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.

Low-complexity Linear Multicast Beamforming for Cache-aided MIMO Communications

A practical and scalable multicast beamformer design in multi-input multi-output~(MIMO) coded caching~(CC) systems is introduced in this paper. The proposed approach allows multicast transmission to multiple groups with partially overlapping user sets using receiver dimensions to distinguish between different group-specific streams. Additionally, it provides flexibility in accommodating various parameter configurations of the MIMO-CC setup and overcomes practical limitations, such as the requirement to use successive interference cancellation~(SIC) at the receiver, while achieving the same degrees-of-freedom~(DoF). To evaluate the proposed scheme, we define the symmetric rate as the sum rate of the partially overlapping streams received per user, comprising a linear multistream multicast transmission vector and the linear minimum mean square error~(LMMSE) receiver. The resulting non-convex symmetric rate maximization problem is solved using alternative optimization and successive convex approximation~(SCA). Moreover, a fast iterative Lagrangian-based algorithm is developed, significantly reducing the computational overhead compared to previous designs. The effectiveness of our proposed method is demonstrated by extensive simulations.

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.

Pilot-Based Uplink Power Control in Single-UE Massive MIMO Systems With 1-Bit ADCs

We propose uplink power control (PC) methods for massive multiple-input multiple-output systems with 1-bit analog-to-digital converters, which are specifically tailored to address the non-monotonic data detection performance with respect to the transmit power of the user equipment (UE). Considering a single UE, we design a multi-amplitude pilot sequence to capture the aforementioned non-monotonicity, which is utilized at the base station to derive UE transmit power adjustments via single-shot or differential power control (DPC) techniques. Both methods enable closed-loop uplink PC using different feedback approaches. The single-shot method employs one-time multi-bit feedback, while the DPC method relies on continuous adjustments with 1-bit feedback. Numerical results demonstrate the superiority of the proposed schemes over conventional closed-loop uplink PC techniques.

Uplink Power Control for Distributed Massive MIMO with 1-Bit ADCs

We consider the problem of uplink power control for distributed massive multiple-input multiple-output systems where the base stations (BSs) are equipped with 1-bit analog-to-digital converters (ADCs). The scenario with a single-user equipment (UE) is first considered to provide insights into the signal-tonoise-and-distortion ratio (SNDR). With a single BS, the SNDR is a unimodal function of the UE transmit power. With multiple BSs, the SNDR at the output of the joint combiner can be made unimodal by adding properly tuned dithering at each BS. As a result, the UE can be effectively served by multiple BSs with 1-bit ADCs. Considering the signal-to-interference-plus-noise-anddistortion ratio (SINDR) in the multi-UE scenario, we aim at optimizing the UE transmit powers and the dithering at each BS based on the min-power and max-min-SINDR criteria. To this end, we propose three algorithms with different convergence and complexity properties. Numerical results show that, if the desired SINDR can only be achieved via joint combining across multiple BSs with properly tuned dithering, the optimal UE transmit power is imposed by the distance to the farthest serving BS (unlike in the unquantized case). In this context, dithering plays a crucial role in enhancing the SINDR, especially for UEs with significant path loss disparity among the serving BSs.

Multi-User Data Detection in Massive MIMO with 1-Bit ADCs

We provide new analytical results on the uplink data detection in massive multiple-input multiple-output systems with 1-bit analog-to-digital converters. The statistical properties of the soft-estimated symbols (i.e., after linear combining and prior to the data detection process) have been previously characterized only for a single user equipment (UE) and uncorrelated Rayleigh fading. In this paper, we consider a multi-UE setting with correlated Rayleigh fading, where the soft-estimated symbols are obtained by means of maximum ratio combining based on imperfectly estimated channels. We derive a closed-form expression of the expected value of the soft-estimated symbols, which allows to understand the impact of the specific data symbols transmitted by the interfering UEs. Building on this result, we design efficient data detection strategies based on the minimum distance criterion, which are compared in terms of symbol error rate and complexity.

Pilot-Aided Distributed Multi-Group Multicast Precoding Design for Cell-Free Massive MIMO

We propose fully distributed multi-group multicast precoding designs for cell-free massive multiple-input multiple-output (MIMO) systems with modest training overhead. We target the minimization of the sum of the maximum mean squared errors (MSEs) over the multicast groups, which is then approximated with a weighted sum MSE minimization to simplify the computation and signaling. To design the joint network-wide multi-group multicast precoders at the base stations (BSs) and the combiners at the user equipments (UEs) in a fully distributed fashion, we adopt an iterative bi-directional training scheme with UE-specific or group-specific precoded uplink pilots and group-specific precoded downlink pilots. To this end, we introduce a new group-specific uplink training resource that entirely eliminates the need for backhaul signaling for the channel state information (CSI) exchange. The precoders are optimized locally at each BS by means of either best-response or gradient-based updates, and the convergence of the two approaches is analyzed with respect to the centralized implementation with perfect CSI. Finally, numerical results show that the proposed distributed methods greatly outperform conventional cell-free massive MIMO precoding designs that rely solely on local CSI.

Distributed Precoding Design for Multi-Group Multicasting in Cell-Free Massive MIMO

We consider multi-group multicast precoding designs for cell-free massive multiple-input multiple-output (MIMO) systems. To optimize the transmit and receive beamforming strategies, we focus on minimizing the sum of the maximum mean squared errors (MSEs) over the multicast groups, which is then approximated with the sum MSE to simplify the computation and signaling. We adopt an iterative bi-directional training scheme with uplink and downlink precoded pilots to cooperatively design the multi-group multicast precoders at each base station and the combiners at each user equipment in a distributed fashion. An additional group-specific uplink training resource is introduced, which entirely eliminates the need for backhaul signaling for channel state information (CSI) exchange. We also propose a simpler distributed precoding design based solely on group-specific pilots, which can be useful in the case of scarce training resources. Numerical results show that the proposed distributed methods greatly outperform conventional cell-free massive MIMO precoding designs that rely solely on local CSI.

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.