Frequency synchronization and reciprocity calibration across base stations (BSs) are crucial for coherent transmission in distributed massive multiple-input multiple-output (MIMO) networks, yet are often disrupted by carrier frequency offsets (CFOs) from distinct BS oscillators and phase offsets caused by radio frequency hardware impairments. Traditional approaches typically employ maximum likelihood or least squares estimation for CFOs and phase offsets, requiring additional estimation of inter-BS channels and resulting in high computational costs. This paper introduces an over-the-air protocol, named Sync4CT, which estimates and compensates CFOs and phase offsets to enable coherent transmission. Sync4CT estimates CFOs utilizing the autocorrelation matrices of the received pilot signals and assesses phase offsets in the frequency domain. Both procedures offer closed-form estimators without the need of inter-BS channel estimation, and are executed in parallel across BSs, thereby significantly reducing computational complexity. Theoretical analysis shows that, for Sync4CT, the mean square error (MSE) of CFO estimation approaches the Cramér-Rao bound (CRB), while the MSE of phase offset estimation achieves the CRB in narrowband systems. Simulations further validate the substantial performance improvements of Sync4CT for coherent transmission in distributed MIMO networks.

This paper addresses the joint beamforming and data stream allocation (DSA) optimization problem for non-coherent joint transmission (NCJT). A critical yet neglected issue in NCJT beamforming is the tightly related DSA, which involves determining the number of streams transmitted from access points (APs) to their serving user equipments (UEs) according to the channel quality, so that the weighted sum-rate (WSR) can be maximized. However, since the integer number of streams directly determines the dimensions of beamformers, the joint optimization problem is mixed-integer and nonconvex with tightly coupled decision variables, making it NP-hard. To solve this problem, we first fix the DSA variables and propose a distributed and reduced weighted minimum mean square error (WMMSE) beamforming algorithm, called distributed RWMMSE, by leveraging the low-dimensional subspace property of the beamformer obtained by the traditional WMMSE. The distributed RWMMSE achieves the same WSR as the traditional WMMSE but with significantly lower computational complexity (scaling linearly with the number of AP antennas) and reduced interaction cost. Building on this, a joint beamforming and DSA optimization algorithm, named RWMMSE-LSA, is proposed by decoupling the decision variables through introduced stream indicator matrices. The RWMMSE-LSA optimizes beamformers and DSA via the distributed RWMMSE and linear programming, respectively, both of which have closed-form solutions. Simulations validate substantial performance gain of our proposed algorithms over existing alternatives in computational and interaction costs.

We consider ergodic weighted sum rate (WSR) maximization in a massive multi-user multiple-input multiple-output system. Existing solutions iteratively minimize the average WSR based on all the historical information, and use bisection search to satisfy the power constraint at each iteration, resulting in both high storage burden and high computational complexity. In contrast, we propose an efficient stochastic proximal weighted minimum mean-square error (SPWMMSE) algorithm, which updates the precoder only based on the current single channel realization, without checking the power constraint at each iteration. Furthermore, we propose a novel proximal term to incorporate all the previous channel and surrogate function information in precoder updates. Our analysis shows that SPWMMSE converges to the stationary point of the original ergodic WSR maximization problem almost surely. Simulation results demonstrate the effectiveness of SPWMMSE over the current best alternatives.

We consider downlink beamforming design to maximize the weighted sum rate (WSR) in a user-centric cell-free network, where distributed access points (APs) are organized in a cluster to jointly serve each user equipment (UE). This architecture ensures uniform service quality even at the cell edge, but synchronization between APs can be problematic, necessitating the utilization of non-coherent joint transmission (NCJT) that eliminates the need for strict synchronization. Most existing works on beamforming design for NCJT assume that the classic weighted minimum mean square error (WMMSE) approach is not applicable, and design their beamforming algorithms based on the successive convex approximation (SCA) method with high computational complexity. In this work, we for the first time demonstrate the applicability of the WMMSE approach for NCJT in cell-free networks. Based on the unique observations on the structures of the WSR maximization problem for NCJT, we propose an efficient WMMSE based beamforming algorithm. Our proposed algorithm is guaranteed to converge to a stationary point of the WSR maximization problem. Furthermore, our beamforming updates are in closed form with low computational complexity. Simulation results demonstrate substantial performance gain of our proposed algorithm over the current best SCA based alternatives in both computational complexity and convergence time.