Downlink beamforming is a key technology for cellular networks. However, computing the transmit beamformer that maximizes the weighted sum rate subject to a power constraint is an NP-hard problem. As a result, iterative algorithms that converge to a local optimum are used in practice. Among them, the weighted minimum mean square error (WMMSE) algorithm has gained popularity, but its computational complexity and consequent latency has motivated the need for lower-complexity approximations at the expense of performance. Motivated by the recent success of deep unfolding in the trade-off between complexity and performance, we propose the novel application of deep unfolding to the WMMSE algorithm for a MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE algorithm into trainable neural network layers, whose architecture reflects the structure of the original algorithm. With respect to traditional end-to-end learning, deep unfolding naturally incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the formulation of the WMMSE algorithm, as described in Shi et al., is not amenable to be unfolded due to a matrix inversion, an eigendecomposition, and a bisection search performed at each iteration. Therefore, we present an alternative formulation that circumvents these operations by resorting to projected gradient descent. By means of simulations, we show that, in most of the settings, the unfolded WMMSE outperforms or performs equally to the WMMSE for a fixed number of iterations, with the advantage of a lower computational load.
We consider minimum mean square error (MMSE) joint precoder and combiner design for single and multi carrier distributed beamforming systems with nonuniform per-antenna transmit power constraints. We show that, similar to the maximum-gain problem, an iterative Gauss-Seidel algorithm can be used for minimizing MSE which alternately optimizes the transmitter and receiver coefficients. In a single carrier system the optimum transmit coefficients are obtained by a simple projection of the effective MISO channel. In the multicarrier case with a sum-MSE objective, the Gauss-Seidel approach is once a…
In this paper, we investigate an intelligent reflecting surface (IRS) assisted multi-user multiple-input multiple-output (MIMO) full-duplex (FD) system. We jointly optimize the active beamforming matrices at the access point (AP) and uplink users, and the passive beamforming matrix at the IRS to maximize the weighted sum-rate of the system. Since it is practically difficult to acquire the channel state information (CSI) for IRS-related links due to its passive operation and large number of elements, we conceive a mixed-timescale beamforming scheme. Specifically, the high-dimensional passive be…
In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division…
In limited feedback multi-user multiple-input multiple-output (MU-MIMO) cellular networks, users send quantized information about the channel conditions to the associated base station (BS) for downlink beamforming. However, channel quantization and beamforming have been treated as two separate tasks conventionally, which makes it difficult to achieve global system optimality. In this paper, we propose an augmented deep unfolding (ADU) approach that jointly optimizes the beamforming scheme at the BSs and the channel quantization scheme at the users. In particular, the classic WMMSE beamformer i…
In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital (AD) beamforming can be used to attain a high directional gain without requiring a dedicated radio frequency (RF) chain for each antenna element, which substantially reduces both the hardware costs and power consumption. While massive MIMO transceiver design typically relies on the conventional mean-square error (MSE) criterion, directly minimizing the symbol error rate (SER) can lead to a superior performance. In this paper, we first mathematically formulate the problem of hybrid transceiver design under the minim…
An Accelerated Mixed Weighted-Unweighted MMSE Approach for MU-MIMO Beamforming
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；Shenzhen International Center for Industrial and Applied Mathematics, Shenzhen Research Institute of Big Data, China（深圳大数据研究院工业与应用数学国际中心）；School of Data Science, The Chinese University of Hong Kong, Shenzhen, China（香港中文大学（深圳）数据科学学院）
Hybrid beamforming (HBF) is a key enabler for wideband terahertz (THz) massive multiple-input multiple-output (mMIMO) communications systems. A core challenge with designing HBF systems stems from the fact their application often involves a non-convex, highly complex optimization of large dimensions. In this paper, we propose HBF schemes that leverage data to enable efficient designs for both the fully-connected HBF (FC-HBF) and dynamic sub-connected HBF (SC-HBF) architectures. We develop a deep unfolding framework based on factorizing the optimal fully digital beamformer into analog and digit…
Linear hybrid beamformer designs are conceived for the decentralized estimation of a vector parameter in a millimeter wave (mmWave) multiple-input multiple-output (MIMO) Internet of Things network (IoTNe). The proposed designs incorporate both total IoTNe and individual IoTNo power constraints, while also eliminating the need for a baseband receiver combiner at the fusion center (FC). To circumvent the non-convexity of the hybrid beamformer design problem, the proposed approach initially determines the minimum mean square error (MMSE) digital transmit precoder (TPC) weights followed by a simul…
