Analyzing the performance of the space-time block codes with partial channel state feedback

The theory of space-time codes for multiple antennas at the transmitter and receiver provided a useful framework for minimizing the probability of pair-wise frame error when the channel is unknown at the receiver. The design criterion for the codes were developed by averaging over all the channel states. In practice, a feedback channel of low bandwidth is usually available where the transmitter can get some channel state information from the receiver. The transmitter can use this information to change its power level or modulation or both. Since the channel state is a matrix instead of a scalar in the single antenna case, we first find out what is the sufficient statistic for space-time orthogonal block codes. It is shown that for a given channel state, the decoder essentially sees an AWGN channel with the signal to noise ratio scaled by the sufficient statistic. We discuss the optimal power control and adaptive modulation strategies. The effect of delay in passing the channel information from the receiver to the transmitter is examined. The results show a significant improvement (more than 10 dB in some cases) over the conventional system without feedback.