Signal detection in additive Gaussian noise, Doppler frequency shift and propagation fading fluctuations environment by using third-order test statistics

The problem of detecting a signal embedded in additive Gaussian noise is considered based on statistical decision theory and Neyman-Pearson criterion. The study is carried out for novel test statistics (TSs) estimated that use third-order moment functions. Performances of signal detection for traditional energy second-order TS calculated as the peak of the matched filter output, the second-order TS estimated as the peak value of the matched filter output autocorrelation function and the third-order TSs computed as the peak values of third-order autocorrelation and cross-correlation functions are investigated and compared between each other. Computer simulations have been performed for typical kinds of signals as LFM waveform, radio-frequency pulse, single video pulse of rectangular shape and two pulses of different amplitudes and triangular shape. The performance of signal detection is evaluated and studied by using binary hypothesis and likelihood ratio for the secondand third-order TSs. Probability of detection curves demonstrate that the use of the third-order TSs provides other advantages. They are insensitivity to random signal shifts that can severely worse traditional matched filter performance, good immunity to additive Gaussian noise of a priori unknown spectral density, and robustness to random Doppler frequency shift and magnitude fluctuations in received signals.