Performance Analysis of Reciprocity Calibration Errors and Local Oscillator Phase Shift: A Stochastic Geometry Approach

In this paper, we study the performance of cell-free massive multiple-input multiple-output (MIMO) systems with reciprocity calibration errors (RCEs) and local oscillator (LO) phase shift. RCEs inevitably occur in the practical implementation, resulting in phase shifts in the channel during signal transmission. We consider a system model where both remote radio units (RRUs) and user equipment (UEs) follow Poisson point processes (PPP) in spatial location. For downlink transmission, we consider two architectures: centralized and distributed, and two precoding schemes: maximum ratio transmission (MRT) and zero-forcing (ZF). By approximating the signal and interference power distributions as Gamma or Nakagami distributions, we derive closed-form expressions for the signal-to-interference-plus-noise ratio (SINR) of the downlink precoding schemes. Then we use a stochastic geometry method to obtain closed-form expressions for the average spectral efficiency (SE) per user considering the distribution of RRU locations and UE locations. Simulation results show that the impact of RCEs and LO phase shift on system performance is more severe for centralized ZF precoding than for MRT and distributed ZF precoding. In addition, we analyze the SE performance with different RRU density, UE density, and when the total number of antennas remains unchanged, the impact of RCEs and LO phase shift is more obvious for the system with higher degree of cooperation.