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This letter studies the performance of an uplink cell-free massive multiple-input multiple-output (MIMO) system with maximum-ratio combining receiver over Rayleigh fading channel, in which many distributed access points configured with multiple antennas provide services to multiple single-antenna users. For such a system, we derive an exact expression for probability density function (PDF) of individual signal-to-interference-plus-noise ratio (SINR). Due to its complexity for performance evaluation purposes, this PDF of SINR is approximated as a gamma distribution, and the resulting expression is used to obtain the approximate expressions of the coverage probability and the ergodic capacity, respectively. Besides, in order to ensure uniformly good coverage probability and ergodic capacity, a max-min power control algorithm is proposed, which can be formed by solving a geometric programming problem. Numerical results verify the correctness of the theoretical analysis and confirm the effectiveness of the proposed algorithm.

This article studies a reconfigurable intelligent surface (RIS)-aided cell-free massive multiple-input multiple-output system and formulate the max–min fairness problem that maximizes the minimum achievable rate among all the users by jointly optimizing the transmit beamforming at access points and the phase shifts at RISs. To address such a challenging problem, we first study the special single-user scenario and propose an algorithm that can transform the optimization problem into a semidefinite program (SDP) or an integer linear program for the cases of continuous or discrete phase shifts, respectively. Then, in order to solve the optimization problem for the multiuser scenario with continuous phase shifts, we propose an alternating optimization algorithm, which can alternately transform the problem into a second-order-cone program and an SDP. Finally, for the multiuser scenario with discrete phase shifts, we design a zero-forcing-based successive refinement algorithm, which can find the suboptimal transmit beamforming and phase shifts by means of alternating optimization. Numerical results show that compared with the benchmark schemes of random phase shifts and without using the RIS, the proposed algorithms can significantly increase the minimum achievable rate. It is also demonstrated that, compared with the case of programming continuous phase shifts, using 2-bit discrete phase shifts can practically achieve the same performance.

In this article, we investigate the downlink (DL) of a cell-free massive multiple-input multiple-output (MIMO) system over spatially correlated Rician fading, in which many distributed access points (APs) equipped with multiple antennas serve single-antenna users. The APs apply minimum mean-square error channel estimation to obtain the uplink channel state information (CSI). Furthermore, in order to obtain DL CSI at users, this article considers the use of maximum-ratio transmission to beamform DL pilots in the DL beamforming training (BT) phase. For such a system, we derive the closed-form expressions of the sum spectral efficiency (SE) and total energy efficiency (EE). Based on the obtained closed-form expressions, we develop two successive approximation algorithms to improve the sum SE and total EE by optimizing the power control coefficients of DL data and pilot. Numerical results are provided to demonstrate the superiority of the proposed algorithms in improving the sum SE and total EE. In addition, the numerical results also show that the sum SE of a cell-free massive MIMO system with exploiting the BT scheme can be significantly improved over the system without employing the BT scheme.