Optimal transmission strategy for multiple antenna systems with uninformed transmitter and correlation

How should the mobile with multiple antennas transmit if it has absolutely no channel state information but the channel is correlated in some way? In this paper, we give the answer to this question. In our case, the objective function is the mutual information. This question leads to a two-player game in which the transmit player wants to maximize the mutual information of the open-loop MISO system while the correlation player minimizes this quantity. At a first guess, one would say that if the transmit array has no idea of the channel state and the correlation it performs equal power allocation in all directions. Depending on the objective function this intuitive belief is true or false. We show that if the objective function is the average mutual information, the belief can be justified. We study the minimax programming problem and show that it does not fulfill the saddle-point property. However, the most robust transmit strategy is shown to be equal power allocation. This theoretical result is illustrated and discussed. Finally, we present an extension to the multiple-input multiple-output case and solve the corresponding minmax and maxmin programming problems. For small SNR values, the minimax problem does not fulfill the saddle-point property as in the single-receive antenna scenario. We discuss the similarities and differences between the MISO and MEMO case.