Transmitter optimization for distributed Gaussian MIMO channels

In this paper, we consider the transmitter optimization problem for a point-to-point communication system with multiple base-stations cooperating to transmit to a single user. Each base-station is equipped with multiple antennas with a separate average power constraint imposed on it. First, we determine certain sufficient conditions for optimality which, in turn, motivate the development of a simple water-filling algorithm that can be applied if H^T H is positive definite (H is the composite channel matrix). The water-filling algorithm is applied to each individual base-station and the symmetric matrix thus obtained is the optimal transmit covariance matrix if it is also positive semi-definite and none of its diagonal elements are zero. Secondly, we show that for a special class of distributed Gaussian MIMO channels, where the individual channel matrices have the same unitary left singular vector matrix, the transmitter optimization problem may be reduced from one of determining the optimal transmit covariance matrix of size N × N to that of determining an optimal vector of length N. Finally, we propose a low-complexity, greedy water-filling algorithm for general channel matrices. The proposed algorithm is shown to attain near optimal rates in various scenarios through numerical simulations.