1.20. Worst case p versus E,IN,-FH/APR (tone jamming). Also, recognizing that Pbo 0 in the limit as Eb/No 80, we obtain from (1.135) and (1.57) the desired limiting behavior to the average bit error prob- ability, namely, lim Pb Eb/No->00 (1.136) The partial-band fraction p corresponding to the worst case jammer (maximum Pb) can be obtained by differentiating (1.136) with respect to p and equating to zero. Assuming that, for a fixed this worst case p Performance of FH/QPR in the Presence of Partial-Band Multitone Jamming Pomax Eb/Nj, dB Figure 1.21. Worst case Pb versus E,/N,-FH/QPR (tone jamming). occurs when 1/9 < pE'/N' < 1, , then analogous to (1.32), we immediately obtain 1.6058 (1.137) Eb/NJ < 1.6058. Substituting (1.137) into (1.136) gives the limiting average bit error proba- bility performance corresponding to the worst case jammer, namely, Eg/N, = 1.6058 Eb/No->00 8/9Eg/N,<1.6058 0 < Eb/NJ < 8/9. (1.138) Coherent Modulation Techniques 1.8 PERFORMANCE OF FH/QPR IN THE PRESENCE OF PARTIAL-BAND NOISE JAMMING Once again, modeling the partial-band noise jammer as an additional addi- tive noise source with power spectral density given by (1.63), the average bit error probability performance in the presence of partial-band noise jam- ming is obtained from (1.131) by replacing No by N° + Nj/p, namely, (1.139) A similar result can be obtained from (1.133) for average symbol error prob- ability in the presence of partial-band noise jamming. Finally, substituting (1.139) and (1.131) in (1.57) then gives the average bit error probability over all detection intervals, namely, (1.140) The limiting behavior of (1.140) as Eb/No approaches infinity is easily seen to be (1.141) Eb/No->00 which yields a partial-band fraction for the worst case jammer given by NEb/NJ-1.1532 (1.142) Eb/N,< 1.1532 and a corresponding worst case average bit error probability 0.2014 E6/N,=1.1532 (1.143) 1.1532. Performance of FH/QPR in the Presence of Partial-Band Noise Jamming 15db = Eb = 20 dB ED=20 Nj Eb = 30 dB Figure 1.22. Pb versus p for