Detection of the pulse signal sequences in the noises with independent values and the probability distribution density

Robust methods for overcoming a priori uncertainty make it possible to find for selected models of input influences close to optimal signal processing procedures, including detection algorithms. A number of studies have solved some of the problems of sustainable detection based on the use of, for example, robust hypothesis testing or locally optimal problem setting. At the same time, the proposed approaches have certain disadvantages. In particular, robust detection of a non-coherent sequence of pulses in noise with independent values and density of probability distribution belonging to a given class of symmetric distributions is not considered. The article proposes a solution to the robust detection problem, proceeding from testing a complex hypothesis against a complex alternative and using an M-detector. The purpose of the article is to analyze the task of robust detection of coherent and non-coherent sequence of pulses in noise with independent values and density of probability distribution belonging to a given class of symmetric distributions. An algorithm for robust detection of a non-coherent sequence of pulses was analyzed, asymptotically providing the best achievable lower bound on the probability of correct detection and an upper bound on the probability of a false alarm, regardless of the density of the noise probability distribution. Using the statistical modeling method, comparative characteristics of various robust detectors and a Gaussian receiver of a coherent and non-coherent sequence of pulses in noise other than normal were obtained at final sample sizes. The effect of the number of sampled values in the pulse and the number of pulses in the sequence on the detector characteristics was analyzed. The degree of stability of the considered detectors was determined. The proposed solutions allow determining conditions and possibilities of using a robust detector of a non-coherent pulse sequence as asymptotically optimal. The characteristics of robust detectors and the Gaussian receiver under the influence of noise with different envelopes are also obtained, which make it possible to calculate and implement optimal signal processing devices.