Performance Analysis of OTFS-based Uplink Massive MIMO with ZF Receivers

This paper considers an orthogonal time frequency space (OTFS)-based uplink massive multiple-input-multiple-output (MIMO) system, in which all users transmit symbols to a base station (BS) that is equipped with an one-dimensional uniform linear array (ULA) in the delay-Doppler domain. The zero-forcing (ZF) decoding scheme is applied at the BS. Different from most existing OTFS works, this paper mainly focuses on the performance analysis. Furthermore, in contrast to the existing massive MIMO works, which assume favorable propagation (FP) conditions, here, we investigate the low but non-zero probability scenario that massive MIMO fails in providing FP. This results in a scenario where the channel matrix cannot be diagonalized with massive MIMO. Thus, to facilitate the performance analysis, a low-complexity approximation of the inverse of the Gram matrix, i.e., the Neumann series expansion, is presented. With this, a simple signal-to-noise-ratio (SNR) approximation is firstly derived, which illuminates the impact of the OTFS system parameters. Moreover, by exploiting the properties of circulant matrices, a compact expression for the OTFS multi-path correlation matrix (OTFS-MPCM) is derived.