 (1.34), where now M = K2 is the total number of symbols or log2M = log is the number of bits/symbol. Clearly, for QASK-16, Ph=1Ps (for (1.56) (1.56) provides an optimistic estimate of . The exact expression can be calculated via the fact that QASK-16 is obtained from independent amplitude-shift-keying on two quadrature components of a carrier. Assuming a perfectly coherent receiver, no interchannel effects exist in the demodulation process. Hence, the bit error probability Pb for QASK-16 is identical to Pb for each individual channel and is given by (1.57) Coherent Modulation Techniques where (1.58) with PQ(0j) as in (1.50) and Po(AJ) equal to (1.59) Furthermore, Pbo of (1.57) represents the average bit error probability in the presence of noise only and is given by (1.60) Once again before presenting numerical results illustrating the evaluation of (1.57), it is of interest to examine its limiting behavior as No Following the approach taken for FH/QPSK, we can arrive at the following result: lim Pb = Eb/No->00 (1.61) The partial-band fraction p corresponding to the worst case jammer (max- imum Pb) is obtained by differentiating (1.61) with respect to p and equat- ing to zero. Assuming that, for a fixed Eb/NJ this worst case p occurs when 1/9 < pE'/N J < 1, , then the solution to the transcendental equation which results from the differentiation is identical to (1.54). Substituting (1.54) into (1.61) gives the limiting average bit error probability performance corre- Performance of FH/QPSK in the Presence of Partial-Band Multitone Jamming No Eb = 20 dB ED=300 Figure 1.7. Pb versus p for FH/QASK-16 in tone jamming with E/ = 20 dB. Ep== 6 db = 15 dB ED , DE , dB Figure 1.8. Worst case p versus E/N/-FH/QASK-16 (tone jamming). Coherent Modulation Techniques sponding to the worst case jammer, namely, 0.0984 E'/N > 0.6306 1/9<Eg/NJ<0.6306 lim Pbmax = Eb/No->00 1/25 < 1/9 0 < Eb/N, < 1/25. (1.62) Pomax Ed 0 dB 50=6dB Ep=7dB Ep=15. Eq. OB Figure 1.9. Worst case Pb versus E./N,-FH/QASK-16 (tone jamming). Performance of F