A robust interference alignment algorithm in a MIMO interference channel

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.

This paper focuses on optimal transmit power allocation to maximize the overall system throughput in a vehicle-to-everything (V2X) communication system. We propose two methods for solving the power allocation problem namely the weighted minimum mean square error (WMMSE) algorithm and the deep learning-based method. In the WMMSE algorithm, we solve the problem using block coordinate descent (BCD) method. Then we adopt supervised learning technique for the deep neural network (DNN) based approach considering the power allocation from the WMMSE algorithm as the target output. We exploit an efficient implementation of the mini-batch gradient descent algorithm for training the DNN. Extensive simulation results demonstrate that the DNN algorithm can provide very good approximation of the iterative WMMSE algorithm reducing the computational overhead significantly.

As the potential candidate of next generation communication networks, rate splitting multiple access (RSMA) has drawn great attentions. Usually to maximize the sum rate of RSMA, weighted minimum mean square error (WMMSE) algorithm is often used. But its computational complexity hinders its practical application. In this paper, we apply a deep learning network called Deep Unfolding (DU) to RSMA in Satellite-Terrestrial Integrated Network (STIN) with the intention of boosting downlink capacity. The momentum accelerated projection gradient descent (PGD) algorithm is adopted to substitute the complex operations and speed up the computations. By selecting the momentum and step size as the trainable parameters, the simulation results indicate that the deep learning approach outperforms the original WMMSE algorithm in sum rate and speed.

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.

Maximizing the weighted sum-rate (WSR) in downlink multi-user multiple-input multipleoutput (MU-MIMO) systems remains computationally challenging due to the prohibitive complexity of classical weighted minimum mean square error (WMMSE) algorithms. In this article, we propose a novel low-complexity WMMSE (LC-WMMSE) precoding method specifically designed for massive MU-MIMO downlink systems. Our algorithm introduces a hybrid switching approach that adaptively blends standard WMMSE updates with computationally simpler approximations derived via the Woodbury matrix identity, coupled with an adaptive damping mechanism to ensure robust and stable convergence. Simulation results demonstrate that the proposed LC-WMMSE method achieves WSR performance comparable to classical WMMSE but with significantly reduced computational complexity, making it particularly suitable for practical implementation for massive MUMIMO systems.

A coordinated beamforming scheme in distributed antenna systems (DASs) used for energy efficient transmission is developed. In this paper, a dynamic circuit power consumption is considered which varies with the sum rate. The major problem is non-convex of the optimization problem and is difficult to solve directly due to the fractional form. It is transformed into an equivalent subtractive-form optimization problem, by which we tackle this problem through a two-layer optimization algorithm. The out layer problem is solved by using one dimension search method while the inner-layer sub-problem is solved with an optimal beamforming algorithm. The simulations illustrate that the proposed algorithm outperform the weighted minimum mean square error (WMMSE) algorithm.

A novel interference alignment (IA) scheme based on the errors-in-variables (EIV) mathematic model has been proposed to overcome the channel state information (CSI) estimation error for the MIMO interference channels. By solving an equivalently unconstrained optimization problem, the proposed IA scheme employing a weighted total least squares (WTLS) algorithm can obtain the solution to a constrained optimization problem for transmit precoding (TPC) matrices and minimizes the distortion caused by imperfect CSI according to the EIV model. It is shown that the design of TPC matrices can be realized through an efficient iterative algorithm. The convergence of the proposed scheme is presented as well. Simulation results show that the proposed IA scheme is robust over MIMO interference channels with imperfect CSI, which yields significantly better sum rate performance than the existing IA schemes such as distributed iterative IA, maximum signal-to-interference-plus-noise ratio (Max SINR), and minimum mean square error (MMSE) schemes.

Rate splitting multiple access (RSMA) has emerged as a promising technique in multi-antenna downlink transmissions, which jointly encodes the private and common messages into a common stream for removing part of interference incurred by signal multiplexing and improving the spectral efficiency. Due to the decodability constraint of the common message at each user, the precoder optimization is non-convex, which lacks efficient algorithms. For facilitating the practical implementation of RSMA in future wireless networks, e.g., massive multiple-input multiple-output (MIMO), we propose an alternating direction method of multipliers (ADMM)-induced iterative algorithm to optimize the precoder, where the precoder is optimized for maximizing the sum rate at multiple users under the decod-ability constraint of the common message. Specifically, we first employ the weighted minimum mean square error (WMMSE) algorithm to transform the non-convex problem into a sequence of convex problems, and then the ADMM algorithm is adopted to decouple the optimization variables and obtain solutions of each subproblem in closed form. Numerical results demonstrate that the proposed algorithm not only can achieve almost the same performance as existing WMMSE-based algorithms, but also has a faster convergence rate and lower computational complexity.

