Residual CFO Effect on Uplink Sum-Rate of Cell Free Massive MIMO Systems

Cell-free (CF) massive multiple input multiple output (MaMIMO) has been suggested to reach future wireless networks demands. Analyzing the effect of hardware impairments on performance of CF MaMIMO systems is of vital importance. In this paper, we investigate the effect of residual carrier frequency offset (CFO) on the uplink sum-rate of CF MaMIMO systems. Therefore, we derive closed form expression for the uplink achievable sum-rate of orthogonal frequency domain multiplexing (OFDM) based CF MaMIMO systems. Our results show that in a fully synchronized CF MaMIMO system, the sum-rate increases unlimitedly as the number of access points (AP) increases. However, when the system is hit by CFO the sum-rate is limited even when the number of APs tends to infinity. Our results also indicate that for finite number of APs, when the number of antennas at each AP tends to infinity, the sum-rate of the system in the presence of CFO is bounded. While, for the fully synchronized system, as the number of antennas at each AP grows large, the sum-rate increases, unlimitedly when the antennas of an AP are independent and is bounded when there is a correlation between the antennas of an AP.