Ergodic MIMO Mutual Information: Twenty Years After Emre Telatar

01/19/2019

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by   Lu Wei, et al.

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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 I = ( I_m + 1/tHH^†) of an m× n MIMO Rayleigh channel matrix H with a SNR 1/t 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 E[I]=∑_k=0^n+m-3a_kt^k+ e^t Ei(-t)∑_k=0^n+m-2b_kt^k,, where Ei(-t) is the exponential integral and a_k, b_k are known constants that do not dependent on t. The renewed interest in this classical information theory problem came from, quite surprisingly, the recent development in quantum information theory.