Detection efficiency of signal with unknown non-power parameter using algorithms based on the Compressive Sensing theory

Dmitry Yu. Golovanov; Vladimir I. Parfenov

doi:10.3103/S0735272718080046

Authors

Dmitry Yu. Golovanov Voronezh State University, Russian Federation https://orcid.org/0000-0002-2070-9944
Vladimir I. Parfenov Voronezh State University, Russian Federation https://orcid.org/0000-0001-9815-5657

DOI:

https://doi.org/10.3103/S0735272718080046

Keywords:

orthogonal matching pursuit, compressive sensing, detection algorithm, likelihood ratio, sufficient statistic, non-power parameter, sparse signal, total probability of error, ideal observer criterion, signal-to-noise ratio, correlation function

Abstract

The problem of detecting quasi-deterministic signals against the background of noise during the digital processing has been considered. In this case, at the specified detection efficiency, the minimum criterion of required arithmetic operations was used as a synthesis criterion for such algorithms. To this end, such algorithms were synthesized based on concepts of the compressive sensing theory. The computer simulation was used to check the efficiency of developed algorithms making it possible to determine the manner in which the total probability of detection errors depends on the signal-to-noise ratio and the compression ratio (ratio of the number of elements in the sufficient statistic vectors before and after “compression”). The detection efficiency losses of proposed algorithms were determined in comparison with the classical optimal algorithm in accordance with the maximum likelihood method at different values of signal-to-noise ratio and compression ratio. At the same time, the paper indicates the gain in the number of used arithmetic operations of proposed algorithms as compared to the classical one. The presented results allow us to make a sound choice of detection algorithm depending on the available hardware resources and admissible degradation of the detection efficiency.

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