Carrier detection of PSK signals

This paper reports on a theoretical study of the detection of the 2f and 4f carrier components of phase-shift keying (PSK) signals produced by passing signal and noise through a nonlinear device. Unbalanced quadrature PSK (QPSK) signals, i.e., QPSK signals with unequal power in the two channels, are studied. The complete range of channel power ratio is covered, with equal emphasis on the general unbalanced case and the two limiting cases of binary PSK and (balanced) QPSK. Analytic expressions are derived for the detected SNR of carrier harmonics 2f and 4f as a function of SNR, channel power ratio, and normalized input bandwidth. The results apply equally well to PSK data signals and direct-sequence spread-spectrum signals. Measurements confirm every aspect of the theory. The least detectable signal type is balanced QPSK, which is detectable (at 4f) at a threshold SNR ranging from -2 to -13 dB as the detection process gain (chip or data rate/detection bandwidth) is varied from 40 to 80 dB