  We study a multiple-input single-output (MISO) communication system assisted
by a reconfigurable intelligent surface (RIS). A base station (BS) having
multiple antennas is assumed to be communicating to a single-antenna user
equipment (UE), with the help of a RIS. We assume that the system operates in
an environment with line-of-sight (LoS) between the BS and RIS, whereas the
RIS-UE link experiences Rayleigh fading. We present a closed form expression
for the optimal active and passive beamforming vectors at the BS and RIS
respectively. Then, by characterizing the statistical properties of the
received SNR at the UE, we apply them to derive analytical approximations for
different system performance measures, including the outage probability,
average achievable rate and average symbol error probability (SEP). Our
results, in general, demonstrate that the gain due to RIS can be substantial,
and can be significantly greater than the gains reaped by using multiple BS
antennas.

Signal Processing