versity of Southern California, August 1982. Chapter Chapter 3 TIME AND FREQUENCY SYNCHRONIZATION OF FREQUENCY-HOPPED RECEIVERS Until now, all our discussions of FH/MFSK communication systems have assumed "ideal" synchronization conditions in the sense that the dehopper in the receiver was assumed to have perfect knowledge of the set of received hop frequencies and the instants in time at which the hop modu- lation changed state. In practice, such ideal conditions are almost never met. This is the lack of perfect knowledge of the phase and Doppler shift pro- duced by the transmission channel; as such, the receiver must provide suit- able means for obtaining and maintaining bona fide estimates of these synchronization state parameters. The accuracy with which this can be accomplished ultimately affects the overall error probability performance of the system. Not unlike the synchronization problem in direct-sequence (DS) spread-spectrum (SS) systems discussed in the previous two chapters, the process of synchronizing the local hop generator with the received sequence of hop tones is ordinarily accomplished in two stages, namely, FH acquisition (coarse synchronization) and FH tracking (fine synchro- nization). We begin this chapter with a discussion of FH acquisition tech- niques, the most common of which, as we shall see shortly, have a direct resemblance to similar techniques previously discussed for PN code acquisition. Once having explained how to coarsely align the local and received hop sequences, we offer next a discussion of a fine synchronization technique for estimation of FH timing [1]. By "fine synchronization," we mean rel- ative timing errors between transmitter and receiver hop generators of less than a hop duration. In presenting the details and mathematical analy- sis of the time synchronization estimation technique, we shall first make the idealistic assumption that the transmitter and receiver hop generators are perfectly synchronized in frequency. Following this, we consider the FH Acquisition Te