## 4 DRFM Performance Results
### Effects of DRFM Coherence and Radar Waveforms  
The most major difference between DRFM implementations is the use of an envelope DRFM, recording the radar pulse amplitude but not its phase, and a full I-Q DRFM that replicates the in-phase and quadrature components of the received signal. This was particularly interesting as when a radar signal with a matched filter receives the envelope signal, how the two interact was not well established.  
The effect of the amplitude and I-Q DRFM systems was compared by using two waveforms: a Linear Frequency Modulated (LFM) wave, and a 13-bit Barker code. In all cases, the SNR in the ES receiver was set to 40 dB, and the ADC resolution to 10 bits; this was done to distinguish the jammer and radar wave without emphasizing the effects of thermal and quantization noise.  
The results for the LFM signal are shown in Figure 9, using a 10 pulse and with a 5 MHz bandwidth to replicate a common radar signal. The transmitted signal and jammer signal are clearly very similar at the output of the correlator, with only minor changes in the side-lobes and effectively no loss in processing gain or change in time delay.  
However, the amplitude signal behaved significantly differently, as the correlation is comparing a square wave with a component of the LFM signal, resulting in the following variation of Equation (2)  
\[\chi=\sum_{n=0}^{N-1}e^{j2\pi\frac{R_{p}}{T_{p}}(nt_{s})^{2}} \tag{3}\]  
where \(N=\tau_{p}/t_{s}\) is the number of samples in the pulse, \(B\) is swept frequency bandwidth, \(t_{s}\) is the sample period, and \(\tau_{p}\) is the pulse width. The output of the correlator makes sense in this context, as the initial oscillation is swept over the frequency range, the ripple in the envelope can be seen to change in Figure 9, resulting in a peak at the trailing edge.  
The difference between the ideal and amplitude variant of the signal is a loss of 7.5 dB in processing gain but with a peak located 8.5 \(\upmu\)s later than the I-Q variant. While both these factors are important,  
Figure 9: Correlation results for a linear frequency modulated wave with a pulse width of 10 \(\upmu\)s and a bandwidth of 5 MHz.  
the loss in signal processing gain was expected and can be compensated for by increasing the jammer power. The range delay is more problematic, as it results in a target appearing 1.3 km farther away, likely well outside the range gate of a tracking radar.  
Interestingly, the power spread by the amplitude DRFM signal over a much larger range will flood any range of bins with likely sufficient power for a target detection in a search radar. In a tracking radar, it would also create significant energy, but inside the range gates and any possible guard gates as well. These two factors will affect countermeasure design, principally by shifting any pulses transmitted by the jammer in time to adjust for the artificial delay in a range caused by the matched filter and the unmodulated pulse.  
For comparison, the same experiment was performed with a 13-bit Barker code, shown in Figure 10, as was done for the LFM waveform. The results were similar, but less pronounced, with only a 5-dB loss in processing gain, as a result of the significant difference in the time-bandwidth product (50 for the LFM wave, and 13 for the Barker code). The range delay displayed a less rippled effect, with peaks and troughs corresponding to the waveform's side-lobes. The results of all the simulations from this sub-section are summarized in Table 1.