  Multiple transmit antennas in a downlink channel can provide tremendous
capacity (i.e. multiplexing) gains, even when receivers have only single
antennas. However, receiver and transmitter channel state information is
generally required. In this paper, a system where each receiver has perfect
channel knowledge, but the transmitter only receives quantized information
regarding the channel instantiation is analyzed. The well known zero forcing
transmission technique is considered, and simple expressions for the throughput
degradation due to finite rate feedback are derived. A key finding is that the
feedback rate per mobile must be increased linearly with the SNR (in dB) in
order to achieve the full multiplexing gain, which is in sharp contrast to
point-to-point MIMO systems in which it is not necessary to increase the
feedback rate as a function of the SNR.
