Considerations on the Optimal and Efficient Processing of Information-bearing Signals

Abstract

Noise is a fundamental hurdle that impedes the processing of information-bearing signals, specifically the extraction of salient information. Processing that is both optimal and efficient is desired; optimality ensures the extracted information has the highest fidelity allowed by the noise, while efficiency ensures limited resource usage. Optimal detectors and estimators have long been known, e.g., for maximum likelihood or minimum mean-squared error criteria, but might not admit an efficient implementation. A tradeoff often exists between the two goals.

This thesis explores the tradeoff between optimality and efficiency in a passive radar system and an analog-to-digital converter. A passive radar system opportunistically uses illuminating signals from the environment to detect and track targets of interest, e.g., airplanes or vehicles. As an opportunistic user of signals, the system does not have control over the transmitted waveform. The available waveforms are not designed for radar and often have undesirable properties for radar systems, so the burden is on the receiver processing to overcome these obstacles. A novel technique is proposed for the processing of digital television signals as passive radar illuminators that eases the need for complex detection and tracking schemes while incurring only a small penalty in detection performance. An analog-to-digital converter samples analog signals for digital processing. The Shannon-Nyquist theorem describes a sufficient sampling and recovery scheme for bandlimited signals from uniformly spaced samples taken at a rate twice the bandwidth of the signal. Frequency-sparse signals are composed of relatively few frequency components and have fewer degrees of freedom than a frequency-dense bandlimited signal. Recent results in compressed sensing describe sufficient sampling and recovery schemes for frequency-sparse signals that require a sampling rate proportional to the spectral density and the logarithm of the bandwidth, while providing high fidelity and requiring many fewer samples, which saves resources. A proposed sampling and simple recovery scheme is shown to efficiently recover the locations of tones in a large bandwidth nearly-optimally using relatively few samples. The proposed sampling scheme is further optimized for full recovery of the input signal by matching the statistics of the scheme to the statistics of the input signal.