Data synchronization and noisy environments

This paper investigates maximum a posteriori probability (MAP) frame alignment strategies based on raw (analog) and quantized samples from a noise-contaminated channel. Particular attention is paid to systems with significant channel noise (for example, wireless systems), where accurate frame alignment is still possible, provided that the noise is compensated for by high transmitter frame integrity. A functional central limit theorem is derived that characterizes the performance of the MAP strategies in such high-noise cases. This prescribes optimal thresholds for the quantization process, and shows in particular that, for binary systems, worthwhile gains can be made by the use of raw or multibit quantized samples, rather than the usual 1-bit samples used by alignment strategies operating post bit decisions. It also shows that, for systems with significant channel noise, the performance of frame alignment strategies depends on the alignment pattern only through its autocorrelation function. Simulations confirm the validity of the characterization.