The Decision Delay in Finite-Length MMSE–DFE Systems

This paper investigates the performance of the minimum mean square error (MMSE) decision feedback equalization system and optimizes its key parameter, decision delay, to minimize the system MSE. For the first typical scenario where the feedback filter length \(N_b\) is larger than or equal to the channel order \(v\), we present an analytical expression of the system MSE in terms of decision delay. A few results in previous literature can be regarded as special cases of this expression. For the second typical scenario where feedback filter length \(N_b\) is less than the channel order \(v\), it is difficult to obtain the explicit solutions. We prove that at a given decision delay, the MSE for \(N_b< v\) is always larger than or equal to that for \(N_b\ge v\). As a corollary of two derived theorems, the optimum feedback filter length should be set to the channel order for large \(N_f\). Furthermore, in this scenario, the optimal decision delay is conventionally found with an exhaustive search over all possible delays, whose computational complexity is linear with the searching space and unaffordable. To lower the complexity, we then propose an efficient algorithm to find the optimal decision delay. The complexity of our algorithm is only a log function of the searching space and its MSE and symbol error rate performance is almost the same as the traditional exhaustive search .