A Hybrid Low-Complexity WMMSE Precoder with Adaptive Damping for Massive Multi-User Multiple-Input Multiple- Output Systems

This paper considers a multi-user multiple-input multiple-output (MU-MIMO) system where the downlink communication between a base station (BS) and multiple user equipments (UEs) is aided by a reconfigurable intelligent surface (RIS). We study the sum rate maximization problem with the objective of finding the optimal precoding vectors and RIS configuration. Due to fronthaul limitation, each entry of the precoding vectors must be picked from a finite set of quantization labels. Furthermore, two scenarios for the RIS are investigated, one with continuous infinite-resolution reflection coefficients and another with discrete finite-resolution reflection coefficients. A novel framework is developed which, in contrast to the common literature that only offers sub-optimal solutions for optimization of discrete variables, is able to find the optimal solution to problems involving discrete constraints. Based on the classical weighted minimum mean square error (WMMSE), we transform the original problem into an equivalent weighted sum mean square error (MSE) minimization problem and solve it iteratively. We compute the optimal precoding vectors via an efficient algorithm inspired by sphere decoding (SD). For optimizing the discrete RIS configuration, two solutions based on the SD algorithm are developed: An optimal SD-based algorithm and a low-complexity heuristic method that can efficiently obtain RIS configuration without much loss in optimality. The effectiveness of the presented algorithms is corroborated via numerical simulations where it is shown that the proposed designs are remarkably superior to the commonly used benchmarks.

This paper considers a lens antenna array-assisted millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) system. The base station's beam selection matrix and user terminals' phase-only beamformers are jointly designed with the aim of maximizing the uplink sum rate. In order to deal with the formulated mixed-integer optimization problem, a penalty dual decomposition (PDD)-based iterative algorithm is developed via capitalizing on the weighted minimum mean square error (WMMSE), block coordinate descent (BCD), and minorization-maximization (MM) techniques. Moreover, a low-complexity sequential optimization (SO)-based algorithm is proposed at the cost of a slight sum rate performance loss. Numerical results demonstrate that the proposed methods can achieve higher sum rates than state-of-the-art methods.

Precoding techniques, particularly linear precoding, are widely employed in multiple-input multiple-output (MIMO) systems. Although well-studied in the literature, linear precoding design still faces two fundamental challenges: high computational complexity and the lack of a general design approach. This paper presents an efficient and unified framework for linear precoding design in downlink multiuser systems that accommodates diverse criteria, such as weighted sum rate (WSR) maximization and weighted symbol error rate (WSER) minimization, while ensuring quality of service (QoS) requirements. The proposed framework achieves an order-of-magnitude reduction in per-iteration computational complexity compared to existing methods. In particular, by accurately characterizing the feasible signal-to-interference-plus-noise ratio (SINR) region, we transform the high-dimensional precoding design problem into a more manageable, low-dimensional SINR allocation problem. We propose an efficient SINR-based precoding (SBP) framework that employs a water-filling solution at each iteration, without the need for matrix inversion. The proposed framework can be extended to broadcast and interference channels with multi-antenna users under pre-fixed receivers. Simulation results demonstrate that our method achieves near-optimal performance while significantly reducing computational complexity compared to existing methods, such as the weighted minimum mean square error (WMMSE) method.

In this paper, we investigate the transmit beamforming design for weighted sum-rate maximization in massive multiple-input multiple-output (MIMO) downlink systems. Currently, the most popular algorithm for this scenario is the weighted minimum mean square error (WMMSE) algorithm. We propose a two-stage majorization-minimization (MM) based beamforming (dubbed TMMBF) which transforms the weighted sum-rate maximization problem into a quadratic convex problem by utilizing the MM method twice. The proposed algorithm converges to a stationary point of the weighted sum-rate maximization problem. Interestingly, we find that the WMMSE algorithm is a special case of the TMMBF algorithm, thus unifying the WMMSE algorithm into the MM framework for the first time. In addition, the surrogate function of TMMBF is tighter than that of WMMSE, resulting in faster convergence of the TMMBF algorithm. The simulation results on 3GPP channel models generated from Quadriga show that the TMMBF algorithm has better performance and faster numerical convergence compared to the WMMSE algorithm.

