Abstract
The improper nature of intersymbol interference (ISI) for signals transmitted over frequency-selective channels is investigated in this paper. Our analysis reveals that for real signals, the improperness originates from both improper signal modulation and the interference cancellation process, whereas for most complex signals, the improperness is only a characteristic of the residual ISI due to interference cancellation. To utilize the improperness of ISI, a multistage widely linear equalization algorithm is introduced, and it is generally applicable for both real and complex signal constellations. The results reveal that accounting for the improper nature of the ISI at both the input and output of the equalizer leads to a noticeable performance gain compared with conventional equalization schemes.