Mutual information distribution of spatially correlated MIMO-OFDM systems in the low signal-to-noise ratio regime

We characterise the distribution of mutual information for spatially correlated multiple-input multiple-output channels using orthogonal frequency division multiplexing (MIMO-OFDM) in the asymptotically low signal-to-noise (SNR) regime. In particular, we derive the moment generating function (MGF) and cumulative distribution function (CDF) of the mutual information random variable as a function of the power delay profile and eigenvalues of the spatial correlation matrices. For the special case of zero spatial correlation and uniform power delay profile, we show that the mutual information is gamma distributed. In the general case, it can be expressed as a sum of weighted exponential distributions, or an infinite sum of weighted gamma distributions. The weights and the parameters of the component distributions are expressed in terms of the power delay profile and eigenvalues of the correlation matrices.