IRS-Assisted Rate-Splitting Multiple Access for Overloaded Multiuser MISO Transmission

An intelligent reflecting surface (IRS)-assisted rate-splitting multiple access (RSMA) system is proposed in this paper for overloaded multiuser multiple-input single-output (MISO) transmission with imperfect channel state information at the transmitter (CSIT). In this proposed system, the weighted minimum mean square error (WMMSE)-based approach and alternative optimization (AO) framework are adopted in order to solve the weighted sum-rate (WSR) problem in RSMA transmission with partial CSIT. In this work, both phase-shifting and beam-forming matrices are iteratively optimized until convergence. The performance of time partitioning RSMA (TP-RSMA) and power partitioning RSMA (PP-RSMA) in terms of the sum-rate is also examined for the purpose of fair comparison. Simulation results showed that the proposed IRS-assisted RSMA systems provide a significant performance gain over the conventional non-IRS-assisted systems. This gain increases with increasing the number of antennas, users and IRS reflecting elements.


I. INTRODUCTION
With the deployment of the fifth generation (5G) networks in different regions across the globe, the research focus has shifted towards ultra-reliable low-latency communications (URLLC) and the development of the next generation of wireless communications.One option is the rate-splitting multiple access (RSMA) technique which has attracted the attention of many researchers as a multiple access technique that will be crucial for the sixth generation (6G) wireless networks.It allows multiple users to access the same frequency band simultaneously without causing interference [1].RSMA has been proposed as a solution for the increasing demand for high data rate and low latency in 6G wireless communications.It is a promising approach for addressing the challenges of the spectrum being a limited resource and interference management in the next-generation of cellular networks.The main idea behind RSMA technique is to divide the user messages into common and private parts, where the former parts being encoded into common streams and the latter being encoded into private streams.It is important to mention that the private streams only require the corresponding users to decode them, while the common streams require multiple users to do so.As a result, RSMA technique offers a flexible interference management feature that enables partial decoding and partial treatment of the interference as a noise [2].
Another option that has gained widespread popularity for 6G networks is the intelligent reflecting surface (IRS).The IRS technology has recently gained wide attention as a promising new technology to intelligently enhance the performance of 6G wireless systems [3], [4].It consists of an array of electronically controlled reflecting elements that can be used to manipulate the wireless environment in a way that is beneficial to the link between the transmitter and receiver [5], [6].
It is demonstrated in the literature that IRS and RSMA can be integrated to address some challenges for future wireless communication systems and can lead to significant improvements in the overall system performance, e.g., [7], [8].These two promising technologies were investigated in most of the existing literature individually and successfully provided efficient solutions to some challenges.In the past few years, tremendous efforts have been made to use RSMA in IRS-aided systems.For example, the authors in [7] explored the potential advantages of combining RSMA and IRS in their research.They found that IRS can increase the flexibility in the precoding design and make RSMA more resistant to errors in successive interference cancellation (SIC), while RSMA can help improve the performance of IRS even when the channel state information (CSI) is not perfect.The authors in [9] proposed the use of RSMA in conjunction with IRS to improve the performance of a multiple-input single-output (MISO) broadcast channel.In this work, the beamforming vectors at the base station (BS) and the scattering matrix of the fully-connected IRS are jointly designed to maximize the sum-rate of the network.They proposed an efficient algorithm to optimize the beamforming and scattering matrices in an iterative manner.In addition, the authors in [10] presented a novel RSMA scheme for IRS-aided multiuser MISO communication systems, while the authors in [11] proposed a two-layer hierarchical rate splitting (2L-HRS) technique for an IRS-aided multiuser MISO downlink communication system.These two research works examined the performance of rate-splitting techniques in IRS-aided communication systems in terms of the outage probability and demonstrated that the proposed schemes outperform the traditional non-RSMA schemes in a multiuser system.In another work [12], the authors analyzed the potential of RSMA for enabling the 6G communications through the use of IRS.They provided an in-depth analysis of the transmitter side of IRS-aided RSMA networks for multiple near and cell-edge users, and compared it with the IRS-assisted non-orthogonal multiple access (NOMA) system in terms of the weighted sum-rate (WSR) with perfect and imperfect CSI at the transmitter (CSIT) cases.In [13], an IRS-aided MISO downlink communication system is considered, and its objective was to maximize the WSR of all users by jointly designing the beamforming at the BS and the phase vector of the IRS elements.More recently, the authors in [14] investigated the use of RSMA in multiple-input multiple-output (MIMO) IRSassisted overloaded network with a number of users is larger than the number of transmit/receive antennas and proposed a general framework for RSMA.This framework can be applied to solve a variety of optimization problems in MIMO IRS-assisted interference-limited networks, such as weightedminimum rate and WSR maximization.
