The idea of using a multiple (more than two) symbol observation interval to improve error probability performance is applied to differential detection of trellis-coded multiple phase-shift keying (MPSK) over an additive white Gaussian noise (AWGN) channels. An equivalent Euclidean distance measure per trellis branch is determined for this detection scheme. This is used to define an augmented (larger multiplicity) trellis code whose distance measure is the conventional squared Euclidean distance typical of conventional trellis-coded modulation on the AWGN. Such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis. Results are obtained by a combination of analysis and computer simulation. It is shown that only a slight increase (e.g. one symbol) in the length of the observation interval will provide a significant improvement in bit error probability performance.>

The effect of filtering on the signal-to-noise ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worst-case amplitude ripple. The problem is formulated as an optimization in the Hilbert space L/sub 2/. The form of the worst-case amplitude ripple is specified, and the degradation in the SNR is derived in closed form. It is shown that, when the maximum passband amplitude ripple is 2 delta (peak-to-peak), the SNR is degraded by at most (1- delta /sup 2/), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple under 0.42 dB.>