This paper finds power division through a bandpass nonlinearity when the input is two spread spectrum signals plus noise. This model applies to code division multiple access (CDMA) satellites or to multiple transmission of CDMA through a common Earth terminal transmitter. The solution requires finding a single attenuation constant for each input signal including the input noise. This approach provides the first exact power division solutions for spectrally overlapping, possibly coherently generated, spread spectrum signals plus noise through a bandpass limiter. Two examples illustrate the approach. Simultaneous transmission of coherently generated QPSK spread signals through a hard limiter without noise may cause whichever is the smaller of the two to suffer a sharp 6 dB suppression. This suppression is highly phase dependent and can be alleviated by proper phasing of the signals prior to hard limiting. In the second example, input/output SNR relations are found and compared with those given by Jones for two unmodulated sine waves and noise. A significant reduction in output SNR exists for spread signals compared to the two sine wave case examined by Jones.

Predictive coders have been suggested for use as analog data compression devices. Exact expressions for reconstructed signal error have been rare in the literature. In fact most results reported in the literature are based on the assumption of Gaussian statistics for prediction error. Predictive coding of first-order Gaussian Markov sequences are considered in this paper. A numerical iteration technique is used to solve for the prediction error statistics expressed as an infinite series in terms of Hermite polynomials. Several interesting properties of predictive coding are thereby demonstrated. First, prediction error is in fact close to Gaussian, even for the binary quantizer. Sencond, quantizer levels may be optimized at each iteration according to the calculated density. Finally, the existence of correlation between successive quantizer outputs is shown. Using the series solutions described above, performance in terms of meansquare reconstruction error versus bit rate can be shown to parallel the theoretical rate distortion function for the first-order Markov process by about 0.6 bits/sample at low bit rates.

This concise paper describes a new technique for upper bounding the performance of coherent binary phase-shift keyed (PSK) systems which derive a phase reference using one-shot maximum likelihood phase estimates. By performance, we mean any positive monotonically increasing function of phase error, such as error probability or power loss. A tight upper bound to the phase error cumulative distribution is shown to consist of the concave support to a previously derived Chernov bound. Performance measures appropriate for binary PSK systems are listed and evaluated with the new bound.