Follower Jammer Considerations for Frequency Hopped Spread Spectrum

In this paper design considerations to be used to account for follower jamming of J-equency hopping (FH) spread spectrum systems are presented. A follower jammer attempts to determine the hop frequency with a “determinator” circuit, and then generates jamming in a range about that jiequency. Geometrical considerations show the spatial limit at which follower jamming becomes impossible. The minimum determination time and the probability of correct determination, Phc, are derived as a function of the intercepted SNR, and the determinator resolution. Both fast hopping (one or more hops per information symbo~ and slow hopping are analyzed. The use of follower jammers against hopped FDM4 systems is also discussed. A summary design rec~e is given. It is concluded that the vulnerability to follower jammers can be reduced to tolerable levels by use of current practical hop rates. INTRODUCTION Frequency hopping (FH) spread spectrum is particularly useful to combat jamming primarily because it is relatively easy to operate over very large spread bands. However, FH can be efficiently jammed by follower (also called “repeat-back”) jammers under certain conditions. In follower jamming, the jammer intercepts the transmitted signal, tries to determine the frequency of the hop, and then generates jamming in a narrow range about this ftequency. It is the purpose of this paper to discuss design considerations to account for such jammers. In designing an anti-jam FH system, the spread bandwidth, Wss, is usually fixed at the start, and often is just the bandwidth available. Practical systems use fixed hop rates, or, at most, a few selectable hop rates. The data rate is otlen the only thing that is allowed to vary as jamming levels change. The selection of the particular fixed hop rate, Rh, is based on a number of tradeoffs [1]. The tradeoff related to the follower jrtmmer threat is how high to make the hop rate so as to reduce the vulnerability to follower jamming to an acceptable level. Geometrical protection against follower jammers is well known, but will be reviewed here. What is not well studied are the methods and the performance of the follower jammer in determining which fi-equency range to jam. The jammer circuit required for the frequency determination is not really a detector, the view point used in [2]. Neither is it an estimator, the view point used in [3]. It is most similar to a demodulator for M-ary NCFSK, but with differences. Since it would be confusing to call it a “demodulator”, it was decided to call the circuit a “determinator”. There are waveform methods of mitigating the effects of follower jammers [4], [5], but these suffer ftom a few problems: more complex to implement (requires more synthesizers at the receiver), doesn’t guarantee good performance, and are not usefid if FDMA used. In the following, emphasis will be on fast frequency hopping (one or more hops per information symbol). At the end, a short discussion will be given on slow frequency-hopping (more than one data bit per hop) performance. FOLLOWER JAMMER CONFIGURATION AND GEOMETRICAL PROTECTION The configuration for follower jammers is shown in Fig. 1. The transmitter to receiver distance is Dtr, the transmitter to jammer distance is Do, and the jammer to receiver distance is Djr, At the follower jammer is a receiver plus a determinator circuit. The hop period is Th which will be assumed = l/Rh. The SNR at the determinator is Ehf / No where Ehf is the energyihop at the jammer’s receiver. At the authorized receiver, there is a SNR of Eht / Nor, and an SJR to be discussed later. If the determinator correctly determines the frequency of the transmitted hop, then it can generate jamming in a small region around this frequency thereby negating the advantage of FH. It will be assumed here that the jammer has available fast frequency synthesizers that can switch to a new frequency in a time <<Th. It has been pointed out in many places [3] that if ) ThSAT=(Dq+Djr–Dtr /C (1) where c is the velocity of light and AT is the differential delay, then the jamming signal arrives at the authorized receiver too late to jam the original hopthe receiver is processing the next hop. The jammer locations that obey (1) are outside of an ellipse given by 4(x -Dtr )2 4/ = ~ + (2) (Dtr + cTh)2 (Dtr + cTh)2 -Dtv2 where the x and y axes are centered on the transmit antenna, and are illustrated in”Fig. 1 along with a typical ellipse. A two-dimensional representation is shown and is suitable for point-to-point communications over flat ground. For applications such as satcom, the results can be extended to three dimensions merely by revolving the ellipse about the x axis. For terrestrial communications, the three distances are of the same order of magnitude so that Fig. 1 is representative in scale. However, for satcom, Dti <<Dtv For example Dtr = 40,000 km for a gee-synchronous ~atellite whereas Dti would be no more than a few hundred km for airborne jamm<rs, and even less for ground based jammers. As an example of the geometrical protection boundary for gee-synchronous satcom, the protection region is plotted in Fig. 2 for Rh z 2000, and 10000 hopsls. Follower Ehf INO jammer