tems may be mitigated by randomly changing parameters of one of the commu- nication links (e.g., by protecting one of the TR wideband links with an SR- like technique). Historical examples of SR-protected TR systems will be given in the next chapter. Spread-spectrum waveform generators for SR systems employing the fol- lowing general modulation formats have been built. The output of an SS waveform generator is given the generic name c(t) and is a (possibly com- plex-valued) baseband representation of the SS waveform. 1. Recorded modulation: The waveform w(t) of duration Tp is recorded, and if necessary, extended periodically to give (1.19) The utility of this type of signal is limited by the problem of distribut- ing recordings to transmitter and receiver SO that reuse of a waveform is not necessary. 2. Frequency hopping (FH): Assuming that p(t) is a basic pulse shape of duration Th (usually called the hop time), frequency-hopping modulation A Spread-Spectrum Overview has the form c(t)expj(2ftpt-nT (1.20) In all likelihood, the complex baseband signal c(t) never physically appears in the transmitter or receiver. Instead, the pseudorandomly gen- erated sequence {fn} of frequency shifts will drive a frequency synthe- sizer to produce a real-valued IF or RF carrier-modulated version of c(t). The sequence {0n} of random phases is a by-product of the modulation process. 3. Time hopping (TH): Assuming that the pulse waveform p(t) has dura- tion at most , a typical time hopping waveform might be (1.21) In this example, time has been segmented into Ts second intervals, with each interval containing a single pulse pseudorandomly located at one of MT locations within the interval. 4. Direct sequence (DS) modulation: Spread-spectrum designers call the waveform (1.22) direct sequence modulation. Here, the output sequence {cn} of a pseudo- random number generator is linearly modulated onto a sequence of pulses, each pulse having a duration T called the chip time. 5. Hybrid modulations: Each of the above techniques possesses c