Sum capacity of MIMO Gaussian broadcast channels with channel energy constraints

The motivation of this paper is to find the class of channels that provides the best sum capacity of a MIMO Gaussian broadcast channel with both transmit power and channel energy constraints when N-t >= K N-r, where N-t, N-r, and K denote the number of transmit antennas, the number of receive antennas, and the number of users in the system, respectively. The best sum capacity is achieved when the user channels are mutually orthogonal to each other. For each individual user, equal energy is distributed to all non-zero spatial eigenmodes. Further, we optimize the number of non-zero eigenmodes for all users and the optimal power distribution among users. Although, we only study the case of N-t >= K N-r in this paper, we conjecture that similar results still hold for N-t < K N-r. The characteristics of the optimal channels can be used to direct antenna configurations.