A novel method of weak impulse detection using the variance of the power spectral density and the discrete Fourier transform
Mieczysław Jessa, Piotr Ślęzak · 2013
Abstract: Typical methods of weak signal detection use a correlation function or a matched filter. They maximize the signal-to-noise ratio (SNR) at the output to make the proper decision about the received symbol. One method for increasing the SNR involves the use of the discrete Fourier transform (DFT). By multiplying the size of the DFT by K, we multiply the value of the SNR. In practice, K cannot be too large because the method works properly when samples are uncorrelated, which is difficult to achieve in a real system because limited bandwidth introduces strong correlations between samples when the sampling frequency is too high. In this paper, we propose a novel method for weak signal detection that uses the discrete Fourier transform but is not based on the SNR concept. The method exploits the flatness of the spectral density of the additive noise jamming data impulses. In the proposed method, we compute the quotient of the variance of the power spectral density of the signal with noise and the variance of the power spectral density of the noise. When the size of the DFT is increased to K times the original size, the increase in this quotient is proportional to K2, which enables the detection of weaker signals than can be detected when a method based on the SNR is used. Analytical expressions are illustrated with simulations, which confirm the utility of the proposed method for rare data and for data filtered with the use of the moving average (MAV). The goal of the MAV is to increase the SNR for the N-point DFT.