Statistical analysis of the SNR loss due to imperfect time reversal

Prefiltering that is, linear processing at the transmitter side of a link, is often used in communication in order to simplify receivers, or to improve performance. Prefiltering requires at least a knowledge of the channel state. When this information is estimated, imperfect estimations impact achievable performance. Time reversal, that is a special kind of prefiltering, where channel is estimated at transmitter side during a training phase, is analyzed, in particular regarding the pattern of channel estimation errors. Results show that a loss in SNR is incurred, and a symbol error probability floor appears, depending on the variance of estimation errors. Exact theoretical expressions were derived for the SNR loss as well as symbol error probability.