# Reinforcement Learning-Based Anti-Jamming in Networked UAV Radar Systems
## 3 System Model
### Beam Synthesis Method under Low-Bit Phase Array  
This section introduces the beam synthesis method used in this paper. For phased array antennas, the phase shifter determines the precision of beam pointing. The higher the bit number of the phase shifter, the smaller the step of the phase difference between adjacent elements and the smaller the step of the synthesized beam pointing. Thus, the phase shifter used in most ground-based radars is large and expensive. Due to the limited size and load capacity of UAVs, the performance of a phase shifter is also very limited. There are many ways to achieve phased array miniaturization and beam synthesis with low-bit phase difference. The development of metamaterial is just an example [26]. In this paper, the antenna material of the UAV radar is not discussed. We only focus on the relatively flexible beam synthesis method for a UAV under low bit (2-3 bit) conditions. A phased array antenna can control the beam pointing by controlling the phase of the array elements, which is a common method in an electric scanning antenna system. At present, one-dimensional phased array and two-dimensional phased array are widely used. They are composed of uniform linear array (ULA) and uniform plane array (UPA). ULA can realize beam scanning in a certain plane, while UPA can realize beam scanning in two-dimensional space. In order to simplify the model, without loss of generality, we first consider the low-bit beam synthesis method of ULA. Assuming that the UAVs in a swarm are arranged to form a ULA, the elements carried by each UAV may independently switch each element on or off. It is assumed that the phase shifter can uniformly take values between 0\({}^{\circ}\)-360\({}^{\circ}\) at intervals of 360\({}^{\circ}\)/2\({}^{M}\) when the coding number of phase shifters \(M\) is determined. To facilitate the representation of the discrete phase, we replace the phase values of 0\({}^{\circ}\)-360\({}^{\circ}\) with the code values of \(0,1,2,\ldots,2^{M-1}\), respectively. According to [27], two methods of repetitive coding and convolution can be applied. The repetitive coding method is performed by repeating the coded values in the ULA elements, and the convolution method is to perform the addition of the repeated codes, which corresponds to the convolution of the antenna pattern. According to the convolution principle of the antenna pattern, if the beam pointings corresponding to the two different coding modes are \(\theta_{1}\) and \(\theta_{2}\) respectively, then the beam pointing after the code modular addition is pointed to \(\theta_{0}\). \[\sin\theta_{0}=\sin\theta_{1}+\sin\theta_{2} \tag{1}\]  
This process is shown in Figure 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Variables** \\ \hline Transmitting Power of Radar Unmanned Aerial Vehicle (UAV) Swarm 1 & \(P_{R}\) \\ Target Scattering Coefficient & \(\sigma_{1},\sigma_{2},\sigma_{3},\sigma_{4},\sigma_{5}\) \\ Antenna Gain of Radar UAV Swarm 1 for Each Scattering Point & \(G_{R1},G_{R2},G_{R3},G_{R4},G_{R5}\) \\ Transmission Link Path Loss of Radar UAV Swarm 1 & \(L_{R1}\) \\ Forwarding Gain of Radar UAV Swarm 1 & \(F_{R}\) \\ Forwarding Link Path Loss of Radar UAV Swarm 1 & \(L_{R2}\) \\ Transmitting Power of Radar UAV Swarm 2 & \(P_{r}\) \\ Antenna Gain of Radar UAV Swarm 2 for Each Target Scattering Point & \(G_{r1},G_{r2},G_{r3},G_{r4},G_{r5}\) \\ Transmission Link Path Loss of Radar UAV Swarm 2 & \(L_{r1}\) \\ Forwarding Gain of Radar UAV Swarm 2 & \(F_{r}\) \\ Forwarding Link Path Loss of Radar UAV Swarm 2 & \(L_{r2}\) \\ Transmitting Power of Jammer 1 & \(P_{j1}\) \\ Antenna Gain of Jammer 1 & \(G_{j1}\) \\ Path Loss of Jamming Link 1 & \(L_{j1}\) \\ Transmitting Power of Jammer 2 & \(P_{j2}\) \\ Antenna Gain of Jammer 2 & \(G_{j2}\) \\ Path Loss of Jamming Link 2 & \(L_{j2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters.