= - cos (1.115) Performance of FH/QPR in the Presence of Partial-Band Multitone Jamming where (1.116) with p the Heaviside operator and (1.117) The sampled values of zc(t) and zs(t) are given by ZIk Z1(2kTb) = A(dk + dk-1) - V4,1, - Nsk (1.118) where (1.119) and we have made use of the fact (see (1.110)) that HR(0) = V4T Table 1.1 lists the four possible combinations of precoded symbols Ck and Ck-1 (or dk and dk-1) and the corresponding duobinary values Ck + Ck-1 (or dk + dk-1). Here we use +1 and - -1 symbols rather than zeros and ones; hence, the modulo-2 operation in the precoder is replaced by arithmetic mul- tiplication. From Table 1.1, it is clear that the detection criteria should be (1.120) Thus, since, the ak's and bk's are equally likely, the in-phase and quadrature Table 1.1 Transformation of the input symbols into their duobinary equivalents. Transmitted Received Symbols Duobinary Value Symbol bk Ck+ck-1 Coherent Modulation Techniques bit error probabilities are given by = Ack Ck-1 = =0} + 1Pr{|zQk <Alk+ck-1 = 2} + = -2} P1(A)) Ill Pr{ # ak} = 1Pr{|ZIk > Adk + dk-1 = 0} + 1Pr{|ZIk| < Adk + dk-1 = 2} + 1Pr{|z1kl + dk-1 = -2} (1.121) or, using (1.118), (1.122) To express (1.122) in terms of more meaningful parameters such as signal- to -Gaussian noise ratio and signal-to-jamming noise ratio, we must relate the signal amplitude A to the average transmitted power S. Since, (1.123) then from (1.108), we have that (1.124) Substituting (1.110) into (1.124), and evaluating the integral gives (1.125) Performance of FH/QPR in the Presence of Partial-Band Multitone Jamming Combining (1.117) and (1.125) gives an effective rms signal-to-Gaussian noise ratio of (1.126) Also, from (1.21) and (1.125), we have (1.127) Finally, substituting (1.126) and (1.127) into (1.122) results in (1.128) where we have further introduced the notation (1.129) Coherent Modulation Techniques The average probability of bit error Pb, in a detection interval which is jammed is obtained by averaging PO(A) or P() of (1.128) over the uniform