A Note on Averages over Random Matrix Ensembles
نویسنده
چکیده
Abstract. In this work we find a closed form expression for matrix averages over the Gaussian ensemble. More precisely, given an n × n Hermitian matrix A and a continuous function f(x) we find a closed form expression for the expectation E(Tr(f(XAX∗))) where X is a Gaussian n × n matrix with complex independent and identically distributed entries of zero mean and variance 1. Taking f(x) = log(1+x) this gives us another formula for the capacity of the MIMO communication channel and taking f(x) = (1 + x) gives us the minimum MMSE achieved by a linear receiver.
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