Optimizing Pilot Spacing in MU-MIMO Systems Operating Over Aging Channels

In the uplink of multiuser multiple input multiple output (MU-MIMO) systems operating over aging channels, pilot spacing is crucial for acquiring channel state information and achieving high signal-to-interference-plus-noise ratio (SINR). Somewhat surprisingly, very few works examine the impact of pilot spacing on the correlation structure of subsequent channel estimates and the resulting quality of channel state information considering channel aging. In this paper, we consider a fast-fading environment characterized by its exponentially decaying autocorrelation function, and model pilot spacing as a sampling problem to capture the inherent trade-off between the quality of channel state information and the number of symbols available for information carrying data symbols. We first establish a quasi-closed form for the achievable deterministic equivalent SINR when the channel estimation algorithm utilizes multiple pilot signals. Next, we establish upper bounds on the achievable SINR and spectral efficiency, as a function of pilot spacing, which helps to find the optimum pilot spacing within a limited search space. Our key insight is that to maximize the achievable SINR and the spectral efficiency of MU-MIMO systems, proper pilot spacing must be applied to control the impact of the aging channel and to tune the trade-off between pilot and data symbols.