dulation with the same data in both inphase and quadrature coordinates. (For further dis- cussion on this see Kullstam [20].) Coherent Direct-Sequence Systems 1.3.2 Random Jammer Consider next characterizing the jammer as a stationary random process with autocorrelation (1.60) and power spectral density (1.61) where (1.62) the constant power of the jammer. The PN waveform c(t) is also stationary (introduce a uniformly distrib- uted time shift) with autocorrelation (1.63) and power spectral density (1.64) Naturally, J(t) and c(t) are independent of each other. S (f) S((f) Snlt) Figure 1.4. Power spectral densities. Uncoded Bit Error Probability for Specific Jammer Waveforms Recall from (1.9) that when received waveform x(t) + J(t) is multiplied by the PN waveform c(t), the resulting noise term is n(t) = c(t)J(t). (1.65) Since J(t) and c(t) are independent, the autocorrelation of n(t) is R,(7) = E(n(++ 7)n(t) = E{c(t+T)c(t)}E{J(t+T)J(t)} = R(T)R}(T), (1.66) which has the power spectral density (1.67) where * indicates the convolution operation. Figure 1.4 illustrates the power spectra of c(t), J(t), and the product n(t) = c(t)J(t). Here S(f) is arbitrary and Sc(f) is a broad sin2x/x2 spectrum of bandwidth roughly 1/T The resulting noise spectrum Sn(f) has value at f = 0 given by < Sc(0) = Sc(0). (1.68) since (1.69) and J is the total jammer power given by (1.62). There is equality in (1.68) when J(t) has a narrow power density spectrum compared to the PN wave- form c(t). In addition Sc(0) = |R.(7)dh = Tc. (1.70) Sn(0) JT (1.71) where Wss SS is given by (1.6) and N1 is our usual definition given as J/W ss. SS* Note that the equivalent noise of power spectral density bounded by N1 represents the total interference power. If we were to divide this power equally between the sine and cosine coordinates of the narrowband Coherent Direct-Sequence Systems (unspread) signal, then each coordinate would have a noise component of variance less than or equal to N/2. With BPSK data modulation and QPSK PN spreading, equal distrib