Receivers with widely linear processing for frequency-selective channels

We propose several equalization schemes based on widely linear processing (WLP). The received signal and its complex conjugate are separately filtered and the results are linearly combined. It is shown that WLP yields a gain in performance if the (noiseless) received signal can be interpreted as the convolution of a real-valued data sequence and an equivalent complex-valued intersymbol interference channel impulse response. Such a model applies to, e.g., amplitude-shift keying, offset quadrature amplitude modulation, and binary minimum-shift keying-type modulation. We consider receivers without and with decision feedback. Finite impulse response filters are derived for these structures, which are optimum with respect to the zero-forcing and minimum mean-squared error (MMSE) criteria, respectively. In the MMSE case, adaptive algorithms for filter adjustment are given. Infinite filter orders are investigated in order to obtain analytical performance results. Furthermore, suboptimum trellis-based detection with widely linear preprocessing is briefly discussed. It is demonstrated analytically and by numerical examples that widely linear schemes may outperform conventional schemes significantly, depending on the considered application.