MIMO Detection with Spatial Sigma-Delta ADCs: A Variational Bayesian Approach

The spatial Sigma-Delta ($\Sigma\Delta$) architecture can be leveraged to reduce the quantization noise and enhance the effective resolution of few-bit analog-to-digital converters (ADCs) at certain spatial frequencies of interest. Utilizing the variational Bayesian (VB) inference framework, this paper develops novel data detection algorithms tailored for massive multiple-input multiple-output (MIMO) systems with few-bit $\Sigma\Delta$ ADCs and angular channel models, where uplink signals are confined to a specific angular sector. We start by modeling the corresponding Bayesian networks for the $1^{\mathrm{st}}$- and $2^{\mathrm{nd}}$-order $\Sigma\Delta$ receivers. Next, we propose an iterative algorithm, referred to as Sigma-Delta variational Bayes (SD-VB), for MIMO detection, offering low-complexity updates through closed-form expressions of the variational densities of the latent variables. Simulation results show that the proposed $2^{\mathrm{nd}}$-order SD-VB algorithm delivers the best symbol error rate (SER) performance while maintaining the same computational complexity as in unquantized systems, matched-filtering VB with conventional quantization, and linear minimum mean-squared error (LMMSE) methods. Moreover, the $1^{\mathrm{st}}$- and $2^{\mathrm{nd}}$-order SD-VB algorithms achieve their lowest SER at an antenna separation of one-fourth wavelength for a fixed number of antenna elements. The effects of the steering angle of the $\Sigma\Delta$ architecture, the number of ADC resolution bits, and the number of antennas and users are also extensively analyzed.

User-Centric Beam Selection and Precoding Design for Coordinated Multiple-Satellite Systems

This paper introduces a joint optimization framework for user-centric beam selection and linear precoding (LP) design in a coordinated multiple-satellite (CoMSat) system, employing a Digital-Fourier-Transform-based (DFT) beamforming (BF) technique. Regarding serving users at their target SINRs and minimizing the total transmit power, the scheme aims to efficiently determine satellites for users to associate with and activate the best cluster of beams together with optimizing LP for every satellite-to-user transmission. These technical objectives are first framed as a complex mixed-integer programming (MIP) challenge. To tackle this, we reformulate it into a joint cluster association and LP design problem. Then, by theoretically analyzing the duality relationship between downlink and uplink transmissions, we develop an efficient iterative method to identify the optimal solution. Additionally, a simpler duality approach for rapid beam selection and LP design is presented for comparison purposes. Simulation results underscore the effectiveness of our proposed schemes across various settings.

Doubly 1-Bit Quantized Massive MIMO

Enabling communications in the (sub-)THz band will call for massive multiple-input multiple-output (MIMO) arrays at either the transmit- or receive-side, or at both. To scale down the complexity and power consumption when operating across massive frequency and antenna dimensions, a sacrifice in the resolution of the digital-to-analog/analog-to-digital converters (DACs/ADCs) will be inevitable. In this paper, we analyze the extreme scenario where both the transmit- and receive-side are equipped with fully digital massive MIMO arrays and 1-bit DACs/ADCs, which leads to a system with minimum radio-frequency complexity, cost, and power consumption. Building upon the Bussgang decomposition, we derive a tractable approximation of the mean squared error (MSE) between the transmitted data symbols and their soft estimates. Numerical results show that, despite its simplicity, a doubly 1-bit quantized massive MIMO system with very large antenna arrays can deliver an impressive performance in terms of MSE and symbol error rate.

Variational Bayes Inference for Data Detection in Cell-Free Massive MIMO

Cell-free massive MIMO is a promising technology for beyond-5G networks. Through the deployment of many cooperating access points (AP), the technology can significantly enhance user coverage and spectral efficiency compared to traditional cellular systems. Since the APs are distributed over a large area, the level of favorable propagation in cell-free massive MIMO is less than the one in colocated massive MIMO. As a result, the current linear processing schemes are not close to the optimal ones when the number of AP antennas is not very large. The aim of this paper is to develop nonlinear variational Bayes (VB) methods for data detection in cell-free massive MIMO systems. Contrary to existing work in the literature, which only attained point estimates of the transmit data symbols, the proposed methods aim to obtain the posterior distribution and the Bayes estimate of the data symbols. We develop the VB methods accordingly to the levels of cooperation among the APs. Simulation results show significant performance advantages of the developed VB methods over the linear processing techniques.

Variational Bayes for Joint Channel Estimation and Data Detection in Few-Bit Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) communications using low-resolution analog-to-digital converters (ADCs) is a promising technology for providing high spectral and energy efficiency with affordable hardware cost and power consumption. However, the use of low-resolution ADCs requires special signal processing methods for channel estimation and data detection since the resulting system is severely non-linear. This paper proposes joint channel estimation and data detection methods for massive MIMO systems with low-resolution ADCs based on the variational Bayes (VB) inference framework. We first derive matched-filter quantized VB (MF-QVB) and linear minimum mean-squared error quantized VB (LMMSE-QVB) detection methods assuming the channel state information (CSI) is available. Then we extend these methods to the joint channel estimation and data detection (JED) problem and propose two methods we refer to as MF-QVB-JED and LMMSE-QVB-JED. Unlike conventional VB-based detection methods that assume knowledge of the second-order statistics of the additive noise, we propose to float the noise variance/covariance matrix as an unknown random variable that is used to account for both the noise and the residual inter-user interference. We also present practical aspects of the QVB framework to improve its implementation stability. Finally, we show via numerical results that the proposed VB-based methods provide robust performance and also significantly outperform existing methods.

