Optimal power allocation for multiuser transmit beamforming via regularized channel inversion

In this paper, we consider an optimal power allocation problem that maximizes the sum-rate of a single-cell MISO broadcast channel with regularized channel inversion (RCI) beamforming at the base station (BS). Unlike the channel inversion or zero forcing beamforming, the optimal power allocation with RCI precoding at the base station is a nonlinear non-convex optimization problem with many local optima. Here, we investigate this problem in the large system limit, i.e., when the number of users K and antennas at the base station N tend to infinity with their ratio β = K/N being held constant. We assume each user has data symbol with power p_k, and slow-varying path-loss a_k. In this setting, we first derive the expression for the signal to interference plus noise ratio (SINR). Then, we divide all K users into L groups where all users in each group are assumed to be co-located or to have approximately the same distance from the BS. In other words, the users in each group have the same path-loss which is distance dependent. Moreover, in each group, we assume that the power allocated to each user is the same. Based on this system model, we investigate optimal power allocation schemes that maximize the sum-rate per antenna, firstly under average power constraint, and then under both average and per-user power constraints. We show that both problems are convex and the power allocation mainly follows the well-known water-filling strategy.