The sum rate maximization problem in Interference Alignment (IA) is hard to be solved, for the sum rate function is non-convex. The Weighted Minimum Mean Square Error (WMMSE) algorithm settles this problem by converting the original problem into an equivalent convex one. In this paper, an enhanced version of the WMMSE algorithm is presented, which takes the statistical information of the channel estimation error into consideration. Simulation results show that this algorithm has better performance than the original WMMSE algorithm and another distributed IA algorithm. Furthermore, the impact of time varying error caused by Doppler Shift is also investigated.

Direct communication between satellites and terminals, known as direct-to-cell (D2C), is currently in the developmental stage and has become one of the key focuses of satellite communications. However, with the increase of orbital altitude, the aperture size of phased array antennas adopted by low-earth-orbit (LEO) satellite grows, introducing excessively complex hardware requirements. Meanwhile, the beam reconfiguration capability of reflectors adopted by geostationary-orbit (GEO) satellites are limited, making it challenging to meet the D2C demands of non-geostationary orbit (NGSO) satellites due to the mobility of both satellites and terminals. In this letter, we utilize the phased array fed reflector (PAFR), which offers dynamic beamforming capability and reduced hardware complexity advantages, and propose the corresponding beamforming mathematical model. We analyze the relation between the weighted sum rate and the weighted minimum mean square error (WMMSE) within this architecture, and design an iterative beamforming optimization method based on the WMMSE criterion that converges to a local optimal solution. Simulation results demonstrate that the proposed method achieves performance comparable to that of a fully connected structure with an equivalent aperture phased array, while offering superior energy efficiency.

<p>This thesis considers the analysis of current and future cellular communication systems. The main focus is on multiuser multiple-input multiple-output (MU-MIMO) antenna systems. The goal of this work is to characterize the achievable spectral efficiency of MU-MIMO systems, as well as to analyze the performance of practical, linear MU-MIMO transceiver structures in heterogeneous propagation environments. The analytical derivations in this thesis are based on the mathematical theory of finite and large dimensional random matrices. A collection of new general random matrix theory results, which permit efficient numerical evaluation are derived. With downlink regularized zero-forcing (RZF) processing at a cellular base station (BS), a general framework for the analysis of the expected (average) signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency is developed for uncorrelated and semi-correlated Rayleigh fading, as well as uncorrelated Ricean fading propagation channels. In contrast to existing results, the presented analyses are extremely general, applicable to single-cellular, multi-cellular, as well as distributed antenna systems. These systems could consist of arbitrary numbers of transmit and receive antennas, link signal-to-noise-ratios (SNRs), equal and unequal transmit correlation structures, and line-of-sight (LoS) levels, respectively. Numerical results are presented for single-cellular, as well as for two-tier multi-cellular systems demonstrating the impact of novel BS coordination strategies to suppress dominant inter-cellular interference. With dominant LoS directions in the propagation channel, the instantaneous downlink zero-forcing (ZF) SNR of a given terminal is analyzed. The ZF SNR is shown to be approximated by a gamma distribution for any number of transmit and receive antennas, link SNRs, and LoS levels. Furthermore, for moderately sized MU-MIMO systems, simplified instantaneous and ergodic sum spectral efficiency analyses are presented with RZF, ZF and matched-filter (MF) transmission on the downlink, and minimum-mean-squared-error, ZF and maximum-ratio combining (MRC) on the uplink, respectively. The simple nature of the derived expressions lead to the discovery of several valuable system level insights as a function of the contributing network parameters. Numerical results are presented for conventional and moderate MU-MIMO systems. Considering downlink semi-correlated Rayleigh fading channels with spatial correlation at the BS, it is mathematically proven that common correlation patterns for each terminal predicts lower ergodic sum spectral efficiencies in comparison to terminal specific correlation patterns. Closed-form approximations for the expected SINR and ergodic sum spectral efficiency are derived for both MF and ZF precoding, demonstrating the sensitivity of unequal correlation structures on the expected signal, interference and noise powers, respectively. The presented numerical results provide a cautionary tale of the impact of unequal correlation patterns on MU-MIMO performance and the importance of modeling this phenomenon. Finally, an approximate uplink performance analysis of large MU-MIMO systems with MRC and space-constrained uniform linear antenna arrays (ULA) is presented for semi-correlated Ricean fading channels. A space-constrained channel model is proposed, encapsulating the effects of unequal receive spatial correlation, unequal LoS levels, and unequal link gains for each terminal. The per-terminal and cell-wide ergodic sum spectral efficiencies are characterized and numerous practical special cases are presented. A limiting analysis of the ergodic per-terminal and cell-wide spectral efficiencies is also carried out, as the number of BS antennas grow without bound with a finite number of terminals and fixed physical dimensions of the ULA. Numerical results demonstrate the impact of space-constrained ULAs on the MU-MIMO system performance with variation in the LoS levels, correlation structures, physical array dimensions, and system size, respectively.</p>

