Generalized Stokes parameters-shift keying: a new perspective on optimal detection over electrical and optical vector incoherent channels

We consider block transmission over the incoherent channel, whereby several symbols either launched consecutively in time, or in parallel over several diversity paths, are equally affected by common isotropic phase and additively corrupted by circularly Gaussian additive noise. Our novel approach toward transmission over such a vector incoherent channel (VIC) model is based on coherency matrix and generalized Stokes parameters (GSP) descriptions of optimal detection inspired by classical optical polarization theory, but further extended to the dual context of generic electrical, as well as optical, communication. The four classical real-valued parameters introduced into optics by Stokes in 1853 to characterize the state of polarization of an optical beam, extended to D² GSP, underlie our new alternative novel description of maximum a posteriori/maximum-likelihood (MAP/ML) optimal detection over the VIC channel. The modulation formats of polarization-shift keying (POLSK), differential phase-shift keying, and amplitude-shift keying, as well as recent and novel combinations thereof, will all be seen to be equivalent to a new conceptual form of modulation called GSP-shift keying. Several forms of the optimal MAP/ML receiver for vector multienergy transmission are developed, generalizing the classical scalar incoherent receiver and the known POLSK receivers.