A Variational Bayesian Perspective on Massive MIMO Detection

Optimal data detection in massive multiple-input multiple-output (MIMO) systems requires prohibitive computational complexity. A variety of detection algorithms have been proposed in the literature, offering different trade-offs between complexity and detection performance. In this paper, we build upon variational Bayes (VB) inference to design low-complexity multiuser detection algorithms for massive MIMO systems. We first examine the massive MIMO detection problem with perfect channel state information at the receiver (CSIR) and show that a conventional VB method with known noise variance yields poor detection performance. To address this limitation, we devise two new VB algorithms that use the noise variance and covariance matrix postulated by the algorithms themselves. We further develop the VB framework for massive MIMO detection with imperfect CSIR. Simulation results show that the proposed VB methods achieve significantly lower detection errors compared with existing schemes for a wide range of channel models.

Leveraging Deep Neural Networks for Massive MIMO Data Detection

Massive multiple-input multiple-output (MIMO) is a key technology for emerging next-generation wireless systems. Utilizing large antenna arrays at base-stations, massive MIMO enables substantial spatial multiplexing gains by simultaneously serving a large number of users. However, the complexity in massive MIMO signal processing (e.g., data detection) increases rapidly with the number of users, making conventional hand-engineered algorithms less computationally efficient. Low-complexity massive MIMO detection algorithms, especially those inspired or aided by deep learning, have emerged as a promising solution. While there exist many MIMO detection algorithms, the aim of this magazine paper is to provide insight into how to leverage deep neural networks (DNN) for massive MIMO detection. We review recent developments in DNN-based MIMO detection that incorporate the domain knowledge of established MIMO detection algorithms with the learning capability of DNNs. We then present a comparison of the key numerical performance metrics of these works. We conclude by describing future research areas and applications of DNNs in massive MIMO receivers.

Deep Learning for Estimation and Pilot Signal Design in Few-Bit Massive MIMO Systems

Estimation in few-bit MIMO systems is challenging, since the received signals are nonlinearly distorted by the low-resolution ADCs. In this paper, we propose a deep learning framework for channel estimation, data detection, and pilot signal design to address the nonlinearity in such systems. The proposed channel estimation and data detection networks are model-driven and have special structures that take advantage of the domain knowledge in the few-bit quantization process. While the first data detection network, namely B-DetNet, is based on a linearized model obtained from the Bussgang decomposition, the channel estimation network and the second data detection network, namely FBM-CENet and FBM-DetNet respectively, rely on the original quantized system model. To develop FBM-CENet and FBM-DetNet, the maximum-likelihood channel estimation and data detection problems are reformulated to overcome the vanishing gradient issue. An important feature of the proposed FBM-CENet structure is that the pilot matrix is integrated into its weight matrices of the channel estimator. Thus, training the proposed FBM-CENet enables a joint optimization of both the channel estimator at the base station and the pilot signal transmitted from the users. Simulation results show significant performance gain in estimation accuracy by the proposed deep learning framework.

Machine Learning-based Reconfigurable Intelligent Surface-aided MIMO Systems

Reconfigurable intelligent surface (RIS) technology has recently emerged as a spectral- and cost-efficient approach for wireless communications systems. However, existing hand-engineered schemes for passive beamforming design and optimization of RIS, such as the alternating optimization (AO) approaches, require a high computational complexity, especially for multiple-input-multiple-output (MIMO) systems. To overcome this challenge, we propose a low-complexity unsupervised learning scheme, referred to as learning-phase-shift neural network (LPSNet), to efficiently find the solution to the spectral efficiency maximization problem in RIS-aided MIMO systems. In particular, the proposed LPSNet has an optimized input structure and requires a small number of layers and nodes to produce efficient phase shifts for the RIS. Simulation results for a 16x2 MIMO system assisted by an RIS with 40 elements show that the LPSNet achieves 97.25% of the SE provided by the AO counterpart with more than a 95% reduction in complexity.

Multi-Agent Reinforcement Learning for Joint Channel Assignment and Power Allocation in Platoon-Based C-V2X Systems

We consider the problem of joint channel assignment and power allocation in underlaid cellular vehicular-to-everything (C-V2X) systems where multiple vehicle-to-infrastructure (V2I) uplinks share the time-frequency resources with multiple vehicle-to-vehicle (V2V) platoons that enable groups of connected and autonomous vehicles to travel closely together. Due to the nature of fast channel variant in vehicular environment, traditional centralized optimization approach relying on global channel information might not be viable in C-V2X systems with large number of users. Utilizing a reinforcement learning (RL) approach, we propose a distributed resource allocation (RA) algorithm to overcome this challenge. Specifically, we model the RA problem as a multi-agent system. Based solely on the local channel information, each platoon leader, who acts as an agent, collectively interacts with each other and accordingly selects the optimal combination of sub-band and power level to transmit its signals. Toward this end, we utilize the double deep Q-learning algorithm to jointly train the agents under the objectives of simultaneously maximizing the V2I sum-rate and satisfying the packet delivery probability of each V2V link in a desired latency limitation. Simulation results show that our proposed RL-based algorithm achieves a close performance compared to that of the well-known exhaustive search algorithm.