English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Motivated by modern applications of light detection and ranging (LIDAR), westudy the model of an optical receiver based on an avalanche photo-diode (APD),followed by electronic circuitry for detection of reflected optical signals andestimation of their delay.This model is known to be quite complicated as itconsists of at least three different types of noise: thermal noise, shot noise,and multiplicative noise (excess noise) that stems from the random gainassociated with the photo-multiplication of the APD. Consequently, thederivation of the optimal likelihood ratio test (LRT) associated with signaldetection is a non-trivial task, which has no apparent exact closed--formsolution. We consider instead a class of relatively simple detectors, that arebased on correlating the noisy received signal with a given deterministicwaveform, and our purpose is to characterize the optimal waveform in the senseof the best trade--off between the false-alarm (FA) error exponent and themissed-detection (MD) error exponent. In the same spirit, we also study theproblem of estimating the delay on the basis of maximizing the correlationbetween the received signal and a time-shifted waveform, as a function of thistime shift. We characterize the optimal correlator waveform that minimizes themean square error (MSE) in the regime of high signal-to-noise ratio (SNR). Theoptimal correlator waveforms for detection and for estimation turn out to bedifferent, but their limiting behavior is the same: when the thermal Gaussiannoise is dominant, the optimal correlator waveform becomes proportional to theclean signal, but when the thermal noise is negligible compared to the othernoises, then it becomes logarithmic function of the clean signal, as expected.

Optimal Correlators for Detection and Estimation in Optical Receivers