 alternate data modu- lation. The cost of independent data modulation is a clearly increased hardware complexity. The data demodulation process in a digital SS system must compute inner products in the process of demodulation. That is, the receiver must mecha- nize calculations of the form (1.27) where in general mt(t) and mr(t) represent complex baseband signals and (mT,MR) is their inner product. However, one or both of these complex base- band signals usually appears in modulated form as a real IF or RF signal (1.28) The inner product (1.27) can be recovered from the modulated signal(s) in several ways, as illustrated in Figure 1.3. For example, the receiver can first demodulate the signal XT(t) to recover the real and imaginary parts of mt(t) and then proceed with straightforward correlation or matched filtering operations using baseband signals. On the other hand, as indicated in Figures 1.3(c) and 1.3(d), there are alternative ways to compute the inner product, which do not require that both signals be shifted to baseband first. In all cases, the heart of the SS receiver is its synchronization circuitry, and the heartbeats are the clock pulses which control almost all steps in forming A Spread-Spectrum Overview ZONAL Re{my(1)8'40) FILTER COS (w7 1--) Re{mp(+)) x-(f) Spread- LOCAL Spectrum OSCILLATOR Generator Im{m&(1)) ZONAL FILTER Im{m-(1)@ (a) Baseband Correlation MATCHED FILTER ZONAL FILTER NR(1) x-(f) LOCAL OSCILLATOR hi(t) ZONAL Im{(mp,mp)e FILTER improfine (b) Baseband MatchedFiltering Figure 1.3. Examples of correlation-computing block diagrams. The dashed portions of the diagrams can be eliminated when the modulations mT(t) and mR(t) are real and, in addition, the local oscillator is phase-coherent, i.e., =0. Solid line processing is often called the "in-phase" channel, while the dashed line processing is called the "quadrature" channel. Spread-Spectrum System Configurations and Components ZONAL BANDPASS FILTER cos(w,1++) Re{mp(+)} x-(+) LOCAL Spread- LOCAL OSCILLATOR Spectrum OSCILLATOR Generator -