Cramer-Rao bounds and methods for knowledge based estimation of multiple FIR channels

This contribution elaborates on the concept of blind identification of multiple FIR channels with prior knowledge (WPK). The prior knowledge considered here corresponds to the transmitter (TX) (pulse shaping) and/or receiver (RX) filters present in digital communication systems. Exploitation of this prior knowledge allows the estimation to concentrate on the impulse response of the actual channel part itself. Hence this estimation can be done more accurately. Since the prior information is expressed in terms of the channel impulse response, we review a number of blind channel estimation methods that are parameterized by the channel and consider their extension to incorporate the prior knowledge. These methods include subchannel response matching (SRM), subspace fitting and maximum likelihood (ML) techniques. We also discuss performance limits in the form of Cramer-Rao bounds (CRBs). Both the methods and the CRBs are discussed in a deterministic and a Gaussian context for the unknown transmitted symbols. Simulation results indicate that the exploitation of the prior knowledge can lead to significant improvements, that one particular SRM WPK method often outperforms another one, and that ML methods can still further improve performance.