention the first and the second decomposition differ in at least the respective diagonal matrices Cc^, Cp,n.

[0120] The method further comprises providing the outputs of the first and the second decomposition to a BF phase design process targeted to optimise the common and private message parts of signals to be transmitted over the multiple antennas, in accordance with a previously selected objective, and outputting the precoding matrices Vc, Vk to a precoder, for accordingly precoding common and private message parts of signals to be transmitted and / or outputting the precoding matrix Vc, Vn and the combining matrix Uc,n, Un to a compression stage, for transmission to one or more second communication devices.

[0121] In one or more embodiments the method further comprises denoising the channel matrices Hn prior to performing the first and / or second decompositions. Denoising may comprise determining the average or the median of a predetermined number of channel estimations, i.e., several realisations of Hk, over a coherent interval of channel fading.

[0122] In one or more embodiments the method further comprises triggering execution of the method triggered in response to changes in the number of second communication devices being served by a first communication device exceeding a predetermined threshold. This permits dynamically adapting the precoding and combining parameters and optimising the resource allocation according to the needs of a current scenario, i.e., fully loaded or underloaded.

[0123] In accordance with a second aspect of the present invention a method of operating a first wireless communication device wirelessly connected to a plurality of second wireless communication devices in a MU-MIMO RSMA communication system is presented. The method comprises executing a generating process in accordance with the first aspect of the invention described above, or receiving precoding and combining parameters Vc, Vk, Uftn, Un determined in accordance with said generating process. The method further comprises providing at least the precoding and combining parameters Vc, V*, Uc,n, Un to a precoder of the first communication device and at least the combining parameters Uc,n, Un to each of the plurality of second wireless devices, to which messages are to be transmitted. The method yet further comprises splitting messages to be transmitted to one or more from the plurality of second wireless communication devices into respective common parts and private parts and providing the split messages to the precoder. The precoder precodes each of the private parts and the common parts in accordance with the received precoding parameters, for obtaining transmission signals for each of a plurality of antennas of the first wireless communication device. The precoded transmission signals are finally transmitted via the multiple antennas.

[0124] In one or more embodiments the method in accordance with the second aspect of the invention further comprises receiving, as an input to the executing step, estimated channel coefficient matrices Hi and data on the error statistics thereof, for all communication channels between the first communication device and the second communication devices.

[0125] In one or more embodiments of the method in accordance with the second aspect of the invention receiving comprises determining the estimated channel coefficient matrices Hi and data on the error statistics thereof at the first wireless communication device, or receiving said information from the respective second wireless communication devices.

[0126] In accordance with a third aspect of the invention, a wireless communication device, e.g., a base station, comprises one or more microprocessors, volatile and nonvolatile memory, and wireless interface circuitry configured for transmitting and / or receiving electromagnetic signals via multiple antennas. The various elements are communicatively connected via one or more data or signal lines or buses. The nonvolatile memory stores computer program instructions which, when executed by the microprocessor, configure the wireless device to execute the method in accordance with the first or the second aspect of the invention as presented above.

[0127] The methods described hereinbefore may be represented by computer program instructions. Accordingly, a computer program product comprises computer program instructions which, when executed by a microprocessor of a transmitter, cause the microprocessor to execute the method and to accordingly control hardware components of the transmitter of an RSMA MU-MIMO communication system in accordance with the first or the second aspect of the invention as presented above.

[0128] 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 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.

[0129] Due to its capability of operating with low latency the proposed method can advantageously be used in general wireless communication systems using RSMA in the downlink, in particular in systems having large numbers of heterogeneous UEs with different numbers of antennas, and generally in any such system where the UEs do not have perfect SIC. However, since the RSMA model harmonises known conventional OMA and NOMA access methods, the proposed method is applicable to any conventional downlink wireless communication system including OMA or NOMA. The possibility of performing the decomposition and consequently the resource allocation separately for the common and private message parts opens the path for improved dynamic adaptation or adjustment of the precoding and combining parameters depending on the number of users, thereby adapting to fully loaded or underloaded operation scenarios.

[0130] The proposed methods may be advantageously used in highly mobile devices, such as vehicles, trains, planes and the like.

[0131] BRIEF DESCRIPTION OF THE DRAWING

[0132] The figures in the attached drawing are used for detailing aspects of the present invention. In the drawing

[0133] Fig. 1 shows main components of a transmitter, e.g., in a base station 300, and a receiver, e.g., in a UE, respectively, configured for executing the method according to the present invention, Fig. 2 shows a swim-lane diagram of the messages exchanged between a BS and a target UE in a TDD communication system in the DL direction, and the respective processing invoked at the respective end,

[0134] Fig. 3 shows a swim-lane diagram of the messages exchanged between a BS and a target UE in a FDD communication system in the DL direction, and the respective processing invoked at the respective end,

[0135] Fig. 4 shows an exemplary simplified block diagram of a block in the BS that handles the BF design and outputs the precoding matrix V and the combiner matrix U required for beamforming in the BS and combining the signals received at the M > 1 antennas in the UE,

