SER Analysis of Cell-Free Massive MIMO System

This paper studies an uplink cell-free massive multiple-input multiple-output (MIMO) system with imperfect channel state information and maximum-ratio combining detectors over Rayleigh fading channel. For such a system, this paper analyzes the performance of symbol error rate (SER), which plays a key role in system reliability. Firstly, the probability density function of the desired signal and the equivalent noise are analytically calculated for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>-ary pulse amplitude modulation, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>-ary quadrature amplitude modulation, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>-ary phase-shift keying, respectively. Next, based on these analyses, the novel analytical expressions for the SER of different modulations are derived, which is verified by numerical results. Then, in order to enhance the SER performance of all users in different geographical locations, a geometric programming based power control (GPPC) algorithm is proposed. Finally, numerical results show that compared with four benchmark schemes of the full power algorithm, the fractional power control algorithm, the traditional max-min fairness power control algorithm, and the genetic algorithm, the proposed GPPC algorithm can effectively minimize the maximum SER among all users through collaborative control of the power control coefficient while ensuring lower computational complexity.