Optimal SIMO MLSE receivers for the detection of linear modulation corrupted by noncircular interference

This paper derives the optimal single input multiple output (SIMO) maximum likelihood sequence estimation (MLSE) receiver for the detection of quadrature amplitude modulations corrupted by potentially noncircular, stationary white or colored zero-mean Gaussian noise. It is proved that this receiver is composed by a widely linear (WL) filter followed by a modified version of the Viterbi algorithm. This WL linear filter is interpreted for complex-valued signal of interest (SOI) symbols as two WL multidimensional matched filter (WL MMF) that reduce to a single WL MMF for real-valued SOI symbols. The performance improvements of this receiver with respect to the standard SIMO MLSE are proved and illustrated.