Minimum mean square error filters for binary phase shift keyed signals

One consequence of the Nyquist theory of minimum bandwidth is that any and all bandwidth above that minimum is redundant. This excess bandwidth has been exploited both in cyclostationary signal processing, under the name spectral correlation, as well as in the design of optimal receiver filters. Such receiver filters have to date only exploited the spectral correlation due to a uniform symbol rate, disregarding the spectral correlation about the center frequency which is present in real signals at bandpass frequencies. This paper investigates using both spectral correlations in the design of an optimal receiver filter for binary phase shift keyed (BPSK) signals in colored noise environments. Two results are demonstrated. First, the optimal filter is shown to be a combination of a matched filter for colored noise followed by a tapped delay line equalizer. Second, it is shown that by using this technique significant gains may be achieved in colored noise over other linear filters used in BPSK demodulation.