Semi-Gridless Variational Bayes Channel Estimation in XL-MIMO: Near-Field Modeling and Inference

Extremely large antenna arrays and high-frequency operation are two key technologies that advance performance metrics such as higher data rates, lower latency, and wider coverage in sixth-generation communications. However, the adoption of these technologies fundamentally changes the characteristics of wavefronts, forcing communication systems to operate in the near-field region. The transition from planar far-field communications to spherical near-field propagation necessitates novel channel estimation algorithms to fully exploit the unique features of spherical wavefronts for advanced transceiver design. To this end, we propose a novel semi-gridless channel estimation approach based on a variational Bayesian (VB) inference framework. Specifically, we reformulate the near-field channel model for both uniform linear arrays and uniform planar arrays into separate direction-of-arrival (DoAs) and distance components. Building on these new representations, we employ a gridless approach for DoAs estimation using a von Mises distribution, and a coarse-to-fine grid search for distance estimation. We then develop a semi-gridless variational Bayesian (SG-VB) algorithm with efficient update rules that enables accurate channel reconstruction. Simulation results validate the effectiveness of the proposed SG-VB algorithm, demonstrating enhanced near-field channel reconstruction accuracy and superior estimation performance for both DoAs and distance components embedded in near-field channels.

Robust SAC-Enabled UAV-RIS Assisted Secure MISO Systems With Untrusted EH Receivers

This paper investigates secure downlink transmission in a UAV-assisted reconfigurable intelligent surface (RIS)-enabled multiuser multiple-input single-output network, where legitimate information-harvesting receivers coexist with untrusted energy-harvesting receivers (UEHRs) capable of eavesdropping. A UAV-mounted RIS provides blockage mitigation and passive beamforming, while the base station employs zero-forcing precoding for multiuser interference suppression. Due to limited feedback from UEHRs, their channel state information (CSI) is imperfect, leading to a worst-case secrecy energy efficiency (WCSEE) maximization problem. We jointly optimize the UAV horizontal position, RIS phase shifts, and transmit power allocation under both perfect and imperfect CSI, considering discrete RIS phases, UAV mobility, and energy-harvesting constraints. The resulting problem is highly nonconvex due to coupled channel geometry, robustness requirements, and discrete variables. To address this challenge, we propose a soft actor-critic (SAC)-based deep reinforcement learning framework that learns WCSEE-maximizing policies through interaction with the wireless environment. As a structured benchmark, a successive convex approximation (SCA) approach is developed for the perfect CSI case with continuous RIS phases. Simulation results show that the proposed SAC method achieves up to 28% and 16% secrecy energy efficiency gains over SCA and deep deterministic policy gradient baselines, respectively, while demonstrating superior robustness to CSI uncertainty and stable performance across varying transmit power levels and RIS sizes.

Variational Bayesian Channel Estimation and Data Detection for Cell-Free Massive MIMO with Low-Resolution Quantized Fronthaul Links

We study the joint channel estimation and data detection (JED) problem in a cell-free massive multiple-input multiple-output (CF-mMIMO) network, where access points (APs) communicate with a central processing unit (CPU) over fronthaul links. However, the bandwidth of these links is limited, and thus, presents challenges to the applicability of CF-mMIMO, especially with an ever-increasing number of users. To address this, we propose a method based on variational Bayesian (VB) inference for performing the JED process, where the APs forward low-resolution quantized versions of the signals to the CPU. We consider two approaches: \emph{quantization-and-estimation} (Q-E) and \emph{estimation-and-quantization} (E-Q). In the Q-E approach, each AP uses a low-bit quantizer to quantize the signal before forwarding it to the CPU, while in the E-Q approach, each AP first performs local channel estimation and then sends a low-bit quantized version of the estimated channel to the CPU. We evaluate the performance of our VB-based approach under perfect fronthaul link (PFL) with unquantized received signals, Q-E, and E-Q in terms of symbol error rate (SER), normalized mean square error (NMSE) of the channel estimation, computational complexity, and fronthaul signaling overhead. We also compare these results with those of the linear minimum mean squared error (LMMSE) method under the PFL scenario. Our numerical results show that both the VB(Q-E) and VB(E-Q) approaches achieve superior performance compared to LMMSE(PFL), benefiting from the nonlinear modeling inherent in VB. Furthermore, the VB(Q-E) method outperforms VB(E-Q) due to errors in the local channel estimation process at the APs within the VB(E-Q) approach.

Variational Bayesian Inference for Time-Varying Massive MIMO Channels: Estimation and Detection

Massive multiple-input multiple-output (MIMO) stands as a key technology for advancing performance metrics such as data rate, reliability, and spectrum efficiency in the fifth generation (5G) and beyond of wireless networks. However, its efficiency depends greatly on obtaining accurate channel state information. This task becomes particularly challenging with increasing user mobility. In this paper, we focus on an uplink scenario in which a massive MIMO base station serves multiple high-mobility users. We leverage variational Bayesian(VB) inference for joint channel estimation and data detection(JED), tailored for time-varying channels. In particular, we use the VB framework to provide approximations of the true posterior distributions. To cover more real-world scenarios, we assume the time correlation coefficients associated with the channels are unknown. Our simulations demonstrate the efficacy of our proposed VB-based approach in tracking these unknown time correlation coefficients. We present two processing strategies within the VB framework: online and block processing strategies. The online strategy offers a low-complexity solution for a given time slot, requiring only the knowledge of the parameters/statistics within that time slot. In contrast, the block processing strategy focuses on the entire communication block and processes all received signals together to reduce channel estimation errors. Additionally, we introduce an interleaved structure for the online processing strategy to further enhance its performance. Finally, we conduct a comparative analysis of our VB approach against the linear minimum mean squared error(LMMSE), the Kalman Filter(KF), and the expectation propagation(EP) methods in terms of symbol error rate(SER) and channel normalized mean squared error(NMSE). Our findings reveal that our VB framework surpasses these benchmarks across the performance metrics.

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.