  This paper investigates the problem of maximizing the signal-to-noise ratio
(SNR) in reconfigurable intelligent surface (RIS)-assisted MISO communication
systems. The problem will be reformulated as a complex quadratic form problem
with unit circle constraints. We proved that the SNR maximizing problem has a
closed-form global optimal solution when it is a rank-one problem, whereas the
former researchers regarded it as an optimization problem. Moreover, We propose
a relaxation algorithm (RA) that relaxes the constraints to that of Rayleigh's
quotient problem and then projects the solution back, where the SNR obtained by
RA achieves much the same SNR as the upper bound but with significantly low
time consumption. Then we asymptotically analyze its performance when the
transmitter antennas n_t and the number of units of RIS N grow large together,
with N/n_t -> c. Finally, our numerical simulations show that RA achieves over
98% of the performance of the upper bound and takes below 1% time consumption
of manifold optimization (MO) and 0.1% of semidefinite relaxation (SDR).
