herent Direct-Sequence Systems This is the energy per bit required for this case to achieve 10-5 bit error prob- ability with this code. The above procedure repeated for various choices of the bit error prob- ability results in the bit error bounds shown in Figure 1.10 for the reference case and three worst case pulse jammer examples. Note that the bit error probability curves shown here are shifted by exactly the same shift shown in Figure 1.8 for the cutoff rates. This is simply because for any given code, the coded bit error bound depends only on the value of R- Similar bit error bounds can be found for other codes by shifting the standard bit error prob- ability curves by the same amount. Figure 1.10 also illustrates the effectiveness of coding and interleaving in combatting pulse jamming. Comparing the coded bit error probabilities of Figure 1.10 with the uncoded case of Figure 1.5, we see that most of the large degradation due to pulse jamming has been neutralized and additional cod- ing gain achieved. At 10-6 bit error probability, for example, there is about a 45 dB coding gain for the soft decision known jammer state decoder for this K = 7 convolutional code compared to no coding. These are against the worst case pulse jammer for each point on the bit error probability curves. 1.6 SLOW FREQUENCY NON-SELECTIVE FADING CHANNELS Here we examine the performance of DS/BPSK sytems in a fading channel [23]-[32]. The fading is assumed to be constant across the total spread spec- trum bandwidth, Wss, and varies slowly in time such that during any data bit time interval, Tb, the fading is assumed to be constant. This slowly varying frequency non-selective fading is sometimes referred to as flat-flat fading [23]. Although our analysis allows for arbitrary fade statistics, the examples will assume commonly used Rayleigh fading amplitude statistics which mod- els the case where there are many similar scatterers causing the fading [33]. 1.6.1 Continuous Jammer with No Coding Suppose the received signal amplitude is A. 