In this paper, we consider hybrid beamforming designs for multiuser massive multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems. Aiming at maximizing the weighted spectral efficiency, we propose one alternating maximization framework where the analog precoding is optimized by Riemannian manifold optimization. If the digital precoding is optimized by a locally optimal algorithm, we obtain a locally optimal alternating maximization algorithm. In contrast, if we use a weighted minimum mean square error (MMSE)-based iterative algorithm for digital precod…
The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for real-time implementation. In our previous work, we considered the MU-MISO case and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case. Our earlier approach does not generalize to this scenario and cannot be applied to re…
Nagoya Institute of Technology（名古屋工业大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Multicast beamforming is a promising technique for multicast communication. Providing an efficient and powerful beamforming design algorithm is a crucial issue because multicast beamforming problems such as a max-min-fair problem are NP-hard in general. Recently, deep learning-based approaches have been proposed for beamforming design. Although these approaches using deep neural networks exhibit reasonable performance gain compared with conventional optimization-based algorithms, their scalability is an emerging problem for large systems in which beamforming design becomes a more demanding tas…
Xihua University（西华大学）；Synopsys Inc.（新思科技公司）；University of Electronic Science and Technology of China（电子科技大学）
Massive multiple-input multiple-output (MIMO) with frequency division duplex (FDD) mode is a promising approach to increasing system capacity and link robustness for the fifth generation (5G) wireless cellular systems. The premise of these advantages is the accurate downlink channel state information (CSI) fed back from user equipment. However, conventional feedback methods have difficulties in reducing feedback overhead due to significant amount of base station (BS) antennas in massive MIMO systems. Recently, deep learning (DL)-based CSI feedback conquers many difficulties, yet still shows in…
Leveraging the available millimeter wave spectrum will be important for 5G. In this work, we investigate the performance of digital beamforming with low resolution ADCs based on link level simulations including channel estimation, MIMO equalization and channel decoding. We consider the recently agreed 3GPP NR type 1 OFDM reference signals. The comparison shows sequential DCD outperforms MMSE-based MIMO equalization both in terms of detection performance and complexity. We also show that the DCD based algorithm is more robust to channel estimation errors. In contrast to the common believe we al…
This paper considers the multi-group multicast beamforming optimization problem, for which the optimal solution has been unknown due to the non-convex and NP-hard nature of the problem. By utilizing the successive convex approximation numerical method and Lagrangian duality, we obtain the optimal multicast beamforming solution structure for both the quality-of-service (QoS) problem and the max-min fair (MMF) problem. The optimal structure brings valuable insights into multicast beamforming: We show that the notion of uplink-downlink duality can be generalized to the multicast beamforming probl…
Owing to the unique advantages of low cost and controllability, reconfigurable intelligent surface (RIS) is a promising candidate to address the blockage issue in millimeter wave (mmWave) communication systems, consequently has captured widespread attention in recent years. However, the joint active beamforming and passive beamforming design is an arduous task due to the high computational complexity and the dynamic changes of wireless environment. In this paper, we consider a RIS-assisted multi-user multiple-input single-output (MU-MISO) mmWave system and aim to develop a deep reinforcement l…
In the sixth-generation (6G) cellular networks, hybrid beamforming would be a real-time optimization problem that is becoming progressively more challenging. Although numerical computation-based iterative methods such as the minimal mean square error (MMSE) and the alternative manifold-optimization (Alt-Min) can already attain near-optimal performance, their computational cost renders them unsuitable for real-time applications. However, recent studies have demonstrated that machine learning techniques like deep neural networks (DNN) can learn the mapping done by those algorithms between channe…
Energy Efficiency Maximization for Hybrid RIS-Aided Communications via Deep Unfolding
University of Oulu（奥卢大学）；CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Université Paris-Saclay（法国国家科学研究中心、中央苏黎世高等师范学院、信号系统实验室、巴黎萨克雷大学）；King’s College London（伦敦国王学院）
Attention-Based SINR Estimation in User-Centric Non-Terrestrial Networks
Department of Electrical, Electronic, and Information Engineering (DEI), Univ. of Bologna（电子、电气与信息工程系，博洛尼亚大学）；National Inter-University Consortium for Telecommunications (CNIT), Bologna, Italy（电信跨大学联合体（CNIT），博洛尼亚，意大利）
Southeast University（东南大学）；National Sun Yat-sen University（国立中山大学）；Georgia Institute of Technology（佐治亚理工学院）
Channel estimation and signal detection are very challenging for an orthogonal frequency division multiplexing (OFDM) system without cyclic prefix (CP). In this article, deep learning based on orthogonal approximate message passing (DL-OAMP) is used to address these problems. The DL-OAMP receiver includes a channel estimation neural network (CE-Net) and a signal detection neural network based on OAMP, called OAMP-Net. The CE-Net is initialized by the least square channel estimation algorithm and refined by minimum mean-squared error (MMSE) neural network. The OAMP-Net is established by unfoldi…
