Generalized differential encoding: a nonlinear signal processing framework

Encoding of communication signals compensates for phase distortions introduced by imperfect local oscillators, fading, and multipath effects. Differential encoding is generalized in this paper using a nonlinear transformation called multi-lag high-order instantaneous moment (ml-HIM). The ml-HIM decoder is capable of removing not only constant phase ambiguity, but also Doppler frequency, Doppler rate, and even higher-order phase distortions. The multiple lags present in the ml-HIM are exploited to improve system performance. Differential encoding is also generalized to non-constant modulus constellations such as M-ary QAM and AM-PM.