In light of the foregoing discussion, the potential of integrating IRS into RSMA technique for overloaded downlink multiuser MISO system is proposed, where a single connected IRS-aided RSMA system is considered with imperfect CSIT.The scattering matrix of IRS and the transmit beamformers of RSMA are jointly optimized in order to maximize the sumrate.In addition, an alternative optimization (AO) framework is considered where the scattering matrix of IRS and the beamformers of RSMA are iteratively optimized as shown in [13].Numerical results showed that integrating IRS technology into RSMA for overloaded multiuser MISO transmission with imperfect CSIT provides a large achievable sum-rate improvement compared to the conventional system model.
The rest of this paper is divided into three sections as follows.In Section II, the system model of the proposed IRSassisted RSMA for overloaded multiuser MISO transmission is presented, and the simulation results and discussions are provided in Section III.Finally, the paper is concluded in Section IV with some possible future research directions.

II. SYSTEM MODEL
Consider a multiuser MISO communication system consisting of one BS equipped with M antennas to simultaneously serve a set of K > M single-antenna users through one IRS comprises of N REF reflecting elements as depicted in Fig. 1.In this system model, the users are divided into two groups indexed by K α = {1, 2, . . ., M } and K 0 = {M + 1, . . ., K} [15].A smart controller is attached to the IRS in order to serve as a gateway for information sharing between the BS and the IRS, and to adjust and determine the reconfigurable impedance network of IRS.Let h r,k ∈ C NREF×1 , k ∈ K, and G ∈ C NREF×M denote the channels from the IRS to the users, and from the BS to the IRS, respectively, while the direct path between the BS and the users is denoted by h d,k ∈ C M ×1 , with assuming that all these channels experience quasi-static flat-fading.In addition, the diagonal phase-shifting matrix, Θ ∈ C NREF×NREF , is defined as Θ = diag e jφ1 , . . ., e jφn , . . ., e jφ N REF , where e jφn is the phase of the n-th passive element with (e jφ1 , . . ., e jφn , . . ., e jφ N REF ) being its diagonal elements.
In this system model, the users in K α are served by linearlyprecoded rate-splitting scheme, where the corresponding message W k for each user k is split into a common part denoted by W c,k and a private part denoted by W p,k .The common parts are then combined into one common message denoted by W c , while the M + 1 resulting messages, W c , W p,1 , . . ., W p,M , are encoded into the independent Gaussian data streams {s c } , {s 1 } , . . ., {s M }, respectively.The M + 1 streams that can be described by the vector s α ≜ [s c , s 1 , . . ., s M ] T are linearly precoded using the digital precoding matrix ) .On the other hand, the users in K 0 are served in an orthogonal multiple access fashion, where each k-th user is allocated a fraction θ 0,k of the phase duration, such that k∈K0 θ 0,k = 1.In this corresponding, it is assumed in this paper that uniform time allocation is considered among 0-users, i.e., θ 0,k = 1 K−M .Moreover, the power partitioning RSMA (PP-RSMA) is considered to jointly treat the two set of users, K α and K 0 .Specifically, the transmit signal is found by superimposing the signals intended to both 0-user and α-users where s k is the data stream of the k-th user in K 0 satisfying the constraint E |s k | 2 = 1, the stream s 0 is time shared amongst 0-users, and p 0 denotes the precoding vector that satisfying the constraint ∥p 0 ∥ 2 ≤ P , where P is the signalto-noise ratio (SNR).
