  Radio-frequency (RF) impairments, which intimately exist in wireless
communication systems, can severely limit the performance of multiple-input
multiple-output (MIMO) systems. Although we can resort to compensation schemes
to mitigate part of these impairments, a certain amount of residual impairments
always persists. In this paper, we consider a training-based point-to-point
MIMO system with residual transmit RF impairments (RTRI) using spatial
multiplexing transmission. Specifically, we derive a new linear channel
estimator for the proposed model, and show that RTRI create an estimation error
floor in the high signal-to-noise ratio (SNR) regime. Moreover, we derive
closed-form expressions for the signal-to-noise-and-interference ratio (SINR)
distributions, along with analytical expressions for the ergodic achievable
rates of zero-forcing, maximum ratio combining, and minimum mean-squared error
receivers, respectively. In addition, we optimize the ergodic achievable rates
with respect to the training sequence length, and demonstrate that finite
dimensional systems with RTRI generally require more training at high SNRs than
those with ideal hardware. At last, we extend our analysis to large-scale MIMO
configurations, and derive deterministic equivalents of the ergodic achievable
rates. It is shown that, by deploying large receive antenna arrays, the extra
training requirements due to RTRI can be eliminated. In fact, with sufficiently
large number of receive antennas, systems with RTRI may even need less training
than systems with ideal hardware.
