 spread-spectrum band. This will be discussed in Part 2, Chapter 2, when modeling the high frequency (HF) channel that uses the skywave reflections off the ionosphere. The pulse jammer discussed above can be generalized to include an arbitrary power distribution in time, keeping average power equal to J. Again, the worst case jammer is usually one that pulses on and off with a worst case value of p, the fraction of time the jammer is on with full peak power. 3.3.5 Repeat-Back Jammers A repeat-back jammer first estimates parameters from the intercepted spread-spectrum signal and then transmits jamming waveforms that use this information. Such jammers are primarily effective against FH systems when the hop rate is slow enough for the repeat-back jammer to respond within the hop duration. This type of jammer can be neutralized by increasing the hop rate or independently hopping each tone in the case of MFSK signals. Here such jammers are sometimes referred to as "frequency-following jam- mers." An analysis of the average repeat-back jammer power reaching the receiver's data detection circuits is given in Scholtz [3]. In this work, the impact of repeat-back jammers is not discussed except to caution against low hop rates in an FH spread system. Generally the effec- tiveness of a repeat-back jammer depends on the hop rate and the distances between the transmitter, receiver, and jammer. 3.4 UNCODED DIRECT-SEQUENCE SPREAD BINARY PHASE-SHIFT-KEYING To illustrate some basic concepts consider the example of an uncoded coherent, direct-sequence spread, binary phase-shift-keying (DS/BPSK) sys- tem. This type of anti-jam system is covered in greater detail in Part 2, Chapter 1. Ordinary BPSK signals have the form s(t) = nTbst<(n+1)T, n=integer. (3.15) Here T is the data bit time and {dn} is the sequence of independent data bits where Uncoded Direct-Sequence Spread Binary Phase-Shift-Keying with probability 1/2 (3.16) with probability Equation (3.15) can also be expressed in the form n = integer. (3.17) Hence, we can view BPSK