  The fundamental performance metrics of an intelligent reflective surface
(IRS)-aided wireless system are presented. By optimizing the IRS phase-shift
matrix, the received signal-to-noise ratio (SNR) is maximized at the
destination in the presence of both reflected and direct channels. The
probability distributions of this maximum SNR are tightly approximated for the
moderate-to-large reflective element regime. Thereby, the probability density
function and cumulative distribution function of this tight SNR approximation
are derived in closed-form for Nakagami-m fading to facilitate a statistical
characterization of the performance metrics. The outage probability, average
symbol error probability, and achievable rate bounds are derived. By virtue of
an asymptotic analysis in the high SNR regime, the diversity order is
quantified. Thereby, we reveal that the overall diversity order can be scaled
as a function of the number of reflective elements (N) such that Gd = mv +
min(mg;mh)N, where mv, mh and mg are the Nakagami-m parameters of the direct,
source-to-IRS and IRS-to-destination channels, respectively. The asymptotic
achievable rate is derived, and thereby, it is shown that the transmit power
can be scaled inversely proportional to N2. The impact of quantized IRS
phase-shifts is investigated by deriving the achievable rate bounds. Useful
insights are obtained by analyzing the system performance for different
severity of fading cases including spatially correlated fading. Our analysis
and numerical results reveal that IRS is a promising technology for boosting
the performance of wireless communications by intelligently controlling the
propagation channels without employing additional active radio-frequency
chains.
