"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 6, 2017

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Detection of signals with a sampling rate not exceeding the Nyquist frequency


V. I. Parfenov, D. Y. Golovanov

Voronezh State University, Universitetskaya pl. 1, Voronezh, 394018, Russia


The paper is received on April 4, after correction - om May 31, 2017


Abstract. In this article detection algorithms of discrete sparse signal with discrete Gaussian white noise with reconstruction and without reconstruction of nonzero signal components from the observed compressed data vector were proposed. Various conditions under which the positions and values of nonzero components in a discrete signal could be known and unknown were considered. Computer modeling of the proposed algorithms was performed and analysis of effectiveness of these algorithms based on investigation of behavior of total error probability depending on signal to noise ratio, compression level and sparsity of original signal was implemented. It was found, that the total probability of error for all synthesized algorithms decreases with increasing signal to noise ratio and decreases with increasing ratio of the number of elements in the observed data vector to the number of elements in the original discrete signal. Besides, for most algorithms, total probability of error decreases with decreasing the number of nonzero components in the signal. In this article approximate theoretical formulas for the total probability of error were represented. These formulas are applicable, when the positions of the nonzero signal components are known and relatively well describe the behavior of the total probability of error from the indicated parameters. Obtained data can be used for a reasonable choice of the parameters of the random demodulator depending on the observation conditions.

Key words: detection algorithm, discrete signal, Nyquist frequency, sparse signal, Compressive Sensing, Orthogonal Matching Pursuit (OMP), likelihood ratio, ideal observer criterion, total probability of error, signal to noise ratio.


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For citation:

V. I. Parfenov, D. Y. Golovanov. Detection of signals with a sampling rate not exceeding the Nyquist frequency. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 6. Available at http://jre.cplire.ru/jre/jun17/1/text.pdf. (In Russian)