dB Eb = IO dB Eb/Nj,dB Figure 1.5. Worst case p versus E,NN--FH/QPSK (tone jamming). PDD max ED=0 = O dB Eb = 3 dB ED==ddd ED = 10 dB Eb/N,,dB Figure 1.6. Worst case P versus E,N,-FH/QPSK (tone jamming). Coherent Modulation Techniques Eb/NJ > 0.6306 (1.38) Eb/No->00 /N,<0.6306. Figure 1.4 is a typical plot of P versus p, with Eb/N, as a parameter for the case Eb/No = 20 dB. It is seen that, for fixed Eb/No and Eb/N1, there exists a value of p which maximizes Pb and, thus, represents the worst case multi- tone jammer situation. In the limit, as Eb/No approaches infinity, this value of p becomes equal to that given by (1.32). Figure 1.5 is a plot of worst case p versus Eb/N,, with Eb/No as a parameter. Figure 1.6 illustrates the corre- sponding plot of Pbmax versus EbIN with Eb/No fixed. 1.2 PERFORMANCE OF FH/QASK IN THE PRESENCE OF PARTIAL-BAND MULTITONE JAMMING An FH/QASK-M signal is characterized by transmitting = V28[b, cos (1.39) in the i-th signalling interval. The total number of signals possible M is typ- ically the square of an even number K, and the quadrature amplitudes am and bn take on equally likely values m and n, respectively, with m, n = 1, +3, + (K - 1). Also, 8 is a parameter which is related to the average power S of the signal set by (1.40) Analogous to the step leading to (1.11), we can arrive at expressions for the in-phase and quadrature decision variables, namely, (1.41) The QASK receiver estimates of a and bi are obtained by passing Z1 and ZQ through K-level quantizers (1.42) where 28T48TS Qk(x) = (1.43) 3); (K <x< (K 2)STs (K - 1); (K Performance of FH/QPSK in the Presence of Partial-Band Multitone Jamming and Qk(x) = - Qk(-x). Hence, given Ai, bi, and 0j, the probability that the i- th symbol is in error is the probability that â or bi is in error. Thus, once again, (1.14) is valid. Here, however, we must compute (1.14) for the K2/4 points in any quadrant in order to obtain the average probability of symbol error conditioned on the jammer phase. Thus, using QASK-16 (K = 4) as an example,