If the transmit symbol to the k-th user in the proposed IRSassisted RSMA system is denoted by b k , which is considered as an independent random variable with zero mean and unit variance, i.e., CN (0, 1), and the corresponding transmit beamforming matrix is denoted by W = [w 0 , w 1 , . . ., w K ] ∈ C M ×(K+1) , the transmitted signal at the BS is given by where T denote the corresponding transmit beamforming vector and the data stream vector for all streams, respectively.Additionally, the transmit power constraint of the BS is where P t is the maximum transmit power of the BS.The total signal received at the k-th user is expressed as where n k ∼ CN 0, σ 2 0 denotes the additive noise at the k-th user, and H eff,k is the effective channel matrix for user k.
As described in [15], a perfect CSI is available at the BS.In this paper, it is considered that H eff,k = Ĥeff,k + E k , where Ĥeff,k is the estimate of the effective channel for the k-th user, and E k is the estimation error matrix at the transmitter.It is assumed in this paper that Ĥeff,k and E k are uncorrelated, with zero mean and covariance matrices 1 − σ 2 k I and σ 2 k I, respectively, where I is the identity matrix and σ 2 k ≤ 1 is the CSIT error variance.This variance decays with increasing the SNR as O (P −α k ) for all k ∈ K α , and O(1) for all k ∈ K 0 , where the exponent α k ∈ [0, 1] is the CSIT quality.It is worth mentioning that α k = 0 for no-CSIT and α k = 1 for perfect CSIT in a degrees-of-freedom (DoF) sense.In this paper, the partial CSIT is considered to be available for M of the K users, (i.e., α k > 0), where it is assumed that all these users have the same quality.On the other hand, no-CSIT is assumed to be available for the remaining K − M users, (i.e., α k = 0).In addition, time partitioning RSMA (TP-RSMA) and PP-RSMA that presented in [15] are considered in this paper.
The following subsections provide a description of the problem formulation to jointly optimize the phase-shifting matrix of IRS and the beamforming matrix of RSMA, and a description of the optimization algorithm is also presented.

A. Problem Formulation
In the proposed system, the common stream is first decoded by each user where all private streams are treated as interference.As a result, the signal-to-interference-plus-noise ratio (SINR) of the common message s 0 at the k-th user is expressed as and the transmission rate of decoding the common message can be found as R 0,k = log 2 (1 + γ 0,k ).The achievable transmission rate of the common message should satisfy R 0 = min k∈K R 0,k for the sake of ensuring that all users are able to successfully decode the common message s 0 .
After decoding s 0 , the common stream is removed from the received signal by employing SIC at each user, and then the desired private stream is decoded with the following SINR and the corresponding rate of decoding the private message can be found as Then, the message of each k-th user can be reconstructed by combining both the sub-message that decoded from the common stream, W c,k , and the sub-message that decoded from the private stream, W p,k .The aim of this work is to jointly optimize the diagonal phase-shifting matrix of IRS, Θ, and the beamforming matrix of RSMA, W, for the sake of maximizing the achievable sumrate.The sum-rate problem for the downlink single-connected IRS-aided RSMA system can be written as This non-convex optimization problem is a joint beamforming matrix and IRS phase-shifting matrix problem, and the constraint (tr WW H ≤ P t ) is the transmit power constraint at the BS.
Since the beamformers and the phase-shifting matrix are coupled with each other in multiple factional expressions for the SINR, an AO framework is considered in this paper to solve P 1 [13].This problem is decomposed into two subproblems that are solved iteratively until they reach a point of convergence.The first sub-problem is considered as the beamforming design which is solved by the weighted minimum mean square error (WMMSE)-based approach, while the second sub-problem is for the phase-shifting matrix that is directly solved by the quasi-Newton algorithm [9].
