ПРОБЛЕМА ОПТИМАЛЬНОСТІ АДАПТИВНИХ РАДІОТЕХНІЧНИХ СИСТЕМ В СИТУАЦІЇ З НЕКЛАСИФІКОВАНОЮ НАВЧАЛЬНОЮ ВИБІРКОЮ СПОСТЕРЕЖЕНЬ

Abstract

Statistical synthesis of adaptive systems for spatiotemporal signal processing in most radio engineering problems occurs under the condition of parametric a priori uncertainty. The prospective direction of overcoming parametric a priori uncertainty is affiliated with the prior learning procedure. As a result of the training, sufficient statistics of likelihood ratios are formed, which are used in decision-making. The asymptotic optimality of adaptive systems with alternative benchmarks, one of which is peculiar to the class of radio structures with an adaptive antenna array and the other with an adaptive interference compensator, is studied subjectively with unclassified training sampling. The optimality of the system is determined by the criterion of maximum signal-to-interference ratio. The energy parameter representing the signal-to-interference ratio at the output of adaptive radio systems with a generalized reference was chosen as an indicator of optimality. As a result of the research, analytical expressions for the estimation and comparative analysis of energy losses at the output of adaptive systems with different standards under conditions of classified and unclassified learning were obtained. The invariance of the system with an adaptive antenna array to any type of training with preservation of the asymptotic properties of the radio system in the situation with a finite size of the training sample is proved. This feature is considered as a basis for factorization of the transfer function of the adaptive system. This makes it possible to form an optimal hierarchical algorithm for compensation of combined passive and active interference, as well as active interference with an arbitrary spatial power spectrum. The obligatory classification of a training sample of observations for radio engineering systems with an adaptive interference compensator under conditions of signal-interference a priori uncertainty is substantiated. Keywords: asymptotic optimality, adaptive system, alternative benchmark, unclassified training sample, correlation matrix of observations, energy index.