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The complexity of the optimal phase control problem in wireless MIMO systems with scalar feedback quantization and equal-gain transmission is studied. The problem is shown to be NP-hard when the number of receive antennas grows linearly with the number of transmit antennas. For the case where the number of receive antennas is constant, the problem can be solved in polynomial time. An optimal algorithm is explicitly constructed. For practical purposes, a low-complexity algorithm based on local search is presented. Simulation results show that its performance is nearly optimal.