The effective channel matrix from the BS and the IRS to the k-th user in ( 4)-( 6), (h H d,k + h H r,k ΘG), can be denoted as g H k for ease of notation.Thus, problem P 1 can be reduced to to be solved by the WMMSE algorithm [16] as follows.Let the equalizers that are used to estimate s 0 and s k be denoted by e 0,k and e k , respectively, and ŝ0,k = e 0,k y k and ŝk = e k y k − g H k w 0 ŝ0,k denote the estimate of s 0 and s k at the k-th user, respectively.Thus, decoding of s 0 and s k results in the following mean square errors (MSEs) and ) respectively, where ε 0,k and ε k are the MSE of decoding s 0 and s k , respectively, P 0,k = K i=0 g H k w i 2 +σ 2 k is the average power of the received signal, while is the signal average power after removing the common stream.
The following MMSE equalizers to estimate s 0 and s k can be obtained by setting ∂ε 0,k /∂e 0,k and ∂ε k /∂e k to zero, respectively [9] e MMSE 0,k and By substituting ( 11) into ( 9), the MMSE of decoding s 0 can be represented by and similarly substituting ( 12) into (10) gives the MMSE of decoding s k as Then, the SINR of the common message s 0 at the k-th user, and the SINR corresponding to the private message s k can be written as In this corresponding, the transmission rates of the common and private streams are given by The sum-rate problem, however, cannot be solved using the aforementioned logarithmic relationships.To address this issue, the augmented MMSEs are introduced as (17) where λ 0,k and λ k denote the auxiliary weights for the rate-WMMSE relationships of R 0,k and R k , respectively.By setting ∂ξ 0,k ∂λ 0,k = 0 and ∂ξ k ∂λ k = 0, the optimum weights can be found as follows By substituting ( 9), ( 10) and ( 18) into ( 17), the rate-WMMSE relationships can be found as Thus, P 2 is transformed into the following WMMSE problem where λ = [λ 0,1 , . . ., λ 0,K , λ 1 , . . ., λ K ] T denotes the weight vector, e = [e 0,1 , . . ., e 0,K , e 1 , . . ., e K ] T denotes the equalizer vector, and ξ 0 = max k∈K ξ 0,k .Since P 3 is still a non-convex problem, an AO framework is used in this paper in order to decompose it into three sub-problems that are convex.For each block, only one of W, λ and e is optimized while the other two blocks are fixed.

C. Phase-shifting Matrix Optimization
Similarly, problem P 1 can be simplified to the following form for a given beamforming design W The constraints on the non-convex matrix equality make it challenging to transform problem P 4 into a convex problem.As a result, P 4 can be rewritten as where X ∈ R is the reactance matrix of the reconfigurable impedance network in IRS, which is a symmetric real matrix, Z 0 is a reference impedance, N REF is the number of ports in a reconfigurable impedance network, n = 1, 2, . . ., N REF , and x n ∈ R is the reconfigurable reactance component that is connected to the n-th port in the N REF -port single-connected IRS that requires to tune only N REF scattering parameters [9].By substituting Θ = (jX + Z 0 I) −1 (jX − Z 0 I) into (P 5 ) max X K k=0 R k , and removing the constraint X = diag{x 1 , . . ., x n , . . ., x NREF } by defining X as a symmetric matrix, problem P 5 is transformed into an optimization problem without constraints.This kind of unconstrained optimization problems can be solved by the quasi-Newton method [17].

