Data-Aided Regularization of Direct-Estimate Combiner in Distributed MIMO Systems

This paper explores the data-aided regularization of the direct-estimate combiner in the uplink of a distributed multiple-input multiple-output system. The network-wide combiner can be computed directly from the pilot signal received at each access point, eliminating the need for explicit channel estimation. However, the sample covariance matrix of the received pilot signal that is used in its computation may significantly deviate from the actual covariance matrix when the number of pilot symbols is limited. To address this, we apply a regularization to the sample covariance matrix using a shrinkage coefficient based on the received data signal. Initially, the shrinkage coefficient is determined by minimizing the difference between the sample covariance matrices obtained from the received pilot and data signals. Given the limitations of this approach in interference-limited scenarios, the shrinkage coefficient is iteratively optimized using the sample mean squared error of the hard-decision symbols, which is more closely related to the actual system's performance, e.g., the symbol error rate (SER). Numerical results demonstrate that the proposed regularization of the direct-estimate combiner significantly enhances the SER, particularly when the number of pilot symbols is limited.

Enhanced Sparse Bayesian Learning Methods with Application to Massive MIMO Channel Estimation

We consider the problem of sparse channel estimation in massive multiple-input multiple-output systems. In this context, we propose an enhanced version of the sparse Bayesian learning (SBL) framework, referred to as enhanced SBL (E-SBL), which is based on a reparameterization of the original SBL model. Specifically, we introduce a scale vector that brings extra flexibility to the model, which is estimated along with the other unknowns. Moreover, we introduce a variant of E-SBL, referred to as modified E-SBL (M-E-SBL), which is based on a computationally more efficient parameter estimation. We compare the proposed E-SBL and M-E-SBL with the baseline SBL and with a method based on variational message passing (VMP) in terms of computational complexity and performance. Numerical results show that the proposed E-SBL and M-E-SBL outperform the baseline SBL and VMP in terms of mean squared error of the channel estimation in all the considered scenarios. Furthermore, we show that M-E-SBL produces results comparable with E-SBL with considerably cheaper computations.

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.

Digital and Hybrid Precoding Designs in Massive MIMO with Low-Resolution ADCs

Low-resolution analog-to-digital converters (ADCs) have emerged as an efficient solution for massive multiple-input multiple-output (MIMO) systems to reap high data rates with reasonable power consumption and hardware complexity. In this paper, we study precoding designs for digital, fully connected (FC) hybrid, and partially connected (PC) hybrid beamforming architectures in massive MIMO systems with low-resolution ADCs at the receiver. We aim to maximize the spectral efficiency (SE) subject to a transmit power budget and hardware constraints on the analog components. The resulting problems are nonconvex and the quantization distortion introduces additional challenges. To address them, we first derive a tight lower bound for the SE, based on which we optimize the precoders for the three beamforming architectures under the majorization-minorization framework. Numerical results validate the superiority of the proposed precoding designs over their state-of-the-art counterparts in systems with low-resolution ADCs, particularly those with 1-bit resolution. The results show that the PC hybrid precoding design can achieve an SE close to those of the digital and FC hybrid precoding designs in 1-bit systems, highlighting the potential of the PC hybrid beamforming architectures.

Uplink Transmit Power Optimization for Distributed Massive MIMO Systems with 1-Bit ADCs

This paper addresses the problem of uplink transmit power optimization in distributed massive multiple-input multiple-output systems, where remote radio heads (RRHs) are equipped with 1-bit analog-to-digital converters (ADCs). First, in a scenario where a single RRH serves a single user equipment (UE), the signal-to-noise-and-distortion ratio (SNDR) is shown to be a non-monotonic and unimodal function of the UE transmit power due to the quantization distortion (QD). Upon the introduction of multiple RRHs, adding properly tuned dithering at each RRH is shown to render the SNDR at the output of the joint receiver unimodal. In a scenario with multiple RRHs and UEs, considering the non-monotonic nature of the signal-to-interference-plus-noise-and-distortion ratio (SINDR), both the UE transmit powers and the RRH dithering levels are jointly optimized subject to the min-power and max-min-SINDR criteria, while employing Bussgang-based maximum ratio combining (BMRC) and minimum mean squared error (BMMSE) receivers. To this end, gradient and block coordinate descent methods are introduced to tune the UE transmit powers, whereas a line search coupled with gradient updates is used to adjust the RRH dithering levels. Numerical results demonstrate that jointly optimizing the UE transmit power and the RRH dithering levels can significantly enhance the system performance, thus facilitating joint reception from multiple RRHs across a range of scenarios. Comparing the BMMSE and BMRC receivers, the former offers a better interference and QD alleviation while the latter has a lower computational complexity.

