# Non-Mypopic Beam Scheduling for Multiple Smart-Target Tracking in Phased Array Radar Networks
## 4 Simulation and Analysis
### Performance Results with Scalar States  
In this subsection, \(N=8\) smart targets are tracked by the radars network with \(K=1,\ 2,\ 3\) radars. For each target, the radar tracking time horizon \(T=40\) s and \(\beta=0.75\). The Whittle index policy is set with the truncated time \(\tau=16\); The TEV index policy defines the index \(\lambda^{\text{TEV}}(P)=d\cdot P\); And the myopic policy that degenerates to \(\lambda^{\text{myopic}}=d\cdot[p_{d}\mu^{1}(P,\mathbf{u}^{1})+(1-p_{d})\mu^{0}(P, \mathbf{u}^{1})]\) to assess tracking performances.  
The parameters \(F_{1}^{1}\), \(F_{2}^{2}\), \(Q_{n}^{1}\), \(Q_{n}^{2}\), \(R_{n}^{1}\), \(R_{n}^{2}\), and \(h_{n}\) of target \(n\) and \(H\) are assumed to be the same as Section 4.1, \(n=1,2,\ldots,N\). The initial dynamic state \(x_{n,0}\) and TEV state \(P_{n,0}\) follow \(\text{U}(0,50)\) and \(\text{U}(0,40)\), respectively. Then, three scenarios are defined with only reckless type, cautious type, and each type of target accounting for 4, respectively. Set \(d_{n}=5\), \(n=1,\ldots,K\), and \(d_{n}=1\), \(n=K+1,\ldots,N\) in the three scenarios.  
Table 1 shows the discounted costs and AWRMSEs obtained by the three policies. Each policy is analyzed by \(N_{\text{mc}}=1000\) Monte Carlo simulations. Meanwhile, the percentages in parentheses indicate the metric value ratio of the corresponding policy over the myopic policy. The Whittle index policy can obtain the best scheduling performance and outperform the TEV index and myopic policies. The myopic policy focuses on minimizing the one-step cost under the detection probability \(p_{d}\), but does not consider multi-step decision making. As a result, it tends to favor conservative actions and fails to outperform the TEV policy. Consequently, the performance of the TEV policy is better than the myopic policy.  
Additionally, this subsection validates the near optimality of the Whittle index policy discussed in Section 3.4 through 1000 Monte Carlo simulations, when the number of radars and targets increases with a fixed ratio \(K/N=1/4\). The parameters \(F_{n}^{1}\), \(F_{n}^{2}\), \(Q_{n}^{1}\), \(Q_{n}^{2}\), \(R_{n}^{1}\), \(R_{n}^{2}\), and \(h_{n}\) of target \(n\) and \(H\) are assumed the same as Section 4.1. Firstly, there are 50% reckless targets with \(d_{n}=5\) in the population of \(N\) and others are cautious with \(d_{n}=1\). Secondly, the initial dynamic state \(x_{n,0}\) and TEV state \(P_{n,0}\) of each target \(n\) follow \(\text{U}(0,50)\) and \(\text{U}(0,40)\), respectively. The Whittle index truncates the corresponding infinite series to \(\tau=16\) terms with \(\beta=0.75\). The simulation population is modified by letting \(K\) vary.  
Figure 4: MP indices for the two target types.  
The average performance of index policies and the lower bound across 1000 Monte Carlo simulations is shown in Figure 5, where the lower bound calculation is similar to the bound calculation with multi-dimensional TEC states in Section 3.3.  
In Figure 5, the Whittle index policy also achieves the lowest discounted cost per target performance, which is stable at about 795. While the TEV index and myopic policies obtain 830 and 870, respectively. Consequently, the Whittle index policy obtains the closest performance to the lower bound. The simulation results of all the scenarios show the superiority of the Whittle index policies.