H/QPSK in the Presence of Partial-Band Noise Jamming Figures 1.7-1.9 are the numerical evaluations of FH/QASK-16 perfor- mance which are analogous to those in Figures 1.4-1.6 characterizing FH/QPSK. 1.3 PERFORMANCE OF FH/QPSK IN THE PRESENCE OF PARTIAL-BAND NOISE JAMMING Now assume that the jammer J(t) spreads his total power J uniformly across a fraction p of the total hop frequency band Wss. SS* Then, insofar as the data demodulation process is concerned, the jammer appears as an additional additive noise source of power spectral density (1.63) Note that the power spectral density of the noise jammer defined in (1.63) is identical to the effective power spectral density defined for the multitone jammer in (1.21). Since the jammer noise can be assumed to be independent of the back- ground AWGN, one can add their power spectral densities and use this sum to represent the total noise perturbing the receiver. Thus, the error proba- bility performance of FH/QPSK in the presence of partial-band noise jam- ming is characterized by taking the well-known results for just an AWGN background and replacing No by No + N'j. Without going into great detail, we then see that the average symbol error probability is once again given by (1.24), with P so as in (1.23); however, (1.64) Substituting (1.63) into (1.64), we can rewrite Ps, in the alternate form: (1.65) Also, the average bit error probability is now (1-me(J2E) (1.66) which is identical to the result for noise jamming of FH/BPSK. Coherent Modulation Techniques The limiting behavior of (1.66) as E/No approaches infinity is easily seen to be (1.67) Eb/No->00 Differentiating (1.67) with respect to p and equating the result to zero gives the transcendental equation (1.68) whose solution for p corresponds to the worst case jammer situation. In par- ticular, letting (1.69) (1.68) then becomes 2(V2x) = (1.70) which, when solved numerically, yields X ==0.842. (1.71) Equating (1.69) and (1.71) gives the partial-band fraction for the worst case Ep=20da Figure 1.10. Pb versus p fo