Sequential Frame Synchronization Based on Hypothesis Testing With Unknown Channel State Information

In this paper, we propose a hypothesis testing based sequential frame synchronization technique that is robust against fluctuations and imperfect estimation of channel gain at the receiver. The proposed detector uses division in the decision rule to cancel the effect of channel gain, and therefore is called division based hypothesis testing (DHT). We show that the receiver operating characteristic (ROC) of DHT is close to the optimal likelihood ratio test (LRT), while the optimal LRT requires perfect knowledge of noise and channel gain at the receiver. Further, we use three performance metrics, namely, the probability of false synchronization P_fs, average reception duration l_rx, and probability of missed synchronization P_ms, to compare the performance of hypothesis testing against that of point estimation. We analytically show that hypothesis testing can have better reliability and lower energy consumption than point estimation if the probability of false alarm of the hypothesis testing is lower than the minimum of two thresholds. The cost of hypothesis testing is an arbitrarily small P_ms while point estimation can have zero P_ms. A modified implementation of hypothesis testing is also introduced to further reduce the energy consumption.