Holding Time of a Frame Alignment System Operating Over Time Variant Channels

In this work, a complete analysis of the average holding time in a frame alignment system operating over time variant channels is developed. In these cases the probability of miss is time variant as well, so that the statistics of the underlying process has to be investigated for properly approaching the system design. In a common frame synchronization strategy, involving a certain number α-1 of pre-alarm states, the probability of miss has to be calculated for α consecutive frames so that any time correlation in the propagation conditions has to be properly reflected in the statistical model of the miss process. The derived expression of the average holding time can be used for designing the alignment strategy for any time variant medium, under the sole hypothesis that the probability of miss can be fully characterized by its second order statistic and that it can be assumed to hold constant for the preamble duration. Sensitivity results for a sample application in a typical system operating in the HF band are also given: the dependence of the average holding time from some parameters related to frequency selectivity (the delay spread) and time selectivity (the frequency spread s) of the propagation medium can be clearly envisaged.