Deterministic equivalent for max-min SINR over random user locations

The max-min signal-to-interference-plus-noise ratio (SINR) problem is considered in a coordinated network wherein L base stations (BSs) each equipped with N antennas serve in total K single-antenna users that are uniformly distributed in the network. We conduct the analysis in the asymptotic regime in which N and K grow large to compute a deterministic approximation for the max-min SINR. The results are independent from fast-fading and users' locations and thus allow one to determine the optimal max-min SINR given basic system parameters such as cell radius, K, N and pathloss exponent. The provided framework can be utilized for analyzing the problem without the need to run system level simulations and for finding the optimal N, K, resource allocation and BS placement. Numerical results are used to validate the analytical results in a finite system regime and to evaluate the effects of system parameters on the system performance.