A receiver cannot decode a signal if it is not aware of the existence of the transmitted signal. Furthermore, if a transmitter and receiver are not aligned in time and frequency, then the transmitted signal will not make any sense to the receiver. Consequently, in order to establish a wireless communication link, the receiver must find or acquire the transmitted signal, and some sort of synchronization in time and frequency between the transmitter and receiver must occur. In this chapter, the process of acquisition and synchronization is simply denoted synchronization. In order for two nodes to be synchronized, they must agree on both the carrier frequency and timing. In this discussion, it is assumed that any frequency errors are small enough that frequency synchronization can be achieved after temporal synchronization. Extensions to the discussions provided here would enable joint temporal and spectral synchronization. In situations in which coherence is required for long durations, frequency is of greater importance , and the techniques discussed in this chapter need to be modified to address this sensitivity.
The performance of synchronization or acquisition techniques is often characterized in terms of probability of detecting the signal of interest given that it is there versus the probability of falsely “detecting” a signal (a false alarm) given that the signal is absent. The function relating these two probabilities for some test statistic is often denoted the receiver operating characteristic (ROC) curve that is discussed in Section 3.7.3.