Optimality of the Bussgang Linear MMSE Channel Estimator for MIMO Systems with 1-Bit ADCs

In this paper, we study the optimality of the Bussgang linear minimum mean squared error (BLMMSE) channel estimator for multiple-input multiple-output systems with 1-bit analog-to-digital converters. We compare the BLMMSE with the optimal minimum mean squared error (MMSE) channel estimator, which is generally non-linear, and we develop a novel framework based on the orthant probability of a multivariate normal distribution to compute the MMSE channel estimate. Then, we analyze the equivalence of the MMSE and BLMMSE channel estimators under specific assumptions on the channel correlation or pilot symbols. Interestingly, the BLMMSE channel estimator turns out to be optimal in several specific cases. Our study culminates with the presentation of a necessary and sufficient condition for the BLMMSE channel estimator to be optimal.

Hybrid Receiver Design for Massive MIMO-OFDM with Low-Resolution ADCs and Oversampling

Low-resolution analog-to-digital converters (ADCs) and hybrid beamforming have emerged as efficient solutions to reduce power consumption with satisfactory spectral efficiency (SE) in massive multiple-input multiple-output (MIMO) systems. In this paper, we investigate the performance of a hybrid receiver in uplink massive MIMO orthogonal frequency-division multiplexing (OFDM) systems with low-resolution ADCs and oversampling. Considering both the temporal and spatial correlation of the quantization distortion (QD), we derive a closed-form approximation of the frequency-domain QD covariance matrix, which facilitates the evaluation of the system SE. Then we jointly design the analog and baseband combiners to maximize the SE. The formulated problem is significantly challenging due to the constant-modulus constraint of the analog combiner and its coupling with the digital one. To overcome the challenges, we transform the objective function into an equivalent but more tractable form and then iteratively update the analog and digital combiner. Numerical simulations verify the superiority of the proposed algorithm compared to the considered benchmarks and show the resilience of the hybrid receiver to beam squint for low-resolution systems. Furthermore, the results show that the proposed hybrid receiver design with oversampling can achieve significantly higher energy efficiency compared to the digital one.

Joint Beamforming Design and Bit Allocation in Massive MIMO with Resolution-Adaptive ADCs

Low-resolution analog-to-digital converters (ADCs) have emerged as a promising technology for reducing power consumption and complexity in massive multiple-input multiple-output (MIMO) systems while maintaining satisfactory spectral and energy efficiencies (SE/EE). In this work, we first identify the essential properties of optimal quantization and leverage them to derive a closed-form approximation of the covariance matrix of the quantization distortion. The theoretical finding facilitates the system SE analysis in the presence of low-resolution ADCs. We then focus on the joint optimization of the transmit-receive beamforming and bit allocation to maximize the SE under constraints on the transmit power and the total number of active ADC bits. To solve the resulting mixed-integer problem, we first develop an efficient beamforming design for fixed ADC resolutions. Then, we propose a low-complexity heuristic algorithm to iteratively optimize the ADC resolutions and beamforming matrices. Numerical results for a $64 \times 64$ MIMO system demonstrate that the proposed design offers $6\%$ improvement in both SE and EE with $40\%$ fewer active ADC bits compared with the uniform bit allocation. Furthermore, we numerically show that receiving more data streams with low-resolution ADCs can achieve higher SE and EE compared to receiving fewer data streams with high-resolution ADCs.

On the Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems

This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory, the MMSE channel estimator has not been fully investigated in this context due to its general non-linearity and computational complexity. Instead, the typically suboptimal Bussgang linear MMSE (BLMMSE) estimator has been widely adopted. In this work, we develop a new framework to compute the MMSE channel estimator that hinges on computation of the orthant probability of the multivariate normal distribution. Based on this framework, we determine a necessary and sufficient condition for the BLMMSE channel estimator to be optimal and equivalent to the MMSE estimator. Under the assumption of specific channel correlation or pilot symbols, we further utilize the framework to derive analytical expressions for the MMSE channel estimator that are particularly convenient for computation when certain system dimensions become large, thereby enabling a comparison between the BLMMSE and MMSE channel estimators in these cases.

Combined DL-UL Distributed Beamforming Design for Cell-Free Massive MIMO

We consider a cell-free massive multiple-input multiple-output system with multi-antenna access points (APs) and user equipments (UEs), where the UEs can be served in both the downlink (DL) and uplink (UL) within a resource block. We tackle the combined optimization of the DL precoders and combiners at the APs and DL UEs, respectively, together with the UL combiners and precoders at the APs and UL UEs, respectively. To this end, we propose distributed beamforming designs enabled by iterative bi-directional training (IBT) and based on the minimum mean squared error criterion. To reduce the IBT overhead and thus enhance the effective DL and UL rates, we carry out the distributed beamforming design by assuming that all the UEs are served solely in the DL and then utilize the obtained beamformers for the DL and UL data transmissions after proper scaling. Numerical results show the superiority of the proposed combined DL-UL distributed beamforming design over separate DL and UL designs, especially with short resource blocks.