[0136] Fig. 5 shows a schematic illustration of the general principle of channel decomposition,

[0137] Fig. 6 shows a schematic exemplary flow diagram of the steps of the procedure of channel decomposition for common and private message part, respectively, as used for generating precoding and / or combining parameters,

[0138] Fig. 7 shows a schematic graphic illustration of the novel channel decomposition in accordance with the present invention,

[0139] Fig. 8 shows a schematic block diagram of a processing block performing the novel decomposition,

[0140] Fig. 9 illustrates the arrangement of the novel decomposition process in the overall process of generating precoding and combining parameters,

[0141] Fig. 10 shows a schematic exemplary flow diagram of the steps of the procedure of phase design for the BF,

[0142] Fig. 11 illustrates an exemplary schematic block diagram of a processing block performing the resource allocation,

[0143] Fig. 12 shows the convergence behaviour of the averaged total SE of the proposed method compared to known methods,

[0144] Fig. 13 shows the averaged total SE over the SNR for the various embodiments of the proposed method and known reference methods,

[0145] Fig. 14 shows the cumulative distribution function (CDF) over the total SE for the various embodiments of the proposed method and known reference methods,

[0146] Fig. 15 shows the CDF over the minimum SE for the various embodiments of the proposed method and known reference methods, Fig. 16 shows the CDF over the each user’s SE for the various embodiments of the proposed method and known reference methods,

[0147] Fig. 17 shows an exemplary block diagram of a transmitter in accordance with embodiments of the second aspect of the present invention, and

[0148] Fig.18 shows an exemplary flow diagram of a method in accordance with the second aspect of the invention.

[0149] In the figures, identical or similar elements may be referenced using the same reference designators.

[0150] DETAILED DESCRIPTION OF EMBODIMENTS

[0151] Figures 1 to 16 have been described further above and will not be discussed again.

[0152] Figure 17 shows an exemplary block diagram of a transmitter 300 in accordance with embodiments of the second aspect of the present invention. The transmitter 300 comprises a microprocessor 350, a volatile memory 352, a non-volatile memory 354, a wireless interface circuitry 356 configured for communicating with a receiver, by transmitting electromagnetic signals via multiple antennas 306. The aforementioned elements are communicatively connected via one or more signal or data connections or buses 358. The non-volatile memory 354 stores computer program instructions which, when executed by the microprocessor 350, cause the transmitter 300 to execute the method according to the first aspect of the present invention as presented herein.

[0153] Figure 18 shows an exemplary flow diagram of a method in accordance with the second aspect of the invention of operating a first wireless communication device 300 in accordance with the third aspect of the invention. The first wireless communication device 300 is wirelessly connected to a plurality of second wireless communication devices 400 in a MU-MIMO RSMA communication system. In step 502 a generating process in accordance with the first aspect of the invention is executed. Alternatively, in step 504, precoding and combining parameters Vc, V*, Uc.*, U* determined in accordance with said generating process are received. In step 506 at least the precoding and combining parameters Vc, V*, UC(*, L’A are provided to a precoder of the first communication device 300, and in step 508 at least the combining parameters Uc>*, U* are provided to each of the plurality of second wireless devices 400, to which messages are to be transmitted. In step 508 the messages to be transmitted to one or more from the plurality of second wireless communication devices 400 are split into respective common signal parts scand private signal parts sk and are provided to the precoder 302. Precoder 302 precodes, in step 510, each of the private signal parts sk and the common signal parts sc, for obtaining transmission signals for each of a plurality of antennas of the first wireless communication device 300. Finally, the precoded transmission signals are transmitted in step 512.

[0154] LIST OF REFERENCE NUMERALS (PART OF THE DESCRIPTION)

[0155] 10 resource allocation processing 270 combine the intermediate block precoding and / or combining

[0156] 12 optimisation block matrices and the optimised pc

[0157] 14a, b intermediate and pP / feprecoding / combining matrix 280 output the final precoding and / or generating block combining matrices

[0158] 16 combiner block

[0159] 300 base station

[0160] 100 channel decomposition method 302 precoder

[0161] 102 execution triggered? 304 BF design / beamformer

[0162] 110 initialise square matrix 4C306 antenna

[0163] 120 compute diagonal matrix Cc k308 channel estimator

[0164] 130 compute rectangular unitary 350 microprocessor matrix BCik352 volatile memory

[0165] 140 Initialise diagonal matrix Cp fc354 non-volatile memory

[0166] 150 compute rectangular unitary 356 wireless interface circuitry matrix B„ p, / kc 358 data / signal line / bus

[0167] 160 compute square matrix 4p399 feedback link

[0168] 400 UE

[0169] 402 antenna

[0170] 404a, b combiner

[0171] 200 resource allocation method

[0172] 406 detector

[0173] 202 receive input signals / values

[0174] 408 signal decoder (common)

[0175] 210 compute intermediate

[0176] 410 IC precoding / combining matrices

[0177] 412 signal decoder (private)

[0178] 220 initialise optimisation block

[0179] 230 update auxiliary variables

[0180] 240 iterative alternating convex

[0181] 500 method of operating first optimisation wireless device

[0182] 250 termination criterion met?

