Quantifying the Performance Gain of Direction Feedback in a MISO System

We consider finite-rate channel-direction feedback in a system with multiple transmit-antennas and single receive-antenna. We address how the symbol error rate performance improves as a function of the amount of feedback. We conclude that when the number of feedback directions is equal to or larger than the number of transmit antennas, transmit beamforming is optimal even with limited feedback. On the other hand, when the number of feedback directions is smaller than the number of transmit antennas, the antennas are divided into two groups, where antenna selection is used in the first group to choose the strongest channel and equal power allocation is used in the second group. At high SNR, the optimal power allocation between these two antenna groups is proportional to the number of antennas in each group. Based on high SNR analysis, we fully characterize the power gain of each feedback bit.