Uplink Spectral Efficiency of Cell Free Massive MIMO based on Stochastic Geometry Approach

Cell-free (CF) Massive multiple-input multiple-output (MIMO) system is one of the most promising technologies for the fifth generation (5G) wireless communication and beyond, in which the concept of cell boundaries is not respected. This new paradigm aims to cover the users simultaneously through many distributed access points (APs) over the same time/frequency resources based on time-division duplex (TDD) system. In this paper, the uplink spectral efficiency (SE) of a CF Massive MIMO system is investigated based on the stochastic geometry (SG) tool and over Rician fading channels. The distribution of APs is assumed to be random based on the Poisson point process (PPP) to emulate the real AP behavior over the mobile network which has not been considered previously. However, deploying the network's APs irregularly may worsen the phase noise effect and thus the SE of the system. The uplink SE of cell free massive MIMO is derived considering the maximum ratio combining (MRC) at the AP receivers and minimum mean-square error (MMSE) to estimate the channels stats. The simulation results have confirmed that CF Massive MIMO system provides higher SE gain when the APs density is unevenly and largely distributed. However, a considerable cost of the uplink SE is observed when the length of the uplink training period increases for the perfect Channel State Information (CSI) case. Moreover, the performance gap between the perfect and imperfect (CSI) converges when the uplink training increases.