Performance analysis of unbiased finite-length DFE receivers

We consider the problem of equalization of linear (finite-impulse-response-FIR) channels with the use of decision feedback equalizers (DFEs). Papadias and Paulraj (1995, 1998) showed that an arbitrary FIR channel can be perfectly equalized in the absence of noise with the use of an FIR-DFE receiver (whether it is fractionally-spaced (FS) or not). In such cases, by properly choosing the filter lengths, as well as recovery delay parameters, it is possible to null perfectly the residual intersymbol interference (ISI) at the decision device (DD) output, without compromising the performance. The simplicity and practical importance of this case calls for a performance analysis of these so-called unbiased DFE receivers. In the absence of residual ISI, the key issue that determines bit error rate (BER) performance is error propagation. We deride both approximate and exact closed-form expressions for the BER of unbiased DFE receivers. These expressions allow for a simple calculation of the equalizer output BER at steady-state, as well as for a quantitative description of issues such as instability and erratic behavior. In support to our findings, we provide computer simulation results that verify the validity of our results.