Cell-Free Massive MIMO with Finite Fronthaul Capacity: A Stochastic Geometry Perspective

Abstract

In this work, we analyze the downlink performance of a cell-free massive multiple-input-multipleoutput system with finite capacity fronthaul links between the centralized baseband unit and the access point (APs). Conditioned on the user and AP locations, we first derive an achievable rate for a randomly selected user in the network that captures the effect of finite fronthaul capacity as a compression error.From this expression, we establish that for the traditional cell-free architecture where each AP serves all the users in the network, the achievable rate becomes zero as the network size grows. Hence, to have a meaningful analysis, for the traditional architecture, we model the user and AP locations as two independent binomial point processes over a finite region and provide an accurate theoretical result to determine the user rate coverage. For a larger (possibly infinite) network, we consider a user-centric architecture where each user in the network is served by a specified number of nearest APs that limits the fronthaul load. For this architecture, we model the AP and user locations as two independent Poisson point processes (PPPs). Since the rate expression is a function of the number of users served by an AP, we statistically characterize the load in terms of the number of users per AP. As the exact derivation of the probability mass function of the load is intractable, we first present the exact expressions for the first two moments of the load. Next, we approximate the load as a negative binomial random variable through the moment matching method. Using the load results along with appropriate distance distributions of a PPP, we present an accurate theoretical expression for the rate coverage of the typical user. From the analyses we conclude that for the traditional architecture the average system sum-rate is a quasi-concave function of the number of users. Further, for the user-centric architecture, there exists an optimal number of serving APs that maximizes the average user rate.