In this paper, M-ary differential phase-shift keying (MDPSK) transmission o
ver possibly time-variant intersymbol interference (ISI) channels is consid
ered. For equalization, we combine noncoherent sequence estimation (NSE) wi
th noncoherent adaptive channel estimation. For this, an efficient noncoher
ent least-mean-square (NLMS) algorithm is employed. It is shown that the re
sulting noncoherent receiver is very robust against carrier phase variation
s. For constant channel phase the convergence speed and the steady-state er
ror of the noncoherent adaptive algorithm are similar to that of a conventi
onal (coherent) LMS algorithm. However, the conventional LMS algorithm dive
rges even for relatively small phase variations, whereas the proposed NLMS
algorithm also converges for relatively large phase variations. Simulations
confirm the good performance of various NSE combined with noncoherent adap
tive channel estimation for both time-invariant and time-variant (fading) I
SI channels.