Numerical optimization has been investigated for decades to solve complex problems in wireless communication systems. This has resulted in many effective methods, e.g., the weighted minimum mean square error (WMMSE) algorithm. However, these methods often incur a high computational cost, making their application to time-constrained problems difficult. Recently data-driven methods have attracted a lot of attention due to their near-optimal performance with affordable computational cost. Deep reinforcement learning (DRL) is one of the most promising optimization methods for future wireless communication systems. In this paper, we investigate the DRL method, using a deep Q-network (DQN), to allocate the downlink transmission power in cell-free (CF) mmWave massive multiple-input multiple-output (MIMO) systems. We consider the sum spectral efficiency (SE) optimization for systems with mobile user equipment (UEs). The DQN is trained by the rewards of trial-and-error interactions with the environment over time. It takes as input the long-term fading information and it outputs the downlink transmission power values. The numerical results, obtained for a particular 3GPP scenario, show that DQN outperforms WMMSE in terms of sum-SE and has a much lower computational complexity.

Expressions are derived for the coverage probability and average rate of both multi-user multiple input multiple output (MU-MIMO) and single input multiple output (SIMO) systems in the context of a fractional frequency reuse (FFR) scheme. In particular, given a reuse region of $\frac{1}{3}$ (FR3) and a reuse region of 1 (FR1) as well as a signal-to-interference-plus-noise-ratio (SINR) threshold $S_{th}$ , which decides the user assignment to either the FR1 or FR3 regions, we theoretically show that: $1)$ the optimal choice of $S_{th}$ which maximizes the coverage probability is $S_{th} = T$ , where $T$ is the target SINR required for ensuring adequate coverage, and $2)$ the optimal choice of $S_{th}$ which maximizes the average rate is given by $S_{th}= T^{\prime}$ , where $T^{\prime}$ is a function of the path loss exponent, the number of antennas and of the fading parameters. The impact of frequency domain correlation amongst the OFDM sub-bands allocated to the FR1 and FR3 cell-regions is analysed and it is shown that the presence of correlation reduces both the coverage probability and the average throughput of the FFR network. Furthermore, the performance of our FFR-aided MU-MIMO and SIMO systems is compared. Our analysis shows that the (2 $\times$ 2) MU-MIMO system achieves 22.5% higher rate than the (1 $\times$ 3) SIMO system and for lower target SINRs, the coverage probability of a (2 $\times$ 2) MU-MIMO system is comparable to a (1 $\times$ 3) SIMO system. Hence the former one may be preferred over the latter. Our simulation results closely match the analytical results.

In multi-user millimeter wave (mmWave) multiple input multiple output (MIMO) systems, obtaining accurate information/knowledge regarding the channel state is crucial to achieving multi-user interference cancellation and reliable beamforming (BF)–to compensate for severe path loss. This knowledge is nonetheless very challenging to acquire in practice since large antenna arrays experience a low signal-to-noise ratio (SNR) before BF. In this paper, a multi-user channel estimation (CE) scheme namely generalized-block compressed sampling matching pursuit (G-BCoSaMP), is proposed for multi-user mmWave MIMO systems over frequency selective fading channels. This scheme exploits the cluster-structured sparsity in the angular and delay domain of mmWave channels determined by the actual spatial frequencies of each path. As the corresponding spatial frequencies of multi-user mmWave MIMO systems with Hybrid BF often fall between the discrete Fourier transform (DFT) bins due to the continuous Angle of Arrival (AoA)/Angle of Departure (AoD), the proposed G-BCoSaMP algorithm can address the resulting power leakage problem. Simulation results show that the proposed algorithm is effective and offer a better CE performance in terms of MSE when compared to the generalized block orthogonal matching pursuit (G-BOMP) algorithm that does not possess a pruning step.

