Multiple Decision Feedback Equalizers for vector systems with complexity/performance tradeoff

We consider detectors for the class of vector systems describable by the matrix equation y = Ax + n, where y is a vector of observations, n the additive noise vector, A the known system matrix, and x are the unknown (to be estimated) symbols drawn from a finite symbol alphabet. A novel detector is developed consisting of the combination of multiple decision feedback equalizers (M-DFE) each with a permutation functionality included in such a way as to produce a detector structure that can significantly out-perform the conventional single DFE. Different arrangements are possible allowing a complexity / performance trade-off. The serial cascade where each DFE adapts its permutation based on reliability metrics from the previous DFE out-performs the parallel autonomous arrangement for the same number of DFEs. We also outline complexity reduction techniques for the special cases of Hadamard based precoded OFDM and single carrier OFDM that are more applicable to the parallel arrangement.