Two nonequivalent structures for widely-linear decision-feedback MMSE equalization over MIMO channels

The paper deals with the design of the equalizer based on the widely linear processing combined with the decision-feedback (DF) procedure and operating over time-dispersive multiple-input multiple-output channel. A basic issue concerns the choice between two widely-linear/widely-linear decision-feedback structures: the former is based on the complex-valued signal representation, whereas the latter utilizes the real-valued representation of the involved signals. Indeed, in previous contributions, both structures have been indifferently used since, in the considered scenarios, they resulted to be equivalent. In this paper, we recognize that there is an important scenario where the above structures are not equivalent. To fairly compare them, the issue of decision-error propagation has been addressed. An extensive set of experimental results shows that the real-valued signal representation-based equalizer outperforms significantly the complex-valued representation-based equalizer as well as the conventional DF equalizer when the effects of decision errors in the feedback filters are taken into account.