SUB-NYQUIST SENSING AND SPARSE RECOVERY OF WIDE-BAND INTENSITY MODULATED OPTICAL SIGNALS
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Intensity modulated optical transmitters, wide-bandwidth electro-optical receivers, high-speed digitizers, and digital matched-filters are being used in hybrid lidar-radar systems to measure the range and reflectivity of objects located within degraded visual underwater environments. These methods have been shown to mitigate the adverse effects of the turbid underwater channel due to the de-correlation of the modulated optical signal after undergoing multiple scattering events. The observed frequency-dependent nature of the underwater channel has driven the desire for wider bandwidth waveforms modulated at higher frequencies in order to improve range accuracy and resolution. While the described system has shown promise, the matched filter processing scheme, which is also widely used in the fields of radar and sonar, suffers from inherent limitations. One limitation is based on the achievable range resolution as dictated by the classical time-frequency uncertainty principle, where the bandwidth dictates the measurable resolution. The side-lobes generated during the matched filtering process also present a challenge when trying to detect multiple targets. These limitations are further constrained by currently-available analog-to-digital conversion technologies which restrict the ability to directly sample the wide-band modulated signals. Even in cases where the technology exists that can operate at sufficient rates, often it is prohibitively expensive for many applications and high data rates can pose processing challenges. This research effort addresses both the restrictions imposed by the available analog-to-digital conversion technologies and the limited resolution of the existing time-frequency methods for wide-band signal processing. The approach is based on concepts found within the fields of compressive sensing and sparse signal recovery and will be applied to the detection of objects illuminated with wide-band intensity modulated optical signals. The underlying assumption is that given the directive nature of laser propagation, the illuminated scene is inherently sparse and the limited number of reflecting objects can be treated as point sources. The main objective of this research is to provide results that show, when sampling at rates below those dictated by the traditional Shannon-Nyquist sampling theorem, it is possible to make more efficient use of the samples collected and detect a limited number of reflecting targets using specialized recovery algorithms without reducing system resolution. Through theoretical derivations, empirical simulations, and experimental investigation, it will be shown under what conditions the sub-Nyquist sampling and sparse recovery techniques are applicable, and how the described methods influence resolution, accuracy, and overall performance in the presence of noise.