We consider a downlink cellular communication system with a multi-antenna base station (BS). A regularized zero forcing precoder is employed at the BS to manage the inter-user interference within the cell. Using methods from random matrix theory, we derive a deterministic approximation for the achievable ergodic sum rate, taking into account the randomness from both fading and random user locations. The obtained approximation describes well the behavior of finite-sized systems and enables efficient optimization of the precoder matrix.
Girnyk, M. A., Muller, A., Vehkaperä, M., Rasmussen, L. K., & Debbah, M. (2015). On the asymptotic sum rate of downlink cellular systems with random user locations. IEEE Wireless Communications Letters, 4(3), 333-336. . https://doi.org/10.1109/LWC.2015.2415796