then letting Pc(Aj; A1) denote the conditional probability of correctly detecting signal point 10, we have, from (2.98) together with (2.95) and (2.99), Pco(Aj;B, = - G(X-1,3(Aj,B,A)) + 2)] X [1 - 2)]. (2.100) At this point, one can write down the remainder of the conditional prob- abilities of correct decision by inspection. Without going into great detail, the results are given as follows:6 Pco(j;,A1)[1-G(X3,3-2)]1-G(Y3,3 -2)] = - - - Pco(Aj; = [G(X1,1 2) - G(X1,1) [G(Y1,1 - 2) - G(Y1,1) Pc@(Aj;B,A1) = [1 - G(X3,1 2) - 2) - G(Y3,1)] Pco(j,A1)[G(X1,-1-2)-G(X1,-1)] = - X [G(Y1,-1) - G(Y1,-1 + 2)] Pco(Oj;,A1)[G(X1,-3-2)-G(1,-3)]G(X1,-3+2) = - Pco(j;B,A1)[1-G(X3,-3-2)]G(Y3,-3+2) = - - Pco(Aj; = G(X_3,3 + 2)[1 G(Y_3,3 - 2)] Pco(Aj;B,A1) = G(X_3,1 + 2)[G(Y_3,1 2) - G(Y_3,1)] Pco(Aj; = [G(X_1,1) - G(X-1,1 + 2)] X [G(Y_1,1 2) G(Y-1,-1 + 2)] Pco(Aj; = [G(X_1,-1) - G(X_1,-1 + 2)] X [G(Y_1,-1) - G(Y_1,-1 + 2)] Pco(Aj;B,A1) = G(X_3,-3 + 2)G(Y_3,-3 + 2) (2.101) Since, as previously mentioned, the jammer phase OJ is uniformly distrib- uted in the interval (0, 2, the average symbol error probability (condi- 'For simplicity of notation, we delete the dependence of Xi, and Yij on AJ, B, and A1. Differentially Coherent Modulation Techniques tioned on A1) is then given by PSB, (2.102) Finally, making use of (2.86) and (2.87) and the fact that only the fraction p of the total number of hop intervals are jammed, then the average uncon- ditional symbol error probability is given by (2.103) Before leaving this subject, we note that the result of substituting (2.96), (2.100), and (2.101) in (2.102) can be put into a compact form. In particular, by replacing each G(X) term in (2.96), (2.100), and (2.101) with its equiva- lent form 1 - G(-X) and summing all terms, we obtain the following result: (2.104) where PS(Aj;B,A1) m(1-1) EEEEGm(( X G(nYm(1-l),m(1-k)+ k). (2.105) For the more general case of FH/DQASK-K with arbitrary K, the summa- tion on j is for values j = 1, +3,..., =(K - 1), while the summations on l and k are for values l,k =