32

can be ignored as it represents the noise of the channel when the jammer is off, and getting rid of

the conditional probability, the theoretical probability of error for the SESS becomes:

(14)

_{ }=

1 − 2_{ }

2_{ } /

By using the upper bound of the Q-function.

(15)

_{ }≤

4

∗ ( − 2 )

Where X = Eb/ Nj and Y=(1-2*Pb). By setting the first derivative of equation (15) with

respect to ρ equal to zero and solving for ρ, the worst-case jamming line can be found.

(16)

0=

^{− } 4 2

−

1 ^{− }2 4 2

−

− ^{− }^{ }

4

2

=

1 2^{2 }

By substituting this back into the equation (14) and assuming a large N:

(17)

_{ }=

1

2^{2 }

_{ }(1 − 2

_{ })^{2 }=

1 2 /

≅

/

0.083 (/ )

# It was shown in [24], and explained earlier in section 3.3, that as N approaches infinity Y

approaches one and drops out and it becomes the same as Equation (12). Also note that under

normal conditions Pb is very small and leads to Pb = Q(1)/(2Eb/Nj).