1 research outputs found
Optimal Correlators for Detection and Estimation in Optical Receivers
Motivated by modern applications of light detection and ranging (LIDAR), we
study the model of an optical receiver based on an avalanche photo-diode (APD),
followed by electronic circuitry for detection of reflected optical signals and
estimation of their delay.This model is known to be quite complicated as it
consists of at least three different types of noise: thermal noise, shot noise,
and multiplicative noise (excess noise) that stems from the random gain
associated with the photo-multiplication of the APD. Consequently, the
derivation of the optimal likelihood ratio test (LRT) associated with signal
detection is a non-trivial task, which has no apparent exact closed--form
solution. We consider instead a class of relatively simple detectors, that are
based on correlating the noisy received signal with a given deterministic
waveform, and our purpose is to characterize the optimal waveform in the sense
of the best trade--off between the false-alarm (FA) error exponent and the
missed-detection (MD) error exponent. In the same spirit, we also study the
problem of estimating the delay on the basis of maximizing the correlation
between the received signal and a time-shifted waveform, as a function of this
time shift. We characterize the optimal correlator waveform that minimizes the
mean square error (MSE) in the regime of high signal-to-noise ratio (SNR). The
optimal correlator waveforms for detection and for estimation turn out to be
different, but their limiting behavior is the same: when the thermal Gaussian
noise is dominant, the optimal correlator waveform becomes proportional to the
clean signal, but when the thermal noise is negligible compared to the other
noises, then it becomes logarithmic function of the clean signal, as expected.Comment: 22 pages, 2 figures, submitted for publicatio