Optimal Correlators for Detection and Estimation in Optical Receivers

Motivated by modern applications of light detection and ranging (LIDAR), we study the model an optical receiver based on avalanche photo-diode (APD), followed electronic circuitry for reflected signals estimation their delay. This is known to be quite complicated as it consists at least three different types noise: thermal noise, shot multiplicative noise (excess noise) that stems from random gain associated with photo-multiplication APD. Consequently, derivation optimal likelihood ratio test (LRT) signal a non-trivial task, which has no apparent exact closed-form solution. We consider instead class relatively simple detectors, are correlating noisy received given deterministic waveform, our purpose characterize waveform in sense best tradeoff between false-alarm (FA) error exponent missed-detection (MD) exponent. In same spirit, also problem estimating delay basis maximizing correlation time-shifted function this time shift. correlator minimizes mean square (MSE) regime high signal-to-noise (SNR). The waveforms turn out different, but limiting behavior same: when Gaussian dominant, becomes proportional clean signal, negligible compared other noises, then logarithmic expected.