ered in previous sections and where the energy per symbol is m times the energy per chip. To emphasize this we use the nota- tion in place of our earlier parameter D(A). That is, define ={{{e (4.104) where D(A) is given by (4.91) where E replaces Es. Next, let c(0) be arbi- trarily large, normalize c(1) = 1/2 and define D(m) = min D(x;m) (4.105) where D is given by (4.92) with E replacing Es. If jammer state knowledge is not available, then choose c(0) = c(1) = 1/2 and D above is given by (4.93) Diversity for FH/MFSK Es/Nj (dB) Figure 4.19e. D(m) with jammer state knowledge: p = .05. again with E for Es. Figure 4.19 shows D(m) versus EJN for the jammer state knowledge case while Figure 4.20 shows D(m) when there is no jam- mer state knowledge. The special case of m = 1 corresponds to Figure 4.15. With m diversity, the channel parameter D defined earlier is now replaced by D(m) given in (4.105). The cutoff rate for this extended channel with diversity is denoted by Ro(m) and given by Ro(m) = log>M - - log2{1 + (M - )D(m)} bits/symbol. (4.106) Thus, if an M-ary alphabet code characterized by G(.) or B() is used, the coded bit error bound for this code with m diversity of the MFSK signals is given by = B(R0(m)). (4.107) m s l 19 20 21 10-41 EgiNo (dB) p=.01. E&/No Figure 7 8 D(m) p=.05. Concatenation of Codes The special uncoded case results in the symbol error bound (4.108) and the bit error bound (4.109) where the energy per bit Eb is related to the symbol energy Es and chip energy E by (4.110) when M = 2K. Note that diversity of order m can also be viewed as a special case of cod- ing where the code rate is Klm bits per chip. This simple repeat m times code can be quite effective against partial-band jamming as seen in Figure 4.19 where jammer state knowledge is assumed. 4.10 CONCATENATION OF CODES Although in principle it is possible to achieve arbitrarily small coded bit error probabilities as long as the data rate is less than the channel capacity or cut- off rate, practical applications are limited by the pro