Generalized Energy Detector with Iterative Processing of Narrowband Signals in Frequency Domain

Abstract

The article is devoted to improvement and study of efficiency of the energy detector of narrow-band signals in background of additive noise of unknown power. Analytical expressions describing the probability density distribution of samples of the generalized energy spectrum of noise are obtained. It is shown that the obtained distributions describe well the broadband noise, which differs from the Gaussian one. For the separation of signal and noise samples in the frequency domain, was proposed the decisive statistics in the form of the standard deviation of generalized power spectral density. The threshold value of the decisive statistics for a given probability of false alarm rate in frequency domain was obtained numerically. An iterative algorithm for detecting narrow-band signals in the frequency domain was proposed. A distinctive feature of the developed algorithm is the normalization of the vector of frequency samples to the sum of its elements after each iteration of processing, which consists of recursively calculating the value of decisive statistics, comparing it with the threshold and, if the threshold is exceeded, discarding the maximum frequency sample from the vector. Each dropped sample is signal sample. This approach will allow to detect narrow-band signals in a dynamic range, which is limited only by the maximum level of side lobes of the window function. During the study of the algorithm, it was found that the highest detection quality indicators are achieved when the value of the exponent to which the frequency samples is about 3. The type of window function has little effect on the probability of detection, and this effect decreases with increasing the load on the analysis frequency band. At the same time, the proposed detector remains operable when the analysis frequency band is loaded up to 20%, and its performance is not worse than for the case of a known noise level. If the value of the exponent deviates from 3, the algorithm will be operational with a smaller bandwidth load.