[0183] 502 execute methods 100 & 200

[0184] 260 output optimised pcand pPjkto the combiner block receive precoding and 508 split messages into private combining parameters Vc, Vk, and common parts Vc,k, U* 510 precode private and common provide precoding and parts combining parameters Vc, Vk, 512 transmit UC(*, U* to precoder

Claims

CLAIMS1 . A method (100) of generating precoding and / or combining parameters (Vc, Vk, Uc.*, U*) for wireless interfaces of a first (300) and a second (400) communication device, respectively, the first wireless communication device (300) being configured for wireless communication with a plurality of second communication devices (400) in a MU-MIMO RSMA communication system, the method comprising, for determining the precoding and / or combining parameters (Vc, Ucjt) of the common part:- performing a first decomposition (110-130) of the estimated channel tensor comprising the channel matrices (H*) for all second communication devices (400) into the product of a matrix (Ac) common to all second communication devices (400), into a rectangular unitary matrix (Bc,*) for each individual second communication device (400), and a diagonal matrix (Cc,*) representing channel spaces occupied by each individual second communication device (400), further comprising, for determining the precoding and / or combining parameters (V*, U*) of the private part:- performing a second decomposition (140 -160) of the estimated channel tensor comprising the channel matrices (EL) for all second communication devices (400) into the product of a matrix (Ap) common to all second communication devices (400), into a rectangular unitary matrix (Bp,*) for each individual second communication device (400), and a diagonal matrix (Cp. / £) representing channel spaces occupied by each individual second communication device (400), wherein the first and the second decomposition (110-130; 140-160) differ in at least the diagonal matrices (Cc,*, Cp,*), and further comprising:- providing the outputs of the first and the second decomposition (110-130; 140-160) to a beamforming (BF) phase design process (200-280) targeted to optimise the common and private message parts of signals to be transmitted over multiple antennas in accordance with a previously selected objective, and -outputting the precoding matrices (Vc, V*) to a precoder, for accordingly precoding common and private message parts of signals to be transmittedand / or outputting at least the combining matrix (UC,A, U*) to a compression stage, for transmission to one or more second communication devices (400).

2. The method (100) of claim 1 , further comprising denoising the channel matrices (HA) prior to performing the first and / or second decompositions (110- 130; 140-160).

3. The method (100) of claim 2, wherein denoising comprises averaging a number of estimated channel matrices (Hk) over a coherent interval of channel fading.

4. The method (100) of any one or more of claims 1 to 3, wherein the first and second decomposition (110-130; 140-160) and / or the beamforming design process (200) are triggered in response to changes in the number of second communication devices (400) being served by a first communication device (300) exceeding a predetermined threshold.

5. Method (500) of operating a first wireless communication device (300) wirelessly connected to a plurality of second wireless communication devices (400) in a MU-MIMO RSMA communication system, comprising:- executing (504a) the generating process (100) in accordance with one or more of claims 1 to 4, or receiving (504b) precoding and combining parameters (Vc, V*, Uft*, U*) determined in accordance with one or more of claims 1 to 4,- providing (506) at least the precoding and combining parameters (Vc, V*, Uft*, Ut) to a precoder (302) of the first communication device (300) and at least the combining parameters (Uc,*, U*) to each of the plurality of second wireless devices (400), to which messages are to be transmitted,- splitting (508) messages to be transmitted to one or more from the plurality of second wireless communication devices (400) into respective common parts and private parts and providing the split messages to the precoder (302),- precoding (510) each of the private parts and the common parts, for obtaining transmission signals for each of a plurality of antennas of the firstwireless communication device (300), and- transmitting (512) the precoded transmission signals.

6. The method (500) of claim 5, further comprising- receiving (502), as an input to the executing step (504a), estimated channel coefficient matrices (Hjt) and data on the error statistics thereof, for all communication channels between the first communication device (300) and the second communication devices (400).

7. The method (500) of claim 6, wherein receiving (502) comprises determining the estimated channel coefficient matrices (H / <) and data on the error statistics thereof at the first wireless communication device (300), or receiving said information from the respective second wireless communication devices (400).

8. A wireless communication device (300) comprising one or more microprocessors (350), volatile (352) and non-volatile (354) memory, a wireless interface circuitry (356) configured for transmitting electromagnetic signals via multiple antennas (306), wherein the non-volatile memory (354) stores computer program instructions which, when executed by the microprocessor (352), configure the wireless device (300) to execute the method of one or more of claims 1 to 4 or 5 to 7.

9. Computer program product comprising computer program instructions which, when executed by a microprocessor (352) of a wireless communication device configured as a transmitter (300), cause the microprocessor (352) to execute methods and to accordingly control hardware components (356) of the transmitter (300) of an RSMA MU-MIMO communication system in accordance with one or more of claims 1 to 4 or 5 to 7.

10. Computer readable medium or data carrier retrievably transmitting or storing the computer program product of claim 9.

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