Different from the opportunistic beamforming system (OBS) randomizing both amplitude and phase of its beamforming vector/matrix, the opportunistic cophasing system (OCS) randomizes the phase only. It significantly reduces the demands on the dynamic range of power amplifiers and even can be implemented just by a set of phase shifters. We first address the single-beam OCS in terms of its analytical system throughput. Then, we design a multi-beam OCS by exploiting the Fourier matrix and finally, we derive its closed-form upper bound on throughput, which is very tight with the Monte Carlo simulation results.