 be "the number of available frequency choices" [1, p. 29], which could refer to either N or Nb our notation. This last definition is actually consistent with (3.4) in Part 1 under certain constraints: the FH/MFSK scheme described earlier has N = WSIIR equally spaced tones SO that PG = NRRJR. For the special case of SFH with uncoded binary FSK (BFSK, or MFSK with M = 2), R = Rb SO that PG reduces to N; this holds even if the SS bandwidth is not contiguous. Although our definition of PG is universally valid for all SS systems, the interpretation of Wss is not always obvious. An instructive case in point is a generalization of the FH/MFSK implementation of Figure 2.3. Consider the structure of Figure 2.4, where each M-ary band again has tones with uniform spacing Rc, but the bands themselves are now uniformly separated by an arbi- trary amount AW, which is algebraically negative if the bands overlap. For clarification, AW = 0 in Figure 2.3(a), while AW = - (M - 1)R in Figure 2.3(b). In the overlapping band case, with - MR AW< 0, the spectrum aver- aged over many hops is approximately rectangular with Wss=NbMRc-(Nb-1)AW. (2.1) However, when AW > 0, there are unused gaps in the multihop spectrum SO that the occupied SS bandwidth that contributes to the PG is given by Wss=NbMR (2.2) under the simplified approximation of a piecewise rectangular spectrum. M-ARY BAND Figure 2.4. A generalization of frequency structure of FH/MFSK systems (shown for M = 4) in Figure 2.3: each M-ary band contains tones with uniform separation Rc, but adjacent bands are spaced AW apart. Non-Coherent Frequency-Hopped Systems All of this underscores our contention that while PG is a gross measure of the SS advantage relative to conventional modulation techniques, it is more accurate and meaningful to quantitatively characterize the perfor- mance of a specific system over a particular jamming channel by the bit error probability (Pb) as a function of the received SNR (see (3.3), Part 1). The remainder of this chapter is devoted to this type of 