sin(w,1++1) Im{mg(+)) ZONAL BANDPASS FILTER (c) IF Multiplication, Baseband Integration xx(i) NARROWBAND FILTER ENVELOPE /(mT,MR)I DETECTOR XR(+) Spread- H(A) 2 LOCAL Spectrum arbitrary Generator OSCILLATOR jluRit+R) (d) IF Multiplication and Integration (Bandpass Correlator) Figure 1.3. Continued. A Spread-Spectrum Overview the desired inner product. Recovery of Re{(mT, MR)} and Im{(mT, mR)} requires three levels of synchronization. 1. Correlation interval synchronization: Correlators require pulses to indi- cate when the interval of integration is to begin and when it is to end. In the bandpass correlator of Figure 1.3(d), interval sync not only pro- vides the timing for the sampling operation, but also initializes the nar- rowband filter's state to zero at the beginning of each correlation interval. Typically, in DS systems these signals correspond to the data symbol clock pulses. In FH systems in which the data symbol time exceeds the hop time, the interval sync pulses must indicate the dura- tion of a single frequency, since correlation operations spanning random phase transitions are not generally useful. 2. SS generator synchronization: Timing signals are required to control the epoch of the system's SS waveform generator's output and the rate at which that output is produced. Direct sequence systems employ a clock ticking at the chip rate 1/T for this purpose, while FH systems have a similar clock operating at the hopping rate 1/T 3. Carrier synchronization: Ideal reduction of the SS signal to baseband in the receiver is possible if a local oscillator (or oscillator network) is avail- able whose output is in frequency and phase synchronism with the received signal's carrier (i.e., = 0 in Figure 1.3). The above level of carrier sync is often available in DS systems, but usually only frequency synchronism is attained in FH systems. In some SS systems, the above synchronization signals are derived from a single clock; in others, the carrier local oscillator is independent of the clock signals which control i