Asymptotic and Non-Asymptotic Analysis of Uplink Sum Rate for Relay-Assisted MIMO Cellular Systems

We consider uplink relay-assisted MIMO cellular systems with multiple relays deployed in each cell that perform the amplify-and-forward operations. We are interested in obtaining deterministic expressions for the ergodic sum rate of such systems. We first consider the large MIMO dimension scenario, and obtain two asymptotic sum rate expressions, corresponding to the cases of fixed number of users and large number of users, respectively. We then consider the case of arbitrary MIMO dimension and large number of users, and obtain an upper and lower bound that the sum rate lies in between with high probability. The bounds are tight when the number of users is large. Both single-cell and multi-cell systems are considered, where the latter assumes full base station cooperation. Numerical experiments show that these deterministic sum rate expressions match well with the Monte Carlo simulation results. Therefore they can be useful tools for the design and analysis of relay-assisted MIMO cellular systems.