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

Abstract : 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 converging 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.
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Romain Couillet, Jakob Hoydis, Mérouane Debbah. Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2012, 58 (10), pp.6392 - 6425. ⟨10.1109/TIT.2012.2201913⟩. ⟨hal-00769412⟩

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