An FMCW (frequency modulated continuous wave) sensor that uses triangular modulation is considered. The sampled output from two range gates are processed so that the device will initiate some function when it passes through a desired range. An expression is obtained for the detection probability from which the expected value and standard deviation of the range of function may be obtained.>

Detection of a memoryless nonlinear functional of a Gaussian process in additive Gaussian white noise is considered. The Volterra functional expansion for the likelihood ratio, and two examples of calculating the kernels are presented. It is shown that kernels up to third order can be obtained for a hard-limited Gaussian process and for the absolute value of a Gaussian process. For the case of hard limiting, the kernels are nonlinear functions of the autocorrelation of the Gaussian process. For the absolute value case, the kernels are nonlinear functions of the kernel derived for the linear problem. A Monte Carlo simulation of receiver performance is presented for the case of detection of the absolute value of a first-order Butterworth process in additive Gaussian white noise. The suboptimal detector is obtained by truncating the log likelihood ratio to second order.

The effect of a Gaussian-distributed phase modulation on the envelope detection of a sinusoid is investigated. Asymptotic receiver operating characteristics are obtained for Gaussian-distributed phase modulation processes that satisfy a central limit theorem due to Sun. Numerical results are presented for a first-order Butterworth phase modulation spectrum.