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.

Recently developed methods of tree source coding with a fidelity criterion are applied to speech coding. We first demonstrate that tree codes are inherent in A-D speech convertors of the waveform following type and point to ordinary and adaptive delta modulation and differential pulse code modulation (DPCM) as examples. Insights of coding theory improve these trees at low rates; we offer two new code classes, one obtained by smoothing the DPCM tree and one using the rate-distortion theory of autoregressive sources. Using these codes, we study the performance of a simple synchronous tree searching algorithm called theM-algorithm that maintains a small fixed number of paths in contention. 1 and 2 bit/sample code trees, used to encode actual speech at 8, 10, and 16 kbits/s, yield improved dynamic range and channel error resistance, and 4-8 dB improvement in mean-square error (mse) over ordinary single-path searched DPCM. These improvements in excess of analytical estimates suggest that tree coding methods perform better with real-life sources than previously thought.