Approaching Helstrom limits to optical pulse-position demodulation using single photon detection and optical feedback

Optical pulse-position modulation (PPM) is one of the primary modulation formats being investigated for use in deep-space communications, as well as terrestrial fiber optical communications. We consider the problem of demodulating M-ary optical PPM waveforms, and propose a structured receiver whose mean probability of symbol error is smaller than all known receivers, and approaches the Helstrom (quantum) limit of the minimum probability of error (MPE) of discriminating between the coherent-state PPM signals. The receiver uses photodetection coupled with optimized phase-coherent optical feedback control through the PPM pulse slots and a phase-sensitive parametric amplifier. We present a general framework of optical receivers known as the ‘conditional pulse nulling receiver’, and present new results on ultimate limits and achievable regions of the trade-off space between the spectral versus photon efficiency of PPM, for the single-spatial-mode far-field pure-loss optical communication channel.