 produce the in-phase and quadrature decision variables (i-1)T (1.11) where (1.12) 3We ignore double-harmonic terms. Performance of FH/QPSK in the Presence of Partial-Band Multitone Jamming are zero mean Gaussian random variables with variance NoT/2 and, in view of the possible values for (ii) given in (1.2), {a}} and {bi} are the equivalent independent in-phase and quadrature binary information sequences which take on values +1. The receiver estimates of a and bi are obtained by passing Z1 and ZQ through hard limiters, giving à = sgn zj; = sgn zq. (1.13) Hence, given ai, bi and 0j, the probability that the i-th symbol is in error is the probability that either or b is in error, i.e., = # bj} - Pr{@;#a;}Pr{b;# bi}. (1.14) Since the signal set is symmetric, we can compute (1.14) for any of the four possible signal points and obtain the average probability of symbol error conditioned on the jammer phase Ps(Aj). Thus, assuming for simplicity that a = =1,b=1, we compute Ps(Aj) from (1.14), combined with (1.11) and (1.13), = = = - Pr{Z,<0a1}Pr{z<0b = = 1} = P1(AJ) + Po(Aj) P1(A))Po(0j) (1.15) where P ( O ) ) = (1.16) with Q(x) the Gaussian probability integral as used in previous chapters. Finally, the unconditional average probability of symbol error Ps, for symbol intervals which are jammed is obtained by averaging Ps(Aj) of (1.15) over the uniform distribution of AJ. Thus, (1.17) Coherent Modulation Techniques Recognizing that, for a QPSK signal, the symbol time Ts is twice the bit time Tb, letting Eb = ST denote the bit energy, we then have (1.18) Furthermore, from (1.4) and (1.5), (1.19) Now, if the hop frequency slots are 1/Ts wide, in terms of the total hop fre- quency band Wss and the number of hop slots N in that band, we then have (1.20) Substituting (1.20) into (1.19) gives (1.21) As in previous chapters, the quantity J/W ss represents the effective jammer power spectral density in the hop band; thus, we have again introduced the notation N1 to represent this quantity. Finally, rewriting (1.16) using (1.18)