  Reconfigurable Intelligent Surface (RIS) can create favorable multipath to
establish strong links that are useful in millimeter wave (mmWave)
communications. While previous works used Rayleigh or Rician fading, we use the
fluctuating two-ray (FTR) distribution to model the small-scale fading in
mmWave frequency. First, we obtain the statistical characterizations of the
product of independent FTR random variables (RVs) and the sum of product of FTR
RVs. For the RIS-aided and amplify-and-forward (AF) relay systems, we derive
exact end-to-end signal-to-noise ratio (SNR) expressions. To maximize the
end-to-end SNR, we propose a novel and simple way to obtain the optimal phase
shifts at the RIS elements. The optimal power allocation scheme for the AF
relay system is also proposed. Furthermore, we evaluate important performance
metrics including the outage probability and the average bit error probability.
To validate the accuracy of our analytical results, Monte-Carlo simulations are
subsequently conducted to provide interesting insights. It is found that the
RIS-aided system can achieve the same performance as the AF relay system with
low transmit power. More interestingly, as the channel conditions improve, the
RIS-aided system can outperform the AF relay system having the same transmit
power with a smaller number of reflecting elements.
