Design and Analysis of Compressed Sensing Radar Detectors

• Published in: IEEE transactions on signal processing Vol. 61; no. 4; pp. 813 - 827
• Main Authors: Anitori, L., Maleki, A., Otten, M., Baraniuk, R. G., Hoogeboom, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation algorithms; Asymptotic properties; Complex approximate message passing (CAMP); Compressed; compressed sensing; Computer simulation; constant false alarm rate (CFAR); Design engineering; detection probability; Detection, estimation, filtering, equalization, prediction; Detectors; Exact sciences and technology; false alarm probability; False alarms; Information, signal and communications theory; Message passing; Monte Carlo methods; Noise; Noise measurement; radar; Radar detection; Reconstruction; Sampling, quantization; Signal and communications theory; Signal, noise; Studies; Target detection; Telecommunications and information theory; Vectors; Performance evaluation; Monte Carlo method; AWGN; Measurement sensor; Complex approximate message passing (CAMP); Background noise; Algorithm; False alarm rate; Radar remote sensing; Message passing; Radar; false alarm probability; Signal processing; Numerical simulation; detection probability; Target detection; Compressed sensing; constant false alarm rate (CFAR); Signal to noise ratio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2012.2225057

We consider the problem of target detection from a set of Compressed Sensing (CS) radar measurements corrupted by additive white Gaussian noise. We propose two novel architectures and compare their performance by means of Receiver Operating Characteristic (ROC) curves. Using asymptotic arguments and the Complex Approximate Message Passing (CAMP) algorithm, we characterize the statistics of the ℓ 1 -norm reconstruction error and derive closed form expressions for both the detection and false alarm probabilities of both schemes. Of the two architectures, we demonstrate that the best performing one consists of a reconstruction stage based on CAMP followed by a detector. This architecture, which outperforms the ℓ 1 -based detector in the ideal case of known background noise, can also be made fully adaptive by combining it with a conventional Constant False Alarm Rate (CFAR) processor. Using the state evolution framework of CAMP, we also derive Signal to Noise Ratio (SNR) maps that, together with the ROC curves, can be used to design a CS-based CFAR radar detector. Our theoretical findings are confirmed by means of both Monte Carlo simulations and experimental results.