## 3 Signal Model of ECM  
The EA-CA model can be used to simulate the process of agent state transition in ECM application scenarios. The jamming consistency to radiation sources can be achieved through the information interaction between agents [18]. In order to realize the distributed noise suppression jamming with the radar [7], each jammer is regarded as an electromagnetic agent that transmits jamming noise that drowns the echo of a radar-detected target.  
The radar detection equation without jamming can be written as [19]  
\[P_{\rm r}=\frac{P_{\rm f}G_{\rm f}G_{\rm r}(\theta_{\rm f})\delta\lambda^{2}K_{ \rm f}K_{\rm C}}{(4\pi)^{3}R^{4}L_{s}} \tag{11}\]  
where \(P_{\rm f}\) and \(G_{\rm f}\) correspond to the transmitting power and the gain of the transmitting antenna, respectively. \(G_{\rm r}(\theta_{\rm f})\) is the gain of the radar antenna in the target direction, \(\delta\) is the radar cross section, \(\lambda\) is the wavelength of signal, and \(K_{\rm f}\) and \(K_{\rm C}\) represent the pulse accumulation correction factor and the pulse compression correction factor, respectively. In the above, \(R\) is the distance between radar and target. \(L_{s}\) is the signal transmission loss in clear air; Appendix A the definition of mathematical symbols, Appendix B gives the specific calculation process.  
The noise power of the system contains the thermal noise power of the receiver and the jamming noise power. The thermal noise power can be written as \(P_{rm}=kT_{0}B_{\rm r}F_{\rm n}\), where \(k\) is Boltzmann constant, and \(T_{0}\) is the standard room temperature. \(B_{r}\) is radar receiver bandwidth, and \(F_{\rm n}\) is noise figure.  
The jamming signal power of \(n\) jammers received by the radar is represented as follows [20]  
\[P_{rj}=\sum_{i=1}^{n}\frac{P_{j}G_{\rm r}G_{\rm r}(\theta_{j})\lambda^{2}}{(4 \pi)^{2}R_{j}^{2}L_{j}}.\frac{B_{r}}{B_{j}} \tag{12}\]  
where \(P_{j}\) and \(G_{j}\) represent the jammer power and gain. \(G_{\rm r}(\theta_{j})\) is the gain of radar antenna in the direction of jammer, and \(R_{j}\) denotes the distance and loss of the jammer, of which \(B_{r}\) and \(B_{j}\) stand for the bandwidth of receiver and jammer, respectively.  
The total noise power of the system is given by \(P_{n}=P_{m}+P_{rj}\)[6]. The total signal-noise ratio (SNR) of the system can be expressed as follows:  
\[\left(\frac{S}{N}\right)_{S}=\frac{P_{\rm r}}{P_{n}}=\frac{P_{\rm f}G_{\rm r} (\theta_{\rm f})\delta\lambda^{2}K_{\rm f}K_{\rm C}}{(4\pi)^{3}R^{4}L_{s}(kT_{ 0}B_{r}F_{n}+P_{rj})} \tag{13}\]  
In practice, it draws more attention to SNR or detection probability of the radar receiver. For a radar receiver, \((SNR)_{o\,\rm min}\) is the minimum output SNR [21]. The minimum detectable signal power is  
\[S_{i\,\rm min}=kT_{0}B_{r}F_{\rm n}(SNR)_{o\,\rm min} \tag{14}\]  
The detection probability is related to false alarm probability \(P_{fa}\), output SNR \((SNR)_{o}\), and the type of target fluctuation. The detection probability of a non-undulating target [22] can be calculated approximately by  
\[P_{d}=0.5 erfc(\sqrt{-ln(P_{fa})}-\sqrt{(SNR)_{o}+0.5}). \tag{15}\]  
where \(erfc()\) represents the complementary error function.