Optimal Sequential Frame Synchronization for Fading Channel

In [1], Chandar et al studied a problem of sequential frame synchronization for a frame transmitted randomly and Uniformly in an interval of size A slots. For a discrete memoryless channel, they showed that the frame length N must scale as e > A for the frame detection error to go to zero (asymptotically with A). α(Q) is defined as the synchronization threshold for the discrete memory-less channel and depends on the channel transition probabilities Q. In our paper, we study the sequential frame synchronization problem for a fading channel and additive noise and seek to characterize the effect of fading. For a discrete ON-OFF fading channel (with ON probability p) and additive noise (with channel transition probabilities Qn), we characterise the synchronisation threshold of the composite channel α(Q) and show that α(Q) ≤ α(Qn)× p. We then characterize the synchronization threshold for Rayleigh fading and AWGN channel as a function of the fading and noise parameters. The asynchronous communication framework permits a tradeoff between sync frame length, N , and channel, Q, to support asynchronism. This allows us to characterize the synchronization threshold with sync frame energy for the wireless channel.