# Data Collection for Target Localization in Ocean Monitoring Radar-Communication Networks
## 2 System Model and Problem Formulation
### System Model
To guarantee the UAV performs SIC more efficiently, the necessary power constraint for each buoy has to be followed as  
\[\frac{p_{k}h_{Ulk}}{\sum_{i=k+1}^{K}p_{i}h_{Uli}}\geq P_{\text{SIC}},\ \forall k\in\mathcal{K}, \tag{3}\]  
where \(P_{\text{SIC}}\) denotes the minimum power difference for SIC. Furthermore, to ensure the uplink transmission requirements of each buoy, the minimum throughput constraint is given by  
\[B\text{log}_{2}\left(1+\frac{p_{k}h_{Uk}}{\sum_{i=k+1}^{K}p_{i}h_{Uli}+\sigma ^{2}}\right)\geq R_{\text{th}},\ \forall k\in\mathcal{K}, \tag{4}\]  
where \(R_{\text{th}}\) is the uplink throughput threshold. As for the radar sensing, the sensing target with a center of mass is located at \(I_{\mathbf{R}}=[x_{R},y_{R}]^{T}\in\mathbb{R}^{2\times 1}\)[47]. It is assumed that the changes of the target center position and the size observed by the buoys are small relative to the resolution capabilities of the radar function (it is assumed that the position of each buoy is known in advance and the radar sensing-based localization is insensitive to multi-path and weather impacts, which is applicable to localizing the target [48]) which tracks the target's position and estimates unknown parameters from previous cycles, such as the target's radar cross-section (RCS). In this premise, by emitting the DFRC signals and then receiving the echoes, the buoys can perform radar detection to sense the location of the target. Since the buoys work in a cooperative method, they can be treated as a distributed MIMO radar. As described in [49], the search cell can be defined as \(x_{R}(y_{R})\pm Ic/B\), where \(I\) is an integer, and \(c\) is the speed of light (all buoys are simultaneous to transmit DFRC signals and receive echo signals by employing a full-duplex transmission implementation. We assume the self-interference is well mitigated according to the existing work [50]). The signal transmitted from buoy \(\phi\) and received at buoy \(\varphi\) can be expressed as  
\[y_{\phi,\varphi}(t)=\sqrt{p_{\phi}}\alpha_{\phi,\varphi}\beta_{\phi,\varphi} s_{\phi}(t-\tau_{\phi,\varphi})+n(t),\ \forall\phi,\varphi\in\mathcal{K}, \tag{5}\]  
where \(\alpha_{\phi,\varphi}\) is the target RCS, \(\beta_{\phi,\varphi}\) is the signal variation due to the path loss effects, \(\tau_{\phi,\varphi}\) denotes the propagation time of the signal transmitted by buoy \(\phi\), reflected by the target, and received by buoy \(\varphi\). A group of waveforms is employed, with each waveform possessing a low-pass equivalent of \(s_{\phi}(t)\). And \(n(t)\sim(0,\sigma_{r}^{2})\) is the zero-mean circularly symmetric complex Gaussian noise. As demonstrated in [47], CRB can be used to provide a lower bound on the mean square error (MSE) of asymptotic unbiased parameter estimators in radar sensing, especially when the SNR is sufficiently large, the MSE of the maximum likelihood estimator is close to the CRB. Then, in our considered distributed MIMO radar system, the CRB for the target location estimation can be written as [32]  
\[\mathbf{C}(\mathbf{p})=\frac{(\mathbf{g}_{a}+\mathbf{g}_{b})^{T}\mathbf{p}}{\mathbf{p}^{T}\mathbf{G}\mathbf{p}}, \tag{6}\]  
where \(\mathbf{p}=[p_{1},p_{2},\ldots,p_{K}]^{T}\) is a vector denoting the buoy transmit power, \(\mathbf{G}=\mathbf{g}_{a}\mathbf{g}_{b}^{T}-\mathbf{g}_{c}\mathbf{g}_{c}^{T}\), \(\mathbf{g}_{a}=[\mathbf{g}_{a1},\mathbf{g}_{a2},\ldots,\mathbf{g}_{aK}]^{T}\).