The vulnerability region of frequency hoppers against follower jammers

Frequency-hopping (FH) spread-spectrum anti-jam systems are susceptible to degraded performance by follower jammers, which intercept the transmitted signal, attempt to determine in which of a number of bins the hop is located, and then jam in that bin only. Three factors are addressed that provide some protection against follower jammers. One is the differential time delay between the direct intended hop and the follower jamming hop. For this delay greater than a hop period, there is complete protection and for a delay less than the hop period there is partial protection. The second factor is that the "determinator" system used by the follower jammer must receive sufficient SNR to achieve a high probability of correct bin determination within a very short time interval after the start of the received hop. The third factor is the determinator hop time synchronization. Each factor defines a region of vulnerability in which the jammer must be located for effective jamming. The combined vulnerability region is the intersection of the three individual vulnerability regions. The determinator system consists of a bank of filters and detectors. The branch with the largest output is selected as the hop branch and is jammed in the remaining part of the hop period. The probability of correct determination is derived as a function of the SNR at the determinator. This SNR is derived as a function of the link budget of both the FH system and of the transmitter to the jammer. The analysis is applied to both fast hoppers (one or more hops per information symbol), and slow hoppers. Terrestrial- and satellite-communications examples are provided. The vulnerability region is found to be surprisingly small because of the limitations of the jammer\´s determinator performance and dominates over the other factors.