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.
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