  Recently, communication systems that are both spectrum and energy efficient
have attracted significant attention. Different from the existing research, we
investigate the throughput and energy efficiency of a general class of
multiple-input and multiple-output systems with arbitrary inputs when they are
subject to statistical quality-of-service (QoS) constraints, which are imposed
as limits on the delay violation and buffer overflow probabilities. We employ
the effective capacity as the performance metric. We obtain the optimal input
covariance matrix that maximizes the effective capacity under a short-term
average power constraint. Following that, we perform an asymptotic analysis of
the effective capacity in the low signal-to-noise ratio and large-scale antenna
regimes. In the low signal-to-noise ratio regime analysis, we utilize the first
and second derivatives of the effective capacity when the signal-to-noise ratio
approaches zero in order to determine the minimum energy-per-bit and also the
slope of the effective capacity versus energy-per-bit curve at the minimum
energy-per-bit. We observe that the minimum energy-per-bit is independent of
the input distribution, whereas the slope depends on the input distribution. In
the large-scale antenna analysis, we show that the effective capacity
approaches the average transmission rate in the channel with the increasing
number of transmit and/or receive antennas. Particularly, the gap between the
effective capacity and the average transmission rate in the channel, which is
caused by the QoS constraints, is minimized with the number of antennas. In
addition, we put forward the non-asymptotic backlog and delay violation bounds
by utilizing the effective capacity. Finally, we substantiate our analytical
results through numerical illustrations.
