Very tight capacity bounds for MIMO-correlated Rayleigh-fading channels

Due to the difficulty in its exact analysis, the ergodic (average) channel capacity of correlated multiple-input multiple-output (MIMO)-fading channels is evaluated mainly by resorting to bounding techniques. Most of bounding techniques, however, are focused on the upper bound, and exploit the information in a Wishart-distributed sample covariance matrix solely in the form of its determinant or mean value. In this paper, we rigorously represent the determinant of form det (I + gamma S) in terms of all possible principal submatrices of S, thereby allowing us to exploit the fine structure of S to derive an upper bound for the channel capacity. To obtain a lower bound, we carefully construct a multivariate function and verify its multivariate convexity. Besides their simplicity in mathematics, the new bounds show superior tightness, as evidenced by various numerical examples.