This paper considers weighted sum rate maximization constrained with a per base station (BS) antenna power problem for multiuser multiple-input multiple-output (MIMO) systems. For this problem, we propose new downlink-uplink duality based solution. We solve the problem as follows. First, by introducing additional optimization variables, we reformulate our problem into an equivalent problem that incorporates a weighted sum mean-square-error (MSE) term. Second, we establish novel weighted sum MSE duality. The duality is established by modifying the input covariance matrix of the dual uplink problem, and formulating the noise covariance matrix of the uplink channel as a fixed point function. Third, we optimize the introduced variables and powers in the downlink channel by a Geometric Program (GP) method. Fourth, using the duality result and the solution of GP, we apply alternating optimization technique to solve the original downlink problem. In our simulation results, we have observed that the proposed duality based solution utilizes less power than that of existing algorithms.

In this paper, we discuss the influence of feedback channel delay on throughput of linear multi-user multiple-input multiple-output (MIMO) systems employing vector quantization (VQ) algorithms for encoding channel state information (CSI). We consider an approach where the mobile receiver estimates the downlink channel and chooses one of the predefined channel characterization codewords whose indices are transmitted back to the base station transmitter. In practice, the feedback channel introduces delay in transmission of the indices and we evaluate the resulting channel throughput loss for different system setups. Moreover, we define two new parameters of VQ MIMO systems: the channel eigenmode coherence time and singular value coherence time, and discuss their influence on system design. We demonstrate the performance of two types of systems, one using time division multiplexing of individual mobile users and another transmitting to multiple users at the same time. The simulation results show that feedback delay sensitivity of the multiple-user system throughput is much higher than in the TDM approach. Based on those results we propose a simple method allowing a selection of the VQ resolution for the given channel characteristics and system setup.

Multiple input multiple output (MIMO) systems have high potential to achieve maximum channel capacity in wireless communication systems. Multi-user (MU) MIMO network with transmit antennas $$T_x$$ at base station can schedule as many single antenna users in one time slot. This necessitates incorporation of a user scheduling strategy. Maximizing sumrate performance without under utilization of channel resources is a primary objective of such scheduling algorithms. Another key design factor for such techniques is to optimize fairness i.e. allowing equal opportunity to all communicating entities. In this paper, we present a simple approach to solve the scheduling problem in MU-MIMO systems while addressing the conflicting objectives of sumrate and fairness. Two variants of the proposed method are also discussed that provide options for maximizing the cumulative sumrate and improving the fairness. Simulations validate the proposed algorithm as a better choice over other conventional methods as it achieves optimal performance with relatively less computational complexity and without compromising fairness. Fairness results are verified by average sumrate method and Jain’s Fariness Index.

In this paper, we consider the precoder design for an under-loaded or critically loaded downlink multi-user multiple-input multiple-output (MU-MIMO) communication system. We propose novel precoding and decoding schemes which enhance system performance based on rate splitting at the transmitter and single-stage successive interference cancellation at the receivers. The proposed successive null-space (SNS) precoding scheme utilizes linear combinations of the null-space basis vectors of the successively augmented MIMO channel matrices of the users as precoding vectors to adjust the inter-user-interference experienced by the receivers. We formulate a non-convex weighted sum rate (WSR) optimization problem, and solve it via successive convex approximation to obtain a suboptimal solution for the precoding vectors and the associated power allocation. Our simulation results reveal that the proposed SNS precoders outperform block diagonalization based linear and rate splitting designs, and in many cases, have a relatively small gap to the maximum sum rate achieved by dirty paper coding.

Multi-user multiple input multiple output (MU-MIMO) system is an excellent choice for the next generation broadband communications because of its great potential in enhancing MIMO system capacity. One major challenge of such system is the jointly optimal transceiver beamforming design that maximizes the sum capacity under a total power constraint. Existing approaches have provided convex optimization solution by exploiting the duality between transmitter and receiver. However, with high computation complexity, these approaches are ineligible of practical implementation. In this paper, we aim to provide complexity efficient transceiver beamformer and power allocation design in MU-MIMO downlink (broadcast) channels. We first develop an iterative sub-optimal algorithm based on cyclic self-SINR-maximization (CSSM) beamforming design and water-filling power allocation. Comparing to convex-optimization-based (COB) approaches, the proposed solution (i.e. CSSM-WF algorithm) have insignificant sum-rate degradation but very low computational complexity and extremely fast converging speed. Trying to improve the performance of CSSM-WF algorithm, we then introduce another algorithm denoted as efficient COB (ECOB) algorithm in which CSSM-WF algorithm is used to generate a good start point for optimal COB approaches. Simulation results prove the efficiency of both proposed algorithms.