Considering virtual cell clusters formed by several overlapping virtual cells in ultra dense network (UDN), virtual cells which are in the same virtual cell cluster coordinate transmissions to reduce inter-virtual cell interference. However, general beamforming scheme design for channel state information (CSI) demand still remains large, and system overhead for high-dimensional channel training and channel state information feedback is explosively-increased. To solve this problem, this paper focuses on hierarchical beamforming scheme based on virtual cell cluster. Specifically, based on perfect intra-cluster CSI, beamforming direction vector is designed by optimizing the achievable rate of each cluster with Zero-Forming block diagonalization method. Based on the large-scale inter-cluster CSI, the strength of beamforming can be devised by solving the sum rate maximization problem and mitigating the residual co-channel interference among different clusters with an iterative power allocation algorithm via a generalized weighted minimum mean square error (WMMSE) approach. Simulation results demonstrate that the proposed scheme achieves significant performance gain and requires less CSI than traditional schemes.

Rate-Splitting Multiple Access (RSMA) has recently appeared as a powerful and robust multiple access and interference management strategy for downlink Multi-user (MU) multi-antenna communications. In this work, we study the precoder design problem for RSMA scheme in downlink MU systems with both perfect and imperfect Channel State Information at the Transmitter (CSIT) and assess the role and benefits of transmitting multiple common streams. Unlike existing works which have considered single-antenna receivers (Multiple-Input Single-Output–MISO), we propose and extend the RSMA framework for multi-antenna receivers (Multiple-Input Multiple-Output–MIMO) and formulate the precoder optimization problem with the aim of maximizing the Weighted Ergodic Sum-Rate (WESR). Precoder optimization is solved using Sample Average Approximation (SAA) together with the proposed vectorization and Weighted Minimum Mean Square Error (WMMSE) based approach. Achievable sum-Degree of Freedom (DoF) of RSMA is derived for the proposed framework as an increasing function of the number of transmitted common and private streams, which is further validated by the Ergodic Sum Rate (ESR) performance using Monte Carlo simulations. Conventional MU–MIMO based on linear precoders and Non-Orthogonal Multiple Access (NOMA) schemes are considered as baselines. Numerical results show that with imperfect CSIT, the sum-DoF and ESR performance of RSMA is superior to those of the two baselines, and is increasing with the number of transmitted common streams. Moreover, by better managing the interference, RSMA not only has significant ESR gains over baseline schemes but is more robust to CSIT inaccuracies, network loads and user deployments.

In existing works of deep learning-based resource allocation, the scalability degrades heavily with the increase of network complexity, which is due to their limited learning ability of shallow neural networks and insufficient knowledge of network. Nowadays, to address the growth of cell density, cooperative beamforming in user-centric network (UCN) is emerged, where the additional degrees of freedom of multi-antenna and cell coordination aggravate the challenges. This letter proposes a deep residual learning framework, UcnBeamNet, to enhance the ability of approximating the iterative algorithm for sum rate maximization, where multi-branch subnets are connected in parallel to extract extra information. Specifically, a weighted minimum mean square error (WMMSE)-based algorithm is derived to determine the optimal clusters and beamforming matrices; then UcnBeamNet is trained to learn the input-output mapping and provide direct insight of UCN from association matrices in addition to plural inputs. Extensive experiments demonstrate UcnBeamNet still reaches 90.38% sum-rate relative to conventional algorithm even with a large network size, and achieves more than 50, $000\times $ speed up in computational efficiency.

This paper proposes an inverse reinforcement learning (IRL)-based method to optimize power allocation for multiuser cellular networks. An optimization problem is formulated to maximize the achievable sum information rate of all receivers. In contrast to traditional reinforcement learning (RL)-based methods, the proposed IRL-based one does not require to design the reward function manually, which is able to determine the reward function efficiently and automatically from the expert policy. The weighted minimum mean square error (WMMSE) method is used to serve as an expert policy to obtain the reward function, and the action space and state space are designed. Simulation results show that the proposed IRL-based method achieves about 99 % of the sum information rate achieved by the pure WMMSE method, but the running time of the proposed IRL-based one is about 1/19 of that required of pure WMMSE method.

We consider a downlink multiuser MISO system with bounded errors in the Channel State Information at the Transmitter (CSIT). We first look at the robust design problem of achieving max-min fairness amongst users (in the worst-case sense). Contrary to the conventional approach adopted in literature, we propose a rather unorthodox design based on a Rate-Splitting (RS) strategy. Each user's message is split into two parts, a common part and a private part. All common parts are packed into one super common message encoded using a public codebook, while private parts are independently encoded. The resulting symbol streams are linearly precoded and simultaneously transmitted, and each receiver retrieves its intended message by decoding both the common stream and its corresponding private stream. For CSIT uncertainty regions that scale with SNR (e.g. by scaling the number of feedback bits), we prove that a RS-based design achieves higher max-min (symmetric) Degrees of Freedom (DoF) compared to conventional designs (NoRS). For the special case of non-scaling CSIT (e.g. fixed number of feedback bits), and contrary to NoRS, RS can achieve a non-saturating max-min rate. We propose a robust algorithm based on the cutting-set method coupled with the Weighted Minimum Mean Square Error (WMMSE) approach, and we demonstrate its performance gains over state-of-the art designs. Finally, we extend the RS strategy to address the Quality of Service (QoS) constrained power minimization problem, and we demonstrate significant gains over NoRS-based designs.

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.

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.