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The specific problem of detecting the presence of either binary-phase-shift-keyed (BPSK) signals or BPSK direct-sequence spread-spectrum (DS/SS) signals with a prefilter-delay-and-multiply (PFDM) device is considered. Using stationary process theory and Fourier analysis, the optimum PFDM structures for signal presence detection of BPSK signals with known bit rates and carrier frequencies and BPSK DS/SS signals with known chip rates and carriers in additive colored Gaussian noise are derived. The structures are optimum in the sense that they maximize the spectral signal-to-noise ratio (SNR) of an output periodic waveform which has fundamental frequency equal to the bit or chip rate of the signal. Two of the optimum structures that are derived and analyzed are the optimal prefilter-square device and the optimal PFDM with delay set to one half of the signal's bit or chip duration. >

A general spectrum-analysis-based approach to the problem of detecting the presence of unknown weak signals in noisy observations is developed. The weak signal assumption enables exploitation of familiar results from the theory of local optimality, from which correlation-based detectors for the presence of known weak signals in additive independent and identically distributed (IID) noise have been derived. The development here follows from the perception that a spectrum analyzer is nothing more than a number of correlators in parallel. The approach has application to any observations that are not IID Gaussian processes. Some practical situations treated here, in which signal presence detection might be better accomplished using the proposed approach, are unknown weak signals: (1) in additive non-Gaussian interference, (2) in additive colored Gaussian noise, and (3) at the output of a nonlinear system, such as a square-law device. Items (2) and (3) required the extension of correlations-based locally optimum detection theory to cover observation processes that are not necessarily signals in additive noise. >

Assuming that a binary phase-shift-keyed (PSK) waveform plus Gaussian noise is input to a delay-and-multiply or squarer, a memoryless locally optimum scheme for detecting the generated rate line is reported. The locally optimum formulation is used because the rate line is a signal in non-Gaussian noise, and it is typically weak. It is found that if the double-frequency output of a bandpass squaring detector is used, the locally optimum spectral technique outperforms standard spectral analysis. >