Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach

Publication Type:

Journal Article


IEEE Transactions on Information Theory, Volume 58, Issue 10, p.6392 - 6425 (2012)


In this work, we study the performance of random isometric precoding over quasi-static and correlated fading
channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise
ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converg-
ing fixed-point algorithms for their computation. Although the deterministic approximations are only asymptotically
exact, almost surely, we show by simulations that they are very accurate for small system dimensions. The analysis
is based on the Stieltjes transform method which enables the derivation of deterministic equivalents of functionals of
large-dimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free
probability theory which allows us to consider random matrix models for which asymptotic freeness does not hold.
Thus, the results of this work are also a novel contribution to the field of random matrix theory and are shown to
be applicable to a wide spectrum of practical systems. In this article, we specifically characterize the performance of
multi-cellular communication systems, multiple-input multiple-output multiple-access channels (MIMO-MAC), and
MIMO interference channels.