Ergodic MIMO Mutual Information: Twenty Years After Emre Telatar
arXiv:1901.06458
Abstract
In the celebrated work of Emre Telatar in the year 1999 (14274 citations to date), it was shown that the expected value of the mutual information \begin{equation*} \mathrm{I} = \ln\det\left( \mathbf{I}_m + \frac{1}{t} \mathbf{HH}^{\dagger} \right) \end{equation*} of an MIMO Rayleigh channel matrix with a SNR can be represented as an integral involving Laguerre polynomials. We show, in this work, that Telatar's integral representation can be explicitly evaluated to a finite sum of the form \begin{equation*} \mathbb{E}\!\left[\mathrm{I}\right]=\sum_{k=0}^{n+m-3}a_{k}t^{k}+\rm e^{t}~\text{Ei}(-t)\sum_{k=0}^{n+m-2}b_{k}t^{k},, \end{equation*} where is the exponential integral and , are known constants that do not dependent on . The renewed interest in this classical information theory problem came from, quite surprisingly, the recent development in quantum information theory.