Rate maximization in multi-antenna broadcast channels with linear preprocessing

The sum rate capacity of the multi-antenna broadcast channel has recently been computed. However, the search for efficient practical schemes that achieve it is still ongoing. In this paper, we focus on schemes with linear preprocessing of the transmitted data. We propose two criteria for precoding matrix design, one maximizing the sum rate and the other maximizing the minimum rate among all users. The latter problem is shown to be quasiconvex and is solved exactly via the bisection method. In addition to precoding, we employ a signal scaling scheme that minimizes average bit-error-rate (BER). The signal scaling scheme is posed as a convex optimization problem, and thus can be solved exactly via efficient interior-point methods. In terms of achievable sum rate, the proposed technique significantly outperforms traditional channel inversion methods, while having comparable (in fact, often superior) BER performance.