Generalized Energy Detector with Iterative Processing of Narrowband Signals in Frequency Domain
Keywords:decisive statistics, signal-to-noise ratio, narrowband signal, iterative processing, threshold, generalized energy detector
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.
Hippenstiel R. D. Detection theory: applications and digital signal processing / R. D. Hippenstiel. - CRC Press LLC, 2002. - 340 p.
Костылев В. И. Статистический анализ эффективности обнаружения случайных сигналов на фоне полигауссовского шума с помощью обобщенного энергетического обнаружителя первого порядка / В.И. Костылев, И.П. Гресь // Вестник ВГУ. Системный анализ и информационные технологии. - 2015. - № 3. - С. 75-83.
Zhang Y. L. Frequency-Domain Entropy-Based Detector for Robust Spectrum Sensing in Cognitive Radio Networks / Y.L. Zhang, Q.Y. Zhang, T.A. Melodia // IEEE Communications letters. - 2010. - Vol. 14, NO. 6.~- pp. 533-535.
Tandra R. SNR walls for signal detection / R. Tandra, A. Sahai // IEEE J. Sel. Topics Signal Process. - 2008. - Vol. 2, NO. 1. - pp. 4-17.
Nuttall A. H. Performance of Power-Law Processor with Normalization for Random Signals of Unknown Structure~/ A.H. Nuttall. - Rhode Island, 1997. 95 p.
Дворников С. В. Обнаружение сигналов с высоким различием динамики их амплитуд / С.В. Дворников, С.С. Дворников // Информационные технологии. - 2010. - № 2. - С. 56−59.
Токарев А. Б. Применение СМОШ – статистик для расчета порога панорамного обнаружения сигналов / А. Б. Токарев // Радиотехника. - 2012. - Вып. 2. - С. 53–59.
Kundu D. Statistical signal processing: frequency estimation / D. Kundu, S. Nandi. - 2012. - 141 p.
Devore J. Probability and Statistics for Engineering and the Sciences. Eighth edition / J. Devore. - Brooks/Cole, Cengage Learning, 2012. - 776 p.
Бугайов М. В. Ітеративний метод виявлення вузькосмугових сигналів на основі аналізу коефіцієнта варіації спектральних оцінок / М.В. Бугайов // Пріоритетні напрямки розвитку телекомунікаційних систем та мереж спеціального призначення. - Київ : ВІТІ. - с. 69–70.
Hippenstiel R. D. (2002) Detection theory: applications and digital signal processing, CRC Press LLC, 340 p.
Kostulev V. I. and Gres I. P. (2015) The statistical analysis of efficiency of detection of random signals against polygaussian noise by means of the generalized energy detector of the first order. Vestnik VGU. Systems Analysis and Information Technologies, No. 3, pp. 75-83.
Zhang Y., Zhang Q. and Melodia T. (2010) A frequency-domain entropy-based detector for robust spectrum sensing in cognitive radio networks. IEEE Communications Letters, Vol. 14, Iss. 6, pp. 533-535. DOI: 10.1109/lcomm.2010.06.091954
Tandra R. and Sahai A. (2008) SNR Walls for Signal Detection. IEEE Journal of Selected Topics in Signal Processing, Vol. 2, Iss. 1, pp. 4-17. DOI: 10.1109/jstsp.2007.914879
Nuttall A.H. (1997) Performance of Power-Law Processor with Normalization for Random Signals of Unknown Structure. DOI: 10.21236/ada327076
Dvornikov S.V. and Dvornikov S.S. (2010) Detecting of Signals with Different Ranges of Amplitudes, Informatsionnyye tekhnologii, no. 2, pp. 56-59.
Tokarev A.B. (2012) Use of MeVMaNS-Statistic as a Basis for the Panoramic Detection Threshold Estimation. Radiotekhnika, No.12, pp. 53-59.
Kundu D. and Nandi S. (2012) Statistical signal processing: frequency estimation. Springer, 141 p.
Devore J.L. (1991) Probability and Statistics for Engineering and the Sciences.. Biometrics, Vol. 47, Iss. 4, pp. 1638. DOI: 10.2307/2532427
Buhaiov M.V. (2018) Iteratyvnyi metod vyiavlennia vuzkosmuhovykh syhnaliv na osnovi analizu koefitsiienta variatsii spektralnykh otsinok [An iterative method for narrowband signals detecting based on the analysis of the coefficient of variation of spectral estimates]. Priority directions for the development of telecommunication systems and networks of special purpose, Kyiv, pp. 69-70.
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