ormance of FH/QPSK in the Presence of Partial-Band Multitone Jamming case jammer, namely, 0.2623 E6/N,> 0.6306 Eb/No->00 0.5 Eb/N1 < 0.6306 Eb/N1 < 0.5. (1.33) The final step in the characterization of the performance of FH/QPSK in the presence of multitone jamming is the conversion of average symbol error probability to average bit error probability. If one encodes the infor- mation symbols using a Gray code, the average bit error probability, P, for a multiple phase-shift-keyed (MPSK) signal is then approximated for large Ep==20 dB No = 15d8 10 2 4 6 10 -4 2 4 6 10 1-3 4 6 IO -2 2 4 6 10 Figure 1.4. Pb versus p-FH/QPSK (tone jamming). Coherent Modulation Techniques Eb/No by (1.34) where logM is the number of bits/symbol. The approximation in (1.34) refers to the fact that only errors in symbols whose corresponding signal phases are adjacent to that of the transmitted signal are accounted for. Since a Gray code has the property that adjacent symbols differ in only a single bit, then an error in an adjacent symbol is accompanied by one, and only one, bit error. Since QPSK is the particular case of MPSK corresponding to M = 4, then from (1.34), Ph=1Ps (1.35) where Ps is given by (1.24) or its limiting form in (1.27). Fortunately, for the case of QPSK, it is straightforward to account for the diagonal symbol errors which result in two bit errors and, thus, arrive at an exact expression for . In fact, Pb for QPSK is identical to P for binary PSK (BPSK) and is given by (1.36) where P(AJ) are given in (1.22). Thus, comparing the approximate result of (1.35) (using (1.17), (1.22), and (1.24)) with the exact result of (1.36), we observe that the difference between the two resides in the terms resulting from the product of error probabilities, namely, and Q2(V2E,/No). Also, by analogy with (1.27), the exact limiting form of Pb becomes (1.37) Eb/No->00 with a worst case p as in (1.32) and corresponding maximum error proba- bility Performance of FH/QPSK in the Presence of Partial-Band Multitone Jamming ED=2dB Ep=3dB = ED=6