Estimation of optimal weight vectors for spatial broadcast channels

In a multi-transmitter broadcast system, the weight vector for each message signal can provide an additional degree of freedom for signal enhancement and interference suppression by taking advantage of the spatial diversity among the users. The design of optimal weight vectors that maximize the overall channel capacity is an open problem. Under certain power constraints, the channel capacity R is a highly nonlinear function of the M-dimensional weight vectors {w_i}, where M is the number of transmitters. Hence, a closed-form algebraic solution that maximizes R over {w_i} does not seem to be tractable. We decouple the weight vectors in R to simplify the optimization problem to a search for the maxima of a smooth multidimensional function. Based on this decoupling, we derive and evaluate two algorithms for computing weight vectors for the two-user and three-user cases: orthogonal and optimal. We also propose a near-optimum algorithm for the two-user case. The optimal algorithm requires an iterative search