Decision-feedback equalization achieves full diversity for finite delay spread channels

This paper considers a SIMO or SISO communication link. In the case of white noise, the Matched filter bound (MFB) is proportional to the total channel energy. Hence all diversity sources present in the channel show up in the MFB. The MFB usually is a close approximation for the performance of maximum likelihood sequence detection (MLSD) and represents an upper bound for the performance of any receiver (Rx). In this paper we consider the diversity performance of suboptimal Rx's of the decision feedback equalization (DFE) type. Two DFE designs are considered: minimum mean squared error (MMSE) or MMSE zero-forcing (MMSE-ZF). The SNR at the detection point of a MMSE(-ZF) DFE exhibits a performance loss w.r.t. the MFB, a loss that is determined by the energy in the feedback filter. It is shown that there exists an upperbound for this loss that is channel independent. Hence the DFE enjoys as much diversity as the MFB.