  This paper considers beamforming for a reconfigurable intelligent surface
(RIS)-aided multiple input single output (MISO) communication system in the
presence of Rician multipath fading. Our aim is to jointly optimize the
transmit beamformer and RIS phase shift matrix for maximizing the mean
signal-to-noise (SNR) of the combined signal received over direct and indirect
links. While numerical solutions are known for such optimization problems, this
is the first paper to derive closed-form expressions for the optimal beamformer
and the phase shifter for a closely related problem. In particular, we maximize
a carefully constructed lower bound of the mean SNR, which is more conducive to
analytical treatment. Further, we show that effective channel gain under
optimal beamforming follows Rice distribution. Next, we use these results to
characterize a closed-form expression for the outage probability under the
proposed beamforming scheme, which is subsequently employed to derive an
analytical expression for the ergodic capacity. Finally, we numerically
demonstrate the efficacy of the proposed beamformer solution in comparison with
the existing algorithmically obtained optimal solution for the exact mean SNR
maximization.
