 and (1.21) gives (1.22) For the fraction (1 - p) of symbol (hop) intervals where the jammer is absent, the average symbol error probability is given by the well-known result [1] (1.23) Thus, the average error probability over all symbols (jammed and unjammed) is simply P,=pp,+(1-p)Ps, = so' (1.24) where Ps, is given by (1.17), together with (1.22), and Pso is given in (1.23). Before presenting numerical results illustrating the evaluation of (1.24), it is of interest to examine its limiting behavior as No 0. Clearly, from (1.23) we have lim Pso=0 (1.25) Eb/No->00 Performance of FH/QPSK in the Presence of Partial-Band Multitone Jamming Also, pEb>1 (1.26) Eb/No->00 This result can be obtained directly from the graphical interpretation given in Figure 1.3. Finally, substituting (1.25) and (1.26) in (1.24) gives the desired Lambel Symbol Error Region Psy=0 Symbol Error Region Symbol Error Region Figure 1.3. Graphical interpretation of (1.26). Coherent Modulation Techniques limiting behavior for the average symbol error probability, namely, (1.27) Eb/No->00 The partial-band fraction p corresponding to the worst case jammer (maximum Ps) can be obtained by differentiating (1.27) with respect to p and equating to zero. Assuming that, for a fixed EIN, this worst case p occurs when 1/2 < pEIN < 1, then (1.28) implies (1.29) where (1.30) The solution to (1.29) may be numerically found to be Z = 0.7654 (1.31) > 0.6306 (1.32) Note that, since Q and N are integers, then p as defined in (1.5) is not a con- tinuous variable. Thus, for a given N, the true worst case p would be the rational number nearest to (1.32) which yields an integer value of Q. Also, the second part of (1.32) comes about from the fact that Q is constrained to be less than or equal to N. Thus, when Eb/N1 is such that the solution of (1.30) and (1.31) gives a value of p > 1, we take p = 1 (full-band jamming) as the worst case jammer. Substituting (1.32) into (1.27) gives the limiting average symbol error probability performance corresponding to the worst Perf