Sparse Sensing With Co-Pprime Samplers and Arrays

• Published in: IEEE transactions on signal processing Vol. 59; no. 2; pp. 573 - 586
• Main Authors: VAIDYANATHAN, Palghat P, PAL, Piya
• Format: Journal Article
• Language: English
• Published: New York, NY Institute of Electrical and Electronics Engineers 01-02-2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Arrays; Detection; Detection, estimation, filtering, equalization, prediction; Estimates; Estimating; Exact sciences and technology; Filter banks; Information, signal and communications theory; Miscellaneous; Samplers; Sampling; Sampling, quantization; Signal and communications theory; Signal processing; Signal, noise; Telecommunications and information theory; Time domain; Parameter estimation; Direction-of-arrival estimation; co-prime arrays; sparse sensing; Signal estimation; Discrete Fourier transformation; Narrow band; Beam forming; Time domain method; Sparse set; Signal processing; Chinese; Filter bank; Stationary signal; Autocorrelation; Sampling; Sensor array; Sinusoidal signal; Signal detection; Co-arrays; Power spectrum
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2089682

This paper considers the sampling of temporal or spatial wide sense stationary (WSS) signals using a co-prime pair of sparse samplers. Several properties and applications of co-prime samplers are developed. First, for uniform spatial sampling with [Formula Omitted] and [Formula Omitted] sensors where [Formula Omitted] and [Formula Omitted] are co-prime with appropriate interelement spacings, the difference co-array has [Formula Omitted] freedoms which can be exploited in beamforming and in direction of arrival estimation. An [Formula Omitted]-point DFT filter bank and an -point DFT filter bank can be used at the outputs of the two sensor arrays and their outputs combined in such a way that there are effectively [Formula Omitted] bands (i.e., [Formula Omitted] narrow beams with beamwidths proportional to [Formula Omitted]), a result following from co-primality. The ideas are applicable to both active and passive sensing, though the details and tradeoffs are different. Time domain sparse co-prime samplers also generate a time domain co-array with [Formula Omitted] freedoms, which can be used to estimate the autocorrelation at much finer lags than the sample spacings. This allows estimation of power spectrum of an arbitrary signal with a frequency resolution proportional to even though the pairs of sampled sequences [Formula Omitted] and [Formula Omitted] in the time domain can be arbitrarily sparse -- in fact from the sparse set of samples [Formula Omitted] and [Formula Omitted] one can estimate [Formula Omitted] frequencies in the range . It will be shown that the co-array based method for estimating sinusoids in noise offers many advantages over methods based on the use of Chinese remainder theorem and its extensions. Examples are presented throughout to illustrate the various concepts.