 we have = = = = 1Pr{0 ZQ > 28Ts|b = 1} + 1Pr{zQ 28Tsb = 3} (1.44) P ( O ) ) = 1Pr{8T + VJoTs < N 1 < -STS + VJoTs 01} (1.45) PQ(AJ) = 1Pr{8Ts - VJoTs (1.46) Letting K = 4 in (1.40) and recognizing that Ts = 4T6, we now have (1.47) where (1.48) Also, (1.49) Finally, then, the unconditional average probability of symbol error Ps, for Coherent Modulation Techniques symbol intervals which are jammed is given by (1.17) with (for QASK-16) (1.50) For symbol intervals which are not jammed, the average symbol error probability is given by the well-known result [2] (1.51) Thus, the average error probability over all symbols is once again given by (1.24) with, however, Ps, SJ of (1.17) together with (1.50) and Pso of (1.51). As was done for FH/QPSK, one can compute the limiting performance of FH/QASK as E/ approaches infinity. In particular, using a graphical interpretation analogous to Figure 1.3, we obtain the following result: (1.52) Eb/No->00 Finally, realizing that (1.25) also applies to Ps SO of (1.51), substituting (1.25) and (1.52) into (1.24) then gives the desired limiting behavior of the aver- age symbol error probability of QASK-16, namely, (1.53) Eb/No->00 Performance of FH/QPSK in the Presence of Partial-Band Multitone Jamming To determine the worst case jamming situation, we again differentiate Ps, now given by (1.53), with respect to p and equate to zero. Recognizing that the expression for Ps of QASK-16 in the interval 1/2 < pEb/NJ < 1 is 3/2 times that for Ps of QPSK in the interval 1/2, pEIN, < 1, we can immedi- ately observe that the worst case p is now 0.6306 > 0.6306 (1.54) and the corresponding worst case average symbol error probability perfor- mance is N, > 0.6306 0.5 < Eb/No->00 (1.55) where we have also made use of (1.48). If one encodes the QASK symbols with a perfect Gray code, then account- ing only for adjacent symbol errors (which is equivalent to one bit error per symbol error), the average bit error probability for large Eb/No and pEIN, is related to the average symbol error probability by