dulation: When FH signalling of the form (1.56) is employed, a correlator set to detect the data frequency dR correlates the received signal with the reference (1.98) where p(t) is a hop pulse of duration Th which is non-zero only on (0, Th), and {0'n} is a sequence of uniformly distributed phase variables. The correlator resets every hop interval, i.e., T = and the squared Upper bound for ligloto Normalized time mismatch Figure 1.6. Normalized RMS detector output as a function of normalized time mis- match t1/Tc for several values of normalized frequency mismatch vTc Random DS modulation is assumed, with an energy gain of N = 100 and square chip pulses. The Advantages of Spectrum Spreading k-th correlator output (1.86) is http= Only two terms in the sum over m contribute to the value of (vm(k) for a given k. Defining the integer N1 and TI to satisfy (1.100) and using techniques similar to those seen earlier, result in - fk-1 - dr+v;7 Th) - fk-1-dp+v;Th)2 (1.101) where O and O' are independent, uniformly distributed phase variables, and Xp(, ) is defined by (1.91). We continue on the assumption that {fn} is a sequence of random vari- ables, each chosen from a set F of possible frequencies according to the probability distribution PF(). Averaging over 0, O', and {fn} in (1.101), produces a variety of expressions depending on the values of N and the data-induced frequency shifts. For simplicity, we assume that all the involved data variables are equal. Ensemble-averaging (1.101) produces N 1 = -1 otherwise (1.102) (1.103) We will use (1.102) as a basis for evaluating the TOA resolution capa- bility of FH signals. Before proceeding, we will develop a useful upper bound on (1.103). For this purpose we assume that F is composed of MF frequencies, A Spread-Spectrum Overview equally likely and uniformly spaced 1/Th Hz apart (the minimum spac- ing required for orthogonality over a hop time). For this calculation's purposes, this assumption is conservative in the sense that the hop fre- quencies in an operational system m