A closed-form bound on correlated MIMO channel capacity

The exact calculation of the ergodic MIMO channel capacity with channel correlation is mathematically at least very challenging. Having no closed-form analytical expression available for the capacity is making it difficult to derive optimum stochastic water-filling schemes that are based on long-term channel state information (channel correlation) only. We therefore derive a closed-form tight upper bound on the ergodic capacity of correlated MIMO channels. The bound takes into account both the effects of correlation at the transmitter as well as the receiver. Furthermore, we give a recursive algorithm for its efficient calculation. Simulations demonstrate the tightness of the bound and show that a long-term water-filling scheme based on the new bound yields almost the same performance as a scheme with full short-term (instantaneous) channel state information.