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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Adaptive quantum receiver for PPM and multi-pulse PPM weak signal discrimination

Chen Tian, Bing Zhu

Published Jul 1, 2017• 1 citation
Publisher

Abstract

We present a quantum receiver for weak signals of the pulse position modulation (PPM) and its modification, multi-pulse PPM, which approaches the Helstrom limit. The adaptive detection strategy is performed by Bayes criterion derived from the records of an on-off single photon detector (SPD).
DOI
10.1109/cleopr.2017.8118744

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Optical pulse position modulation (PPM) places a laser pulse, a.k.a. a coherent state of amplitudeα\alphaαof mean photon numberN=∣α∣2N=\vert \alpha\vert ^{2}N=∣α∣2, in one ofMMMconsecutive time slots, Ideal photon detection on each slot achieves a mean probability of error((M−1)/1M)e−N((M-1)/1M)e^{-N}((M−1)/1M)e−Nof distinguishing theiMiMiMPPM codewords, sincee−Ne^{-N}e−Nis the probability the pulse-containing slot does not produce a click, per Poisson-shot-noise photo-detection theory. The quantum (Helstrom) limit of the minimum probability of error is lower than above, has a closed-form expression, and scales as∼e−2N\sim e^{-2N}∼e−2NwhenMe−N≪1Me^{-N}\ll 1Me−N≪1. The optimal receiver must make a quantum joint measurement on allMMMslots. Even though receiver algorithms exist that achieve the∼e−2N\sim e^{-2N}∼e−2Nscaling in the highNNNregime, none are known that bridge the classical-quantum gap for smallNNN, the primary regime of interest for optical PPM. It is also not known how close to the Helstrom limit can one get using LOCC. (local operations and classical communications), i.e., a receiver that slices each of theMMMslots intonnntiny slices, makes a measurement on the first slice, and based on the measurement result picks a measurement to apply to the next slice, etc., until all theMnMnMnslices have been measured. In this paper, we propose an LOCC receiver for demodulating PPM that uses semiclassical coherent feedback control and photon detection, which outperforms all known PPM receivers, including one that employed squeezing, a non-classical operation. To bridge the remaining gap to the Helstrom limit, one might need truly quantum operations within a joint (non-LOCC) receiver.
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.
Conditional pulse nulling (CPN) receiver is proposed by Dolinar to discriminate pulse position modulation (PPM) signals. The receiver, which uses a beam splitter and an on-off photon detector can outperform the standard quantum limit (SQL) for PPM signals. In this paper, this receiver is applied to multi-pulse PPM (MPPM) and binary quantum coding signals, and a dynamic programming algorithm is proposed to optimize the control strategy. The MPPM signals are used to improve the band-utilization efficiency, and the binary quantum coding enables the communication system to correct the error. Numerical simulation results show that the CPN receiver with optimized strategy outperform SQL for both MPPM and binary quantum coding signals.