esulting modification to (2B.3) is ¹ 1/LLS1 (2B.4) where the summation is understood to be zero for the singular case L > (J - 1)/2 discussed above. Derived by Dr. Laif Swanson of the Jet Propulsion Laboratory, Pasadena, California. Non-Coherent Frequency-Hopped Systems For the band multitone jamming application, we do not actually need the individual N L's. A sufficient parameter is S1,1(L) = number of I - number of patterns T Imax  L (2B.5) where we have made use of the disjointness of the N (i.e., none of the pat- terns in N coincide with any pattern in Nj for i # j). As noted earlier, before S1,J(L) was defined, S1.1(1)=1. = (2B.6) Also, (2B.7) Finally, adopting the conventions that denotes the integer portion of x and can write (2B.8) So for J V 8, we can compute S1.j(L) for the entire range of L E [1, J]; for J > 8, we are missing the region 3 < L VI J/3. In principle, we could extend (2B.4) to the next region, J/4 < L VI J/3, and SO on, but this is increas- ingly more complex and not really a worthwhile cause. Chapter Part 3 OTHER FREQUENCY-HOPPED SYSTEMS This Page Intentionally Blank Chapter Chapter 1 COHERENT MODULATION TECHNIQUES Thus far in our discussions, we have considered only those frequency- hopped (FH) systems in which the carrier phases of the individual trans- mitted hop frequency pulses bear no relation to one another. Such a spread-spectrum (SS) technique was referred to as non-coherent FH and the method for recovering the data modulation appropriately employed some form of energy detection. Clearly, another possibility exists for implement- ing the FH modulator, wherein phase continuity is maintained from one hop pulse to another thereby resulting in so-called coherent FH. Assuming that the coherent frequency synthesizer in the receiver is capable of estimating and correcting for the phase errors associated with the electrical path length over the transmission channel and the Doppler shift, then following the dehopping operation one could employ coherent detection techniques for recovery of