## 6 Optimization Scenarios for 6G MCNs
### Dynamic Spectrum Allocation in Heterogeneous Maritime Environments  
In MCNs, multiple communication entities (e.g., ships, UAVs, satellites, buoys) and other mobile nodes often share overlapping radio spectrum resources. The reuse of frequency bands across different communication layers (e.g., UAV-to-ship, ship-to-ship) is essential for achieving high spectral efficiency, especially in spectrum-constrained regions [85]. However, this reuse introduces inter-domain interference, which can significantly degrade overall network performance. Therefore, one of the key challenges is to allocate spectrum resources dynamically across all maritime nodes in a way that maximizes total data throughput while minimizing mutual interference and satisfying individual QoS constraints. Although different assumptions and problem-specific settings may be considered, below, we provide the key elements of the mathematical problem formulation for dynamic spectrum access [86]:  
**Optimization Problem Formulation:** If we assume \(N\) communication nodes (e.g., ships, UAVs, buoys) drawn from the set \(\mathcal{N}=\{1,2,\ldots,N\}\) and \(F\) available frequency channels selected from the set \(\mathcal{F}=\{1,2,\ldots,F\}\). A binary variable \(x_{i,f}\) can indicate whether node \(i\in\mathcal{N}\) occupies frequency channel \(f\in\mathcal{F}\). Let also the communication data rate achieved by node \(i\) be denoted as \(R_{i}\) (in bps). The data rate \(R_{i}\) typically refers to the achievable Shannon capacity on a wireless channel, assuming a single-user channel (or orthogonal multiple access). A standard formulation is:  
\[R_{i}=B_{i}\text{log}_{2}\bigg{(}1+\frac{P_{i}h_{i}}{I_{i}+N_{0}B_{i}}\bigg{)} \tag{1}\]  
where \(B_{i}\) is the bandwidth allocated to node \(i\) (in Hz), \(P_{i}\) is the transmission power of node \(i\) (in Watts), \(h_{i}\) is the channel power gain between node \(i\) and its serving transmitter, \(I_{i}\) is the total interference received at the node's receiver (Watt), and \(N_{0}\) is the noise power spectral density (W/Hz) at the receiver. In this optimization model, it can be assumed that channel state information (CSI) is known (which can be realistic if CSI is periodically measured or estimated), then \(h_{i}\) is known. Also, the aggregated interference of node i across its multiple interferers (i.e., nodes transmitting over the same channel) can be derived as:  
\[I_{i}=\sum_{j\in\mathcal{N},j\
eq i}\sum_{f\in\mathcal{F}}x_{i,f}x_{j,f}P_{j}h _{j,i} \tag{2}\]  
where \(h_{j,i}\) the channel power gain from interferer node \(j\) to the wanted node \(i\). Note that, in nearshore, port, or MEC-based settings, the controller may periodically collect CSI and traffic parameters and compute estimated interference level \(I_{i,j}=P_{j}h_{j,i}\) (caused between nodes when they use the same frequency) based on propagation models (e.g., path loss, fading). Thus, in the above formulation, the data rate \(R_{i}\) is derived from the Shannon capacity, while interference \(I_{i,j}\) represents the received interference power at node \(i\) from node \(j\) sharing the same frequency. In centralized or simulation settings, \(I_{i,j}\) can be computed from known positions, power levels, and channel models. In distributed or dynamic environments, \(I_{i,j}\) may also be approximated or learned through environmental feedback. Based on the above definition, the optimization objective function can be written as follows:  
\[ \begin{array}{c}\underset{x_{i,f}}{\max}\left(\sum\limits_{i\in\mathcal{N}}R_{i }-\sum\limits_{i,j\in\mathcal{N}}\sum\limits_{f\in\mathcal{F}}x_{i,f}x_{j,f}I_ {ij}\right)\\ \text{s.t. (C1)}\quad\sum\limits_{f\in\mathcal{F}}x_{i,f}\leq 1,\ \forall i\in \mathcal{N}\\ \text{(C2)}\quad\ R_{i}\geq R_{min,i},\ \forall i\in\mathcal{N}\end{array}  \tag{3}\]  
where the goal is to find the channel allocation policy to jointly maximize throughput and minimize interference.