The growing demand for reliable communications leads to the need for very large mean time to lose lock (MTLL) of PLL based synchronization subsystems. These large MTLLs, of the order of months, cannot be simulated or tested in a lab. In this work a systematic approach is given to computing the MTLL of a second order PLL with parasitic delay at low SNR and high phase noise. Computed and simulated results are shown to be in good agreement for values that can be simulated.

In modern voiceband data communication, the received signal is subject to nonlinear quantization noise due to companding. Under certain conditions, this quantization noise may become dominant and cause serious degradation in performance. In this paper, we first calculate the Bhattacharyya bound on the error probability between two signal points, which we then use to obtain some insight into the effects of the companding channel. Next, we compute the cutoff rate, and then use these results to design new "optimal" signal constellations for the companding channel. The bound, cutoff rate, and new constellations are computed assuming a signal-dependent noncircular Gaussian channel transition density. In addition, we obtain "optimal" a priori probabilities for this channel.

In modern voiceband data communication, the received signal is subject to nonlinear quantization noise due to companding. Under certain conditions, this quantization noise may become dominant and cause serious degradation in performance. In order to design better signal constellations for this environment, it is of interest to characterize this noise. We study the conditional probability density function (PDF) for the quantization noise found on a PCM companding channel. We obtain an analytical expression for the conditional PDF of the nonlinear quantization noise and an algorithm to compute the conditional PDF of the filtered noise, which is the actual noise at the slicer input of the linear receiver. We compare the results to a Gaussian PDF (with second-order moments that depend on the signal point) and conclude that a Gaussian approximation, although not entirely accurate, is not unreasonable.