# Intelligent Interference Management in UAV-Based HetNets +
## 3 System Model
### Parameter Optimization  
The SE is a function of \(\boldsymbol{\alpha}\), \(\boldsymbol{\beta}\), \(\boldsymbol{\tau}\), \(\boldsymbol{\rho}\), \(\boldsymbol{\rho}^{\prime}\), and \(\mathbf{X}_{\text{uabs}}\), which are our optimization space. Either these parameters can be optimized for individual MBSs and UABSs, or the same value of each parameter can be used for all MBS and UABS, which is sub-optimal but computationally less complex.  
To show that optimizing the above parameters individually for each MBS and UABS gives a better performance than optimizing the ICIC parameters jointly, we consider the hypothetical situation depicted in Figure 2. Here, UE 3 is the critical UE to be protected from interference. Intuitively, as MBS 1 is closer to UE 3 compared to MBS 2, it is desirable for MBS 1 to transmit at a lower power during CSFs. Mathematically, \(\alpha_{1}=0.4<\alpha_{2}=0.8\). As UE 4, which is served by UABS 2, is farther away from all the MBSs, UABS 2 does not have to use a large CRE to encourage UE 4 to associate with itself. In contrast, UABS 1 would have to use a larger CRE to encourage UE 3 to associate with itself. Mathematically, \(\tau_{1}=15\) dB \(>\tau_{2}=0\) dB. Therefore, optimizing the parameters individually for each MBS and UABS gives better performance.  
The large size of the search space can be appreciated by referring to Tables 2 and 3, which list the range and size of the parameters to be optimized. In this table, the parameters \(\Delta_{\alpha}\), \(\Delta_{\beta}\), \(\,\Delta_{\rho}\), \(\Delta_{\rho^{\prime}}\), \(\Delta_{x}\), and \(\Delta_{y}\) denote the step sizes for \(\alpha\), \(\beta\), \(\rho\), \(\rho^{\prime}\), \(x\) coordinate of a UABS's location, and \(y\) coordinate of a UABS's location, respectively, while \(\rho_{\text{low}}\) and \(\rho_{\text{low}^{\prime}}\) denote the lower bounds for \(\rho\) and \(\rho^{\prime}\), respectively. Similarly, \(\rho_{\text{high}}\) and \(\rho_{\text{high}}^{\prime}\) denote the upper bounds for \(\rho\) and \(\rho^{\prime}\), respectively. The actual size of the parameter space is depicted in Figure 4, which shows the number of possible states in \(\mathbf{S}\), over which the individual or joint optimization algorithms have to search, in order to find the best state, \(\mathbf{S}^{\prime}\).  
Figure 4 shows that, as the geographical area and correspondingly the number of MBSs and UABSs increase, the size of the search space increases much more rapidly for individual optimization than for joint optimization. This behavior can be understood by calculating the number of possible permutations of \(\alpha\) for two MBSs considered by joint and individual optimization approaches, assuming that \(\alpha\) can take four different values from 0 to 1.  
While the joint optimization approach will only compare the SE metric at these four values of \(\alpha\), the individual optimization approach will need to compare the SE metric for \(4^{2}=16\) different permutations of \(\alpha\) values of the two MBSs. In this way, the parameter search size for joint optimization is agnostic to the number of MBSs or UABSs in the simulation area. The parameter search space of individual optimization, on the other hand, increases exponentially with number of MBSs and UABSs. We also observe that, for the individual optimization approach, the size of the state space exceeds a googol (\(10^{100}\)) of states as the simulation area increases beyond \(15\) km\({}^{2}\).  
we present the brute force and greedy algorithms, while Section IV presents the DDQN learning algorithm.