 arbitrary time shift of the interference modula- tion relative to the reference modulation, this shift being inserted to model the fact that the interference is assumed asynchronous with respect to all clocks generating the transmitted signal. Stored reference modulations (e.g., mi(t) if the interference is SSMA in nature) are generally cyclo-stationary, i.e., they may be made stationary by inserting a time-shift random variable (e.g.,t1) which is uniformly distributed on a finite interval. Hence, we assume that t1 is uniformly distributed on a finite interval which makes mi(t - t1) a wide-sense stationary random process. This assumption and the further assumption that any random variables in mi(t) are independent of any in MR(t), effectively allow us to treat asynchronous multiple-access interference and jamming identically in average power calculations. The Advantages of Spectrum Spreading Averaging (1.70) over t gives = dt dt' (1.71) where R() and S1() are the autocorrelation function and PSD respectively of the unit power process milt - t1). That is, ()mf(17 - - = and MRk(f) is the Fourier transform of the reference modulation MR(t) in the k-th correlation interval. (1.73) Certainly when the correlation time T is not a multiple of the reference mod- ulation generator's period (and this must be the case to avoid problems with simple repeater jammers), then MRk(f)R will vary with k. Using the fact that the modulation forms are normalized to unit energy, and combining (1.65)-(1.68) and (1.71), demonstrates that the improvement in signal-to-interference ratio achieved in the correlation calculation is SIRout(freq sync) (1.74) Again we emphasize that (1.74) applies both to asynchronous multiple- access interference and independent jamming. Example 1.4. Suppose that a DS/BPSK communication system employs binary antipodal modulation and phase coherent reception over a symbol time T Hence, in the k-th correlation interval, mT(t) in (1.45) is equal to c(t) or - c(t), and reception is performed by correlating the rece