  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 asymptotic 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.
