  In this paper, we investigate the impact of the high-power amplifier
non-linear distortion on multiple relay systems by introducing the soft
envelope limiter, traveling wave tube amplifier, and solid-state power
amplifier to the relays. The system employs amplify-and-forward either fixed or
variable gain relaying and uses the opportunistic relay selection with outdated
channel state information to select the best relay. The results show that the
performance loss is small at low rates; however, it is significant for high
rates. In particular, the outage probability and the bit error rate are
saturated by an irreducible floor at high rates. The same analysis is pursued
for the capacity and shows that it is saturated by a detrimental ceiling as the
average signal-to-noise ratio becomes higher. This result contrasts the case of
the ideal hardware where the capacity grows indefinitely. Moreover, the results
show that the capacity ceiling is proportional to the impairment's parameter
and for some special cases the impaired systems practically operate in
acceptable conditions. Closed-forms and high SNR asymptotes of the outage
probability, the bit error rate, and the capacity are derived. Finally,
analytical expressions are validated by the Monte Carlo simulation.
