ived signal with c(t) as given in (1.22). Then, kNc-1 (1.75) n=(k-1)Nc where again N denotes the number of chips per data bit, F denotes the Fourier transform oooperation, and P(f) is the Fourier transform of the chip A Spread-Spectrum Overview pulse p(t). Denoting the period of {cn} by N and time-averaging the squared magnitude of MRk(f) over k gives = TsSm(f), (1.76) where P is defined in (1.51) and Sm(f) is given by (1.52). This result can be verified analytically, despite the fact that Sm(f) is the PSD of the data-mod- ulated waveform mt(t) while (1.76) represents an average of short-term energy spectra of mR(t). However, this result is reasonable because averag- ing over the zero-mean independent data symbols, which leads to the result (1.52), breaks up the PSD calculation into a time average of short-term energy spectra. The SIR improvement ratio for a DS/BPSK system is determined by sub- stituting (1.76) into (1.74) and using the fact that mT(t) = dmR(t) in a cor- relation interval. (1.77) Since both Si(f) and Sm(f) have fixed areas and are non-negative, the worst- case interference PSD S1(f - A) in (1.77) is a Dirac delta function located at the frequency which maximizes Sm(f). Therefore, (1.78) A well-designed spreading sequence {cn} should result in a PSD Sm(f) close to that of a purely random sequence, namely P(f)/Tc In keeping with our power normalizations, let's assume that (1.79) and hence, max|P(f) = Tc. Therefore, a well-designed spreading sequence has maxSm(f) = T and from (1.78) (1.80) This lower bound on signal-to-interference ratio improvement is the energy gain indicated in Example 1.1. When the interference is spectrally similar to the transmitted signal, e.g., in the SSMA case, and both signals possess the spectra of a purely random The Advantages of Spectrum Spreading binary sequence modulated on rectangular chip pulses (1.79), then =3Nc. (1.81) The above example illustrates the following points concerning SIR improvement calculations based on long-term energy averages: 1. The jammer can m