Spectral line detection using integrated trispectrum

In this dissertation, the trispectrum and the integrated trispectrum are studied as alternative to the delay and multiply (D&M) nonlinearity circuit. The D&M receiver can be used in the detection/estimation of the symbol rate parameter of a digitally modulated carrier. A symbol spectral line is found in the power spectrum of the delay-and-multiply output along with other background noise terms due to the signal itself and receiver input additive Gaussian noise. The correlation function of the delay-and-multiply non-linearity output is a special case of the one-dimensional slice of the fourth moment function (sequence) of the input process. The relation between the output power spectrum and the fourth moment spectrum of the input is established. The spectral line generating components of the input signal are shown to be contained in the fourth cumulant sequence of the input. Signal self-noise terms are also in the fourth cumulant sequence. Since the cumulant sequence with order greater than two is zero for a Gaussian process, a spectral line detection scheme which employs the integrated fourth cumulant spectrum (integrated trispectrum) is investigated.; In this research, we investigate the spectral line detection and propose the use of high-order spectra (HOS) (trispectrum and integrated trispectrum) approach for improving performance of the spectral line detection over the use of a power spectral estimate. The signal considered is a random binary pulse amplitude modulation (PAM).; The approach is composed of two stages. First, the integrated trispectrum scheme is developed, and the integrated trispectrum equivalent to the D&M nonlinearity is estimated using the direct conventional method. Then, the estimation performance is analyzed and evaluated in the HOS domain. The required processor with combining peridograms is also derived.; The theoretical performance bounds which present the lower limit for the detection probability of the integrated trispectrum are also derived. The performance measures for a spectral line detector which are based on the integrated trispectral estimates, the detection probability, and the output signal-to-noise ratio (SNR) are analyzed and evaluated. The performance measures of the integrated trispectrum are also based on the assumption that the detection statistics of the spectral estimates are asymptotically Gaussian distributed. It is verified empirically by showing the plots of the normalized histogram (probability density function estimates) of the integrated trispectrum. With the probability density functions (pdfs) and a Neyman-Pearson frame work, the detection probability is evaluated.; The simulation results of this dissertation provide the comparison between the integrated trispectrum approach and the standard D&M moment spectral method and also validate their theoretical results.; Finally the integrated trispectrum is demonstrated as a superior tool for analyzing a non-Gaussian signal corrupted by unknown additive Gaussian noise; however, simulation practicalities limit the ability of the proposed integrated trispectrum processor to suppress the Gaussian noise completely. For an input signal-to-noise ration (SNR) of 0 dB, the Monte Carlo simulation shows that an output spectral line SNR improvement of about 3.0 dB may be possible.