Throughput maximization for uplink and downlink beamforming with independent coding

We study the optimal throughput that is achievable for uplink and downlink multiuser communication, assuming that spatial linear filtering is performed at the base station, and each mobile station is equipped with a single antenna. Channel state information is assumed to be available at the base station. The total transmission power is constrained. Independent precoding/decoding is assumed. The resulting sum rate objective is generally non-convex, thus known algorithms for determinant maximization cannot be applied. In this paper we analyze this nonconvex optimization problem and provide partial solutions. For the low-SNR regime we prove that the sum capacity is achieved by focusing all the energy on the user with the largest 2-norm of the channel vector. The SNR range for which single user transmission is optimal is characterized. For arbitrary SNR an algorithmic approach is discussed, which exploits some beneficial properties of the sum rate function