# Theory and Design of Blink Jamming
## 2 Analysis of Formation Jamming
### Formation Jamming Techniques  
In any individual situation, (9) is related to the weighted sum of the two targets. This should allow a pair of jammers to control the angle in the receiver, by using the relative power of the two sources to \"pull\" the tracking system towards the more powerful source.  
This presents several options for attacking the monopulse receiver; first, a constant power signal from both sources could be transmitted to the monopulse system. Weighted by their received power and angle of arrival, the indicated angle would be calculated at some point between the two sources. In the second case, commonly known as blink jamming, the monopulse system would be deceived by switching the jammers on and off at opposing times, causing the tracking point to oscillate between the two target locations. Blink jamming, like most electronic attacks, would be expected to perform optimally when operating at the frequency of the tracking system [4].  
In the final scenario, a new technique proposed in this chapter, uses a set jamming signals would operate similar to that in conventional blink jamming, but a sinusoidal amplitude modulation would be applied to each source. With the amplitude modulation from the two sources 180\({}^{\circ}\) out of  
Figure 3: The formation jamming scenario, with two jammers indicated by the aircraft icons, and a monopulse tracking radars beams shown in a single plane. The \(A\) and \(B\) beams are used for amplitude comparison, and the sum beam location is indicated by \(A+B\).  
synchronization with each other, they should cause the same reaction as blink jamming, oscillating the tracking antenna between the two sources, with an additional benefit as the two signals approached zero power. As the power of both signals drops to zero, the noise in the receiver and tracking system can cause spurious high indicated angles. Taking (9), the point where both jammer sources approach zero power can be expressed mathematically as a limit  
\[\theta_{i}=\lim_{s_{a}s_{b}\to 0}\frac{\theta_{a}s_{a}+\theta_{b}s_{b}}{s_{a}+s_{b}} \tag{10}\]  
while (10) can be understood strictly as a conventional limit, that analysis is practically irrelevant as the tracking radar is not performing that operation in the strict sense. Instead the two variable \(s_{a}\) and \(s_{b}\) are approaching zero from the positive and negative directions, in combination with various sources of noise, and the result is solved for using an analogue beamforming network or digitally with fixed or floating point math. As the two signals taper off to almost zero power the thermal noise in the receiver becomes the dominant signal. While random, in some cases \(s_{a}\approx-s_{b}\), as described by  
\[\theta_{i}=\lim_{s_{a}\to s_{b}}\frac{\theta_{a}s_{a}}{s_{a}+s_{b}}+\frac{ \theta_{b}s_{b}}{s_{a}+s_{b}} \tag{11}\]  
This has the potential to create an extremely small denominator relative to the numerator. The resulting division, while not creating a true divide by zero situation, does create abnormally large errors in the indicated angle.  
These concepts are validated using the FPGA model later in this paper, but the results from (11) are shown in Figure 4. The two jammer sources are shown with thermal noise at a SNR of 20 dB in Figure 4, as the powers approach zero every half-period of the jammer signal spikes in the indicated angle can be seen in the lower graph.