The detection of a sequence of echo pulses with random carrier phase is an important problem in radar. It is well known that, to a first approximation, the optimum receiver is a quadratic detector for small signal-to-Norse ratios and is a Iinear detector for large signal-to-noise ratios. In this paper, a detector based on scaling and rounding envelope samples into digital words of only a few bits is presented and analyzed. This detector is essentially a generalization of a suboptimum detector known as a binary detector which performs postdetection intqqration by digital counting and is particularly useful in automatic detection systems. The asymptotic reiative eficiencies of this detector relative to the quadratic detector and the linear detector are obtained. Also, nob-asymptotic performance comparisons based on relative efficiency and on probability of detection are made. It is shown that this detector is more eficient than the other two detectors in most signal-to-noise ratio ranges. In addition, this detector is o~pI~~able when the noise environment is somewhat dl~erent from Gaussian.
The detection of a sequence of echo pulses of incoherent phase is an important radar problem (l-3). In terms of statistical hypothesis testing, this problem is to test Ho:r,(t) = n,(t) i= 1,2,...,n against HI :rj(t) = A sin (~~t+~i)+~i(t) tE(tj, ti4T)
where rl(t), rz(t), . . . , r,,(t) are n statistically independent received waveforms, and nr(0, ~(0, . . . , .q(t) are sample functions of additive white Gaussian noise with power spectral density N,,/2. Also, A, o, and 7' are the constant amplitude, frequency and duration of each signal pulse, respectively, and each & is unifo~ly distributed (0, 2~). For this detection problem, it is known that the optimum receiver has a structure as given in Fig. . Theoretically, the nonlinearity g( *) in