Space-time coding for the parametric fading channel-capacity

In order to exploit transmit diversity in the multiple antenna parametric wireless channel, we studied the pairwise error probability (PEP). Our channel consisted of parallel paths with unequal average powers and independent fading. We obtained the exact PEP with ML decoding as a function of segment Euclidean distances (distances between segments of the codeword transmitted on different paths). Here we provide an upper bound on the PEP. Subject to a constraint on the total distance, the bound is minimized by the waterpouring solution. Since this solution is for Euclidean distances, it does not constrain Hamming distances and transmit powers separately. We study the average capacity as a function of the transmit covariance matrix in order to obtain constraints on segment powers. Subject to a transmit power constraint it is difficult to maximize capacity analytically. We employ upper and lower bounds for analysis. We conclude that waterpouring of segment powers is very close to the optimal covariance matrix.