Spread-spectrum signals that use spreading codes chosen to give a low probability of chip rate detection are examined. Pulse shaping and pseudorandom amplitude weighting are used to defeat the interceptor who uses a nonlinear circuit to generate a tone at the chip rate of the signal. The case of low input signal-to-noise ratio (SNR) is considered. Under this assumption, the detector output spectrum is found, and the output SNR is then used as a measure of detectability. The effect of signal pulse shape, i.e., band-limiting, on performance is studied. It is shown that a combination of band-limiting and correctly chosen amplitude weightings can, ideally, defeat any such circuit. The performance of a fourth-power envelope detector is analyzed with a combination of signal pulse shape and amplitude weighting. The amplitude distributions are binary, Gaussian, and quantized Gaussian.>

A method for finding the nonstationary moments of a random binary pulse train with arbitrary pulse shape is described and used to find the joint moments of the pulse train with a delayed version of itself. These moments are used in the analysis of nonlinear synchronization circuits. The method uses the moment generating function and a recursive relationship for moments and cumulants. Example derivations are given for moments up to eighth order.>

The detectability of the symbol rate of a digitally modulated signal by a delay and multiply receiver is investigated. Two signal pulse types are considered: Nyquist pulses and rectangular pulses. Since many digital transmission systems use rectangular pulse shapes, symbol rate-line detectability is considered for receivers optimized for rectangular pulses. For a receiver configuration that is reasonable for rectangular pulses, it is found that with a Nyquist pulse parameter alpha =0.25, the rate-line signal-to-noise ratio is down about 20 dB from that for a rectangular pulse signal.>