III. SIMULATION RESULTS
To validate the effectiveness of the proposed IRS-assisted RSMA system for overloaded multiuser MISO transmission, simulation results are provided in this section.In this paper, two settings are considered.In the first setting, the BS is equipped with 2 antennas to support 3 single-antenna users (K = 3) through an IRS composed of N REF passive elements, while in the second one the BS is equipped with 4 antennas to serve 5 users (K = 5).The users in these two settings are distributed randomly within a circle with its center at (200 m, 30 m) and radius of 10 m, and the BS is located at the origin, (0 m, 0 m).The IRS is deployed at (200 m, 0 m), and the positions of all users are fixed after being randomly generated.In the proposed system, the IRS is applied to create a high-quality connection between the BS and users, with assuming that the channel between the BS and IRS and the channel between IRS and each mobile user have the line of sight (LOS) components.In addition, the IRS-aided channels, G and h r,k , follow Rician fading, while the direct channel link, h d,k , follows Rayleigh fading.It is also assumed that a half-wavelength uniform linear array (ULA) configuration is formed by the antenna array elements at the BS and the IRS, and as a result, the channels G and h r,k are modelled by where L 1 and L 2,k are the corresponding path-losses, ε denotes the Rician factor which is set in this paper as ε = 10, a is the steering vector, while ϑ, ψ and ς k are the angular parameters.In addition, G and h r,k are the non-line of sight (NLOS) components whose elements follow the distribution of zero mean and unit variance, CN (0, 1).According to the aforementioned assumption, it is necessary to estimate only the small-scale fading channels, h d,k , G, and h r,k , in each frame.The path-loss as a function of the distance d (in m) for G and h r,k is modelled as 35.6 + 22.0 log 10 (d) (dB), while for h d,k it is considered as 32.6+36.7 log 10 (d) (dB).It is also assumed that the reference impedance of IRS is Z 0 = 50 Ω, the convergence tolerance is 10 −3 , the transmission bandwidth is set as 180 KHz, and the noise power spectral density is considered as -170 dBm/Hz.Fig. 2 shows the sum-rate performance against the SNR of users 1 and 2 of IRS-assisted PP-RSMA and IRS-assisted TP-RSMA schemes employing M = 2 antennas, N REF = 64 reflecting elements and serving K = 3 users.In contrast, the sum-rate performance of the same schemes with N REF = 128 passive elements is shown in Fig. 3.It is clear from these two figures that the proposed IRS-aided RSMA schemes outperform the conventional schemes without IRS, and the SNR gain of all schemes is about 5 dB and 6 dB to achieve the same sum-rate performance with N REF = 64 and 128 reflecting elements, respectively.
The sum-rate performance of IRS-assisted PP-RSMA and IRS-assisted TP-RSMA schemes employing M = 4 antennas and supporting K = 5 users is shown in Figs. 4 and 5, with N REF = 64 and 128 reflecting elements, respectively.These two figures show that the proposed IRS-aided RSMA schemes outperform the conventional schemes without IRS, and the SNR gain of all schemes is about 8 dB and 9 dB with N REF = 64 and 128 reflecting elements, respectively.In addition, at the SNR value of 40 dB, IRS-assisted PP-RSMA scheme with 10 dB, IRS-assisted PP-RSMA scheme with 20 dB and IRSassisted TP-RSMA scheme with N REF = 64 passive elements outperform the conventional schemes without IRS by almost 5.5 bps/Hz, 5.5 bps/Hz and 3.5 bps/Hz, respectively.On the

IV. CONCLUSIONS
In this paper, an IRS-assisted RSMA system for overloaded multiuser MISO transmission with imperfect CSIT is proposed.It is demonstrated from the simulation results of the proposed IRS-aided RSMA system that the sum-rate performance of the multiuser multi-antenna networks increases significantly.In addition, it is found that the SNR gain in the proposed IRS-assisted RSMA schemes increases as the number of reflecting elements increases, and also improves as the number of transmit antennas and mobile users increases.Our future work will focus on multi-IRS-assisted RSMA with large number of users, and deploying simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) in the proposed system model will be also considered.
WS19 IEEE ICC 2023 5th Workshop on ULMC6GN -Ultra-high speed, Low latency and Massive Communication for futuristic 6G Networks 1507 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
WS19 IEEE ICC 2023 5th Workshop on ULMC6GN -Ultra-high speed, Low latency and Massive Communication for futuristic 6G Networks 1508Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.