Rate-line detection using higher-order spectra

The delay and multiply (D&M) receiver can be used in the detection/estimation of the symbol rate parameter of a digitally modulated carrier. A symbol rate-line is found in the power spectrum of the D&M output along with other background noise terms due to the signal itself and receiver input additive Gaussian noise. The correlation function of the D&M nonlinearity output is a special case 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 rateline generating components of the input signal are shown to be contained in the fourth cumulant sequence of the input. Since the cumulant sequence of order greater than two is zero for a Gaussian process, a rate-line detection scheme which uses the fourth cumulant spectrum (trispectrum) is investigated. For an input signal-to-noise ratio (SNR) of 0 dB computer simulation shows that an output rate-line SNR improvement of about 4.3 dB may be possible