A Theoretical Analysis of Favorable Propagation on Massive MIMO Channels with Generalized Angle Distributions

Abstract

Massive MIMO obtains the multiuser performance gain based on the favorable propagation (FP) assumption, defined as the mutual orthogonality of different users’ channel vectors. Until now, most of the theoretical analyses of FP are based on uniform angular distributions and only consider the horizontal dimension. However, the real propagation channel contains full dimensions, and the spatial angle varies with the environment. Thus, it remains unknown whether the FP condition holds in real deployment scenarios and how it impacts the massive MIMO system performance. In this paper, we analyze the FP condition theoretically based on a cluster-based three-dimensional (3D) MIMO channel with generalized angle distributions. Firstly, the FP condition’s unified mathematical expectation and variance expressions with full-dimensional angular integral are given. Since the closed-form expressions are hard to derive, we decompose generalized angle distributions, i.e., wrapped Gaussian (WG), Von Mises (VM), and truncated Laplacian (TL) into the functions of Bessel and Cosine basis by introducing Jacobi-Anger expansions and Fourier series. Thus the closed-form expressions of the FP condition are derived. Based on the above, we theoretically analyze the asymptotically FP condition under generalized angle distributions and then compare the impact of angular spreads on the FP performance. Furtherly, the FP condition is also investigated by numerical simulations and practical measurements. It is observed that environments with larger angle spreads and larger antenna spacing are more likely to realize FP. This paper provides valuable insights for the theoretical analysis of the practical application of massive MIMO systems.

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