ers are equally effective against uncoded FH/MFSK signals for low P's. WORST CASE BAND MULTITONE JAMMING WORST CASE INDEPENDENT JAMMING (DASHED) WORST CASE PARTIAL-BAND NOISE JAMMING BROADBAND NOISE JAMMING Eb/Nj, dB Figure 2.22. Comparison of relative effectiveness of various worst case jamming strategies against uncoded, non-coherently detected FH/16-ary FSK signals. Coding Countermeasures (even worse than broadband noise for low E/N. Furthermore, all of the worst case jammers result in the inverse linear performance characteristic for large enough Eb/NJ. 2.3 CODING COUNTERMEASURES Up to this point, each M-ary symbol was sent entirely on a single hop. And we have seen that sophisticated non-adaptive (i.e., non-repeat back) jammers can severely degrade the performance of such systems. These jammers all concentrate their available power over portions of the total spread-spectrum bandwidth W although only a small fraction of the data may be hit, those data suffer a relatively high conditional error rate. An effective countermeasure against this form of concentrated jamming is to introduce coding redundancy, SO that if a given hop is jammed other hopefully more reliable received data can be used to resolve the contami- nated data. By basing data decisions on multiple hops, the jammer will have to deconcentrate its power SO as to hit a larger fraction of the transmitted data. The ultimate goal is to force the jammer to retreat back towards the original broadband (unconcentrated) noise jamming strategy. In this man- ner, we would expect to recover the desired exponential performance char- acteristic. In computing the performance of a coded system for which each data deci- sion depends on multiple uses of a noisy channel, it is generally impractical to derive closed form exact error rate expressions. Such computations typ- ically involve the integrals of special functions which are at best cumbersome or must be evaluated numerically. Furthermore, these calculations must often be repeated when a single system parameter