s for non-coherent detection of conventional (unhopped) M-ary orthogonal signals in AWGN. The derivation of this performance has been widely documented (e.g., [3, Section 8.10]): however, it is reviewed here for the sake of completeness. The M-ary symbol error probability (Ps) is given by P,=Pr{UCazza)} (2.10a) 1 -mpa = 1 - (2.10b) Broadband Noise Jamming where (2.8) and (2.9) were used with the change of variables = V2e1 and v=V2e2.But = -(-1)-- (2.11) SO that (2.10b) reduces to (2.12) The elimination of the integral in (2.12) is based on the identity (2.13) with appropriate parameter changes. Letting i = j + 1, (2.12) becomes (2.14) For larger values of K (i.e., K's of the order of 5 or more), the summation of (2.14) involves an exponentially large number of terms with alternating signs, each of which is composed of the product of a factor (M) which can be very large in the neighborhood i ~ M/2, and a very small factor, xp[-(E,/N,)(1 - 1/i)]. Consequently, evaluation of this expression on a dig- ital computer often yields unsatisfactory results. A more practical approach is to apply numerical integration techniques to the integral of (2.10b) and (2.11): P1(215 However, for larger values of EJN1 (i.e., small Ps), the value of the integral is close to 1, and the expression is again inherently inaccurate. To reduce the computational burden, make the variable change X = u2/2: (2.16) Non-Coherent Frequency-Hopped Systems Now, integrating (2.16) by parts, and introducing the Marcum Q-function [4] defined by (2.17) QM(V2y,0)= we can write (2.18) In practice, (2.18) can be evaluated accurately by using about 300 equally spaced increments for x between 0 and 30; iterative formulas exist for com- puting QM(,.). As an alternative to computing Ps exactly using the techniques discussed above, it is often more convenient and insightful to evaluate the simple, closed form expression for its union upperbound: from (2.10a), P,S(M - 1)Pr{ezze}} -(M-1)exp(~E,/2N) (2.19) where we have applied (2.14) with M = 2. Note that the upper