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Joint detection – recognition of signals with singular correlation matrix

Keywords:

Yu.S. Radchenko – Dr. Sc. (Phys.-Math.), Professor, Department of Radiophysics, Voronezh State University E-mail: ysradchenko@yandex.ru


The problem of joint detection-recognition of M signals with amplitude-phase modulation is solved. A Bayesian decision rule for decision on the (M + 1)-th hypothesis is synthesized. An extended set of characteristics of this algorithm is proposed. Calculation of characteristics for multiposition amplitude-phase modulation results in calculation of multivariate normal integrals with a singular correlation matrix. A method to work with singular normal distribution is proposed. It is shown that the constellation of signals with QAM has only two nonzero eigenvalues of the correlation matrix and two non-singular components of multivariate probability density of the decisive statistics. The other components have δ form structure. For illustration exact analytical characteristics of joint detection-recognition of signals are obtained for systems with 2- and 4 positional phase modulation. A comparison of the obtained characteristics with similar ones for separate detection and recognition are presented. It is established that the addition of the hypothesis about absence of a signal leads to an increase in the number of wrong decisions in the full group of events. Comparison of probabilities of correct decisions for the joint detection-recognition of signals with similar probabilities for separate detection and recognition show their substantial decrease. The obtained results generalize known expressions for errors of the demodulation signals with phase modulation.
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