Optimal Power Allocation for Correlated Rayleigh Fading MIMO Wireless Systems with Statistic Information Feedback

Optimizing the input covariance matrix of a MIMO system with partial channel-structure feedback is an important issue to fully exploit the channel capacity. Efficient design of the optimal input covariance matrix, however, remains unavailable although its eigenvector structure was clearly revealed. In this paper, we obtain an upper bound of the capacity by matrix operation and concavity of the capacity function. Then by optimizing this upper bound using Lagrange multiplier method and matrix differentiation, we develop an efficient algorithm for determining the optimal eigenvalues. The technique is illustrated through numerical examples.