Method for spectrum holes detection based on mode analysis of spectral samples histogram

Abstract

The subject of this article is the process of detection and estimation frequency boundaries of spectrum holes under conditions of high spectrum occupancy when using receivers with narrow instantaneous bandwidths. The work increases the probability of spectrum holes correct detection in conditions of high occupancy of the radio frequency spectrum and variable noise levels by developing a method to distinguish signal and noise samples based on the analysis of the histogram of spectral sample modes. The tasks to be solved are: development of a method for separation signal and noise samples in the frequency domain; development of a methodology to find the minimum mode of a multimodal probability distribution; determination of frequency boundaries of spectrum holes; formulation of recommendations for the practical implementation of developed method. The methods used are: methods of probability theory and mathematical statistics, methods of statistical modeling. The essence of the proposed method is to distinguish the set of energy spectrum samples using a threshold, obtained for the value of the histogram mode, which corresponds to noise, and to determine the frequency boundaries of spectrum holes. The following results were obtained: an expression for calculating the threshold value for separation signal and noise samples in the frequency domain using the value, which corresponds to the noise mode of the frequency samples of the probability density function. It was found that the noise mode has the smallest value among other modes, since noise samples have a smaller value compared to the signal ones. A technique for estimating the value of the noise mode has been developed, which consists of a histogram of energy spectrum frequency samples and finding the partition interval that corresponds to the value of the minimal mode. An approach was proposed to determine the frequency boundaries of noise samples in the presence of one signal in the analyzed band. Conclusions. The developed method allows detecting spectrum holes with a probability of at least 0.9 at signal-to-noise ratio values of at least 5 dB for the spectrum with a rectangular shape envelope and 12 dB for other envelopes under occupancy of up to 80%.

Keywords

• histogram
• mode
• spectrum occupancy
• test statistics
• spectrum hole
• welch periodogram