 is changed. Consequently, it is more expedient to use Chernoff upperbounding techniques which involve the statistics of a single channel use. This approach often yields closed form expressions which can produce useful insights. Furthermore, these bounds are exponentially accurate in the region of greatest interest, namely, small Pb's. Our analysis will be based extensively on such bounds; where exact results have been documented, they will be used to determine the accuracy of our bounds. 2.3.1 Time Diversity One of the simplest yet effective coding techniques is to subdivide each infor- mation symbol into equal energy subsymbols which are then transmitted over independent channel states. This is referred to as diversity transmission or a repetition code. In the context of the FH/MFSK structure, each M-ary symbol is parti- tioned into m subsymbols or "chips" (not to be confused with the PN spreading code chips) with energy E = KEm. As illustrated in Figure 2.23, FH/MFSK SIGNAL FH CARRIER (WITHOUT DATA) FH/MFSK SIGNAL FH CARRIER (WITHOUT DATA) Figure 2.23. Two ways to achieve FH/MFSK diversity. For example, suppose M = 4,n = 3 chips/4-ary symbol, Rb = 10 Kb/s (Rs = R/K = 5 Ks/s; R = mRs = 15 Kchips/s), and we want to send the 4-ary symbol 3 followed by 1. In (a), Rh = R = 15 Khops/s; in (b), Rh = 7.5 Khops/s and interleaving of depth d = RJR = 2 is required (the message is that a slow FH synthesizer hop rate does not preclude the use of diversity). Coding Countermeasures each chip is transmitted on a different hop using fast frequency hopping (FFH) or slow frequency hopping (SFH) with pseudorandom interleaving. The intention is that each chip comprising an M-ary symbol will have an independent chance of being jammed. Because these chips are distributed in time, this technique is often termed "time diversity," although "jamming- state diversity" would be an equally descriptive label. The resulting chip rate R = mRb/K; recall that we use the term FFH to denote the condition R = Rh (the hop rate), whereas SFH implies