A Closed-Form Approximation for Uplink Average Ergodic Sum Capacity of Large-Scale Multi-User Distributed Antenna Systems

Despite extensive studies on the capacity analysis of distributed antenna systems (DASs), how to derive the average ergodic capacity in a closed form still remains largely unknown, which is mainly attributed to the lack of explicit expressions of ergodic capacity and joint distribution of large-scale fading coefficients. To address this issue, this paper first proposes closed-form approximations, i.e., zero order and first order, of the asymptotic ergodic capacity by solving the fixed-point equations using an iterative method, where a flexible tradeoff between accuracy and computational complexity can be achieved by adjusting the number of iterations. For a large-scale multi-user DAS with both users and base station antenna clusters uniformly distributed in a circular cell, the proposed zero-order approximation of the ergodic sum capacity is further averaged over the large-scale fading coefficients to obtain a closed-form approximation of the average ergodic capacity by approximating the large-scale fading coefficients as independent and identically distributed Pareto random variables. Simulation results show that the proposed approximation of the average ergodic capacity is accurate in various scenarios, which sheds plenty of practical insights for system design.