Maximizing the Sum Rate in Cellular Networks Using Multiconvex Optimization

In this paper, we propose a novel algorithm to maximize the sum-rate in interference-limited scenarios where each user decodes its own message with the presence of unknown interferences and noise. The problem of adapting the transmit and receive filters of the users to maximize the sum-rate with a transmit power constraint is nonconvex. Our novel approach is to formulate the sum-rate maximization problem as an equivalent multiconvex optimization problem by adding two sets of auxiliary variables. An iterative algorithm, which alternatingly adjusts the system variables and the auxiliary variables is proposed to solve the multiconvex optimization problem and we show that the algorithm converges to a stationary point. The proposed algorithm is applied to a downlink cellular scenario consisting of several cells each of which contains a base station serving several mobile stations. We examine the two cases, with or without several half-duplex amplify-and-forward relays assisting the transmission. A sum power constraint at the base stations and at the relays are assumed. The applicability of our approach to the individual power constraints case is also shown. Finally, we show that the proposed multiconvex formulation of the sum-rate maximization problem is applicable to many other wireless systems in which the estimated data symbols are multiaffine functions of the system variables.