Double Error Rates in Differentially Coherent Phase Systems

In digital communication systems using binary phase modulation and differentially coherent detectors, it seems reasonable to suspect that errors tend to occur in pairs. The intuitive arguments are plausible, since these receivers obtain their reference from past bits. To put these arguments on a firmer ground, an analysis of this phenomenon was undertaken. It is shown that when the cause of errors is additive Gaussian noise the ratio of double-errors to single errors is less than 25 per cent when the SNR is larger than 5db. As a matter of fact, this ratio approaches zero as the SNR increases without bound. This analytical result was verified experimentally using a practical data set. The system was also tested using isolated impulses as the disturbance instead of Gaussian noise. For this disturbance most errors occurred in isolated pairs.