## 2 Multistatic Radar System Model  
### Signal Model  
As shown in Figure 1, a multistatic radar system T/R-R\({}^{N}\) is considered in this paper with one transmitter/receiver \(T_{1}\) and \(N\) receivers \(R_{n}\) (\(n=1,2,...N\)), which distribute widely over a given area. The transmitter is also one of the receivers, which can be denoted by \(R_{0}\). There is one physical target (PT) in the monitoring area of the multistatic radar system. To protect the target, a joint range-velocity deception false target (FT) is generated by the self-defense repeater jammer by delaying, modulating and retransmitting the intercepted radar signals.  
The time and phase synchronization among the multistatic radar system have been assumed accomplished [33]. The signal received by the \(n\)th receiver, denoted by \(r_{n}(t)\), can be presented as  
Figure 1: Illustration of multistatic radar architecture with active deception jamming.  
\[r_{n}(t)=e_{n}(t)+j_{n}(t)+n_{n}(t) \tag{1}\]  
where \(0\leq t\leq PRT\), \(PRT\) is the length of a pulse repetition interval (PRI). \(e_{n}(t)\), \(j_{n}(t)\) and \(n_{n}(t)\) are the echo signal reflected by physical targets, deception jamming signal and internal noise, respectively. The ideal echo of physical targets \(e_{n}(t)\) can be modeled as  
\[e_{n}(t)=\alpha_{n}\exp\{j2\pi(f_{0}-f_{dn})(t-\tau_{n})\}s(t-\tau_{n}) \tag{2}\]  
where \(\alpha_{n}=\lambda\sigma_{n}\sqrt{P_{T}G_{T}G_{n}}/(4\pi\sqrt{4\pi}R_{T}R_{n})\) accounts for the complex amplitude of the physical target PT. \(P_{T}\) is the transmitted power of the transmitter. \(G_{T}\) and \(G_{n}\) are the antenna gain of the transmitter and the \(n\)th receiver, respectively. It is obvious that \(R_{T}=R_{1}\). \(\sigma_{n}\) is the radar cross section (RCS) of PT with regard to the \(n\)th receiver. \(R_{T}\) and \(R_{Rn}\) are the range from the transmitter to PT, and the one from PT to the \(n\)th receiver, respectively. \(f_{0}=c/\lambda\) is the carrier frequency. The term \(c\) is the propagation speed of the electromagnetic wave and \(\lambda\) is the wavelength. \(\tau_{n}=R_{Tn}/c\) is the time delay of the physical target PT. \(R_{Tn}=R_{T}+R_{n}\) is the range along the path from transmitter to \(n\)th receiver via the physical target PT. \(s(t)\) is the transmitted signal of the transmitter, which is assumed to be a narrow-band signal. \(f_{dn}\) is the bistatic Doppler frequency of the physical target  
\[f_{dn}=\frac{v_{T}+v_{nr}}{c} \tag{3}\]  
where \(v_{T}\) and \(v_{nr}\) are the radial velocity of the PT with regard to the transmitter and the \(n\)th receiver.  
The joint range-velocity deception jamming signal \(j_{n}(t)\) can be represented as  
\[j_{n}(t)=\beta_{n}\exp\{j2\pi(f_{0}-f^{\prime}_{dn})\big{(}t-\tau^{\prime}_{n} \big{)}\}s\big{(}t-\tau^{\prime}_{n}\big{)} \tag{4}\]  
where the term \(\beta_{n}=\gamma\lambda\sqrt{P_{I}G_{I}G_{n}}/(4\pi R_{n})\) is the complex amplitude of the false target FT. \(P_{J}\) and \(G_{J}\) are the transmitted power and the antenna gain of the jammer, respectively. \(f^{\prime}_{dn}\) is the bistatic Doppler frequency of the false target  
\[f^{\prime}_{dn}=\frac{v_{T}+v_{nr}}{c}+\triangle f_{d}=f_{dn}+\triangle f_{d} \tag{5}\]  
and \(\tau^{\prime}_{n}=\tau_{n}+\triangle\tau\) is the actual time delay of the false target FT. \(\gamma\), \(\triangle\tau\) and \(\triangle f_{d}\) are the jammer's random complex amplitude modulation with unknown distribution, time delay and doppler frequency modulation for the intercepted radar signals to produce the false target FT.