Capacity Analysis for Spatially Non-wide Sense Stationary Uplink Massive MIMO Systems

TL;DR

This paper introduces a new channel model for massive MIMO systems that accounts for spatial non-stationarity, deriving an upper bound on sum capacity and showing how non-stationarity can enhance capacity with larger arrays.

Contribution

A novel channel model incorporating partially and wholly visible clusters for non-stationary massive MIMO channels and a derived capacity upper bound.

Findings

Non-stationarity can improve sum capacity by spreading channel eigenvalues.

More partially visible clusters and larger arrays lead to better-conditioned channels.

Numerical results confirm the theoretical analysis and the tightness of the upper bound.

Abstract

Channel measurements show that significant spatially non-wide-sense-stationary characteristics rise in massive MIMO channels. Notable parameter variations are experienced along the base station array, such as the average received energy at each antenna, and the directions of arrival of signals impinging on different parts of the array. In this paper, a new channel model is proposed to describe this spatial non-stationarity in massive MIMO channels by incorporating the concepts of partially visible clusters and wholly visible clusters. Furthermore, a closed-form expression of an upper bound on the ergodic sum capacity is derived for the new model, and the influence of the spatial non-stationarity on the sum capacity is analyzed. Analysis shows that for non-identically-and-independent-distributed (i.i.d.) Rayleigh fading channels, the non-stationarity benefits the sum capacity by bringing a more even spread of channel eigenvalues. Specifically, more partially visible clusters, smaller cluster visibility regions and a larger antenna array can all help to yield a well-conditioned channel, and benefit the sum capacity. This shows the advantage of using a large antenna array in a non-i.i.d. channel: the sum capacity benefits not only from a higher array gain, but also from a more spatially non-stationary channel. Numerical results demonstrate our analysis and the tightness of the upper bound.