# Data Collection for Target Localization in Ocean Monitoring Radar-Communication Networks
## 3 Method
### CRBC Optimization (Baseline)  
In this subsection, we present a traditional approach to compare the communication and localization performance between our proposed algorithm and the traditional method [32]. An optimization problem is formulated to maximize the system throughput with the given CRBC, which can be expressed as follows  
\[\max_{\mathbf{u},\mathbf{p}} \sum_{k=1}^{K}B\text{log}_{2}\Bigg{(}1+\frac{p_{k}h_{\mathbf{U}k}}{ \sum_{i=k+1}^{K}p_{i}h_{\mathbf{U}i}+\sigma^{2}}\Bigg{)}\] (20a) s.t. \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\] \[\frac{p_{k}h_{\mathbf{U}k}}{\sum_{k=k+1}^{K}p_{i}h_{\mathbf{U}i}}\geq P_{ \text{SIC}},\;\forall k\in\mathcal{K},\] (20c) \[R_{k}\geq R_{\text{th}},\;\forall k\in\mathcal{K},\] (20d) \[\min(l_{x})\leq x\leq\max(l_{x}),\] (20e) \[\min(l_{y})\leq y\leq\max(l_{y}),\] (20f) \[\frac{(\mathbf{g}_{x}+\mathbf{g}_{b})^{T}\mathbf{p}}{\mathbf{p}^{T}\mathbf{G}\mathbf{p}} \leq\eta_{\max},\] (20g) \[||\mathbf{l}_{\mathbf{U}}-\mathbf{l}_{\mathbf{R}}||^{2}\geq D_{\min}^{2}, \tag{20h}\]  
where \(\eta_{\max}\) denotes the given localization accuracy threshold. Noting that problem (20) is a non-convex problem and is extremely difficult to solve directly, we decouple problem (20) into two sub-problems, the UAV location and the power control problems. We first select a proper UAV location by transforming the objective function into a minimization of the sum distance from the UAV to the buoys with respect to the constraints of UAV location [57], which can be written as \[\min_{\mathbf{l}_{\mathbf{u}}} \sum_{k=1}^{K}||\mathbf{l}_{\mathbf{u}}-\mathbf{l}_{k}||^{2}\] (21a) s.t. \[\min(l_{x})\leq x\leq\max(l_{x}), \tag{21b}\] \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]0 (21c) \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]1  
Noting that problem (21) is not convex due to the non-convex constraint (21d), we adopt the successive convex optimization technique to obtain the UAV location. The left-hand term in (21d) is convex with respect to \(\mathbf{l}_{\mathbf{U}}\) and the lower-bound of the convex term can be attained according to the first-order Taylor expansion [46]. Specifically, define \(\mathbf{l}_{\mathbf{U}}\) as the given point in the \(r\)-th iteration and the left hand term in (21d) can be lower bounded as  
\[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]2  
Then, (21) is transformed into  
\[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]3 (23a) s.t. \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]4 \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]5 (23c) \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]6  
which is a convex problem and can be easily solved by standard convex optimization solvers such as CVX toolbox [58]. With the obtained UAV location in (23), the system throughput can be maximized by power control at the buoys. We relax the constraint (20g) as in [47] and the power control sub-problem can be given as  
\[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]7 (24a) s.t. \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]8 \[P_{\min}\leq p_{k}\leq P_{\max},\;\forall k\in\mathcal{K}, \tag{20b}\]9 (24c) \[\frac{p_{k}h_{\mathbf{U}k}}{\sum_{k=k+1}^{K}p_{i}h_{\mathbf{U}i}}\geq P_{ \text{SIC}},\;\forall k\in\mathcal{K},\]0 (24d) \[\frac{p_{k}h_{\mathbf{U}k}}{\sum_{k=k+1}^{K}p_{i}h_{\mathbf{U}i}}\geq P_{ \text{SIC}},\;\forall k\in\mathcal{K},\]1  
We remark that (24) is a convex problem, which can be easily solved.