S. V. Petrov - Post-graduate Student, Leading Engineer, OAO "VNIIRT". E-mail: petrovsv@list.ru

In this paper, we solve the problem of estimating the number of stochastic signals for a multi-element antenna array, which is very relevant in radar and other fields of science and technology. For practical applications, it is important to obtain a solution to this problem for conditions where noise power in the channels of the antenna is not known beforehand, and be able to control the level of false alarms by means of the objective threshold value. The problem has been solved for arbitrary antenna array that receives narrowband signals from an external source and the background noise of the antenna elements. The algorithm of estimation of number of stochastic signals based on the theory of detection has been synthesized in the form of a sequence of tests of statistical hypotheses. We obtain an expression for the decision statistic based on the generalized likelihood ratio test. The statistical characteristics of the decision statistic have been analyzed and the expression for calculating the threshold for a given level of false alarms has been derived. The analytical expressions for the probability of false alarm and missing signal have been obtained. The analytical results have been compared with the results of simulations. Comparison of the characteristics of the derived algorithm and the known ones shows high performance of the synthesized algorithm.

 

1. Wax M., Kailath T. Detection of signals by information theoretic criteria // IEEE Trans. Acoustics, Speech, and Signal Processing. 1985. V. 33. № 2. P. 387-392.
2. Nadakuditi R.R., Edelman A. Sample eigenvalue based detection of high dimensional signals in white noise using relatively few samples // IEEE Trans. Signal Processing. 2008. V. 56. № 7. P.2625-2638.
3. Nadler B.Nonparametric detection of signals by information theoretic criteria: performance analysis and an improved estimator // IEEE Trans. Signal Processing. 2010. V. 58. № 5. P.2746-2756.
4. Lu Z., Zoubir A.M. Flexible detection criterion for source enumeration in array processing // IEEE Trans. Signal Processing. 2013. V. 61. № 6. P. 1303-1314.
5. Schott J.A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix // Journal of Multivariate Analysis. 2006. V. 97. № 4. P. 827-843.
6. Kritchman S., Nadler B. Non-parametric detection of the number of signals: hypothesis testing and random matrix theory // IEEE Trans. Signal Processing. 2009. V. 57. № 10. P.3930-3941.
7. Nechaev JU.B., Zotov S.A. Bystryjj metod ocenki chisla signalov pri nalichii gaussovskogo i negaussovskogo shumov // Antenny. 2008. Vyp. 7-8 (134-135). S. 104-110.
8. Van Tris G. Teorija obnaruzhenija, ocenok i moduljacii. T. 1. M.: Sov. radio. 1972.
9. KHorn R., Dzhonson CH. Matrichnyjj analiz. M.: Mir. 1989.
10. Bejan A.Largest eigenvalues and sample covariance matrices. Tracy-Widom and Painleve II: computational aspects and realization in S-Plus with applications. URL: www.cl.cam.ac.uk/~aib29/TWinSplus.pdf.