Optimal transmit covariance for MIMO channels with statistical transmitter side information

We give an optimality condition for the input covariance for arbitrary ergodic Gaussian vector channels under the condition that the channel gains are independent of the transmit signal, the transmitter has knowledge of the channel gain probability law and the receiver has knowledge of each channel realization. Using this optimality condition, we find an iterative algorithm for numerical computation of optimal input covariance matrices

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