phase component re = d V E + n (1.14) where (1.15) Here we assume that lette cos sin WOT dt = 0 (1.16) for all T where T is the "chip" time interval for both PN sequences. Similar results hold for the quadrature component (1.17) where (1.18) Thus, as in the conventional case, QPSK modulation can be viewed as two independent BPSK modulations each at half the data rate. 2This is the usual assumption that inphase and quadrature signal components are orthogonal. Perfect phase synchronization is assumed for the receiver. Orthogonality is approximately true for the weaker condition Uncoded Bit Error Probability for Arbitrary Jammer Waveforms 1.2 UNCODED BIT ERROR PROBABILITY FOR ARBITRARY JAMMER WAVEFORMS Without coding, the BPSK detector decision rule is to decide d is the data bit where (1.19) The bit error probability is thus Pb = =Pr{r=0|d=-1} = Pr{n = VE}}. (1.20) Naturally, this bit error probability depends on the random variable n given by (1.12). For QPSK the same decision rule (1.19) can be applied to r and r's to obtain a and a. This results in the same bit error probability expres- sion (1.20) with nc and ns replacing n. For BPSK modulation the noise component given by (1.12) has the form J(t)cos wot dt (1.21) where C1,..., CN-1 are the N PN bits occurring during the data bit time interval. Defining the jamming component (1.22) we have (1.23) as the final form for the noise component. The PN sequence is approximated as an independent identically distrib- uted binary sequence where Pr{ck=1} =Pr{ck=-1 1 = (1.24) Then for any fixed jammer sequence (1.25) the noise component given by (1.23) is a sum of independent random variables. We next examine ways of evaluating the conditional bit error probability P,(J) = Pr(n = VE,JJ (1.26) Coherent Direct-Sequence Systems for given jammer components J. The bit error probability may be in terms of a parameter set characterizing a deterministic jammer model or a statis- tical characterization of the jammer with evaluation of the overall average bit error probability by (1