# Shapley's Value as a Resource Optimization Strategy for Digital Radio Transmission over IBOC FM
## 4 Discussion  
The digital broadcasting system operates in two specific modes: hybrid mode and fully digital mode. In hybrid mode, simultaneous transmission of analog and digital components occurs, utilizing the channel assigned to the analog signal under the traditional  
Figure 5: BW requested and BW assigned by Linear Programming for a channel saturation state. radio model. Conversely, in the fully digital mode, the transmitted signal utilizes the entire bandwidth allocated to the station, with its component being purely digital. It is noteworthy that digitalization aims to enhance service quality reaching the listener while optimizing transmission efficiency. Advantages of digital radio over analog radio include better audio quality, improved interference response, enhanced spectrum utilization, similar coverage with less power, and the incorporation of multimedia information such as graphics and video in the receiver, enabling services like displaying song lyrics, weather updates, and news. In the context of digital radio, a significant challenge lies in optimizing bandwidth to meet each station's specific needs, given the limited spectrum and increasing service demand. Efficient allocation and utilization of this resource, alongside dynamic adaptation to demand fluctuations and radio-electric environment conditions, are crucial for optimal performance and effective bandwidth utilization. Dynamic optimization techniques like the Shapley value offer a promising approach by evaluating each station's relative contribution to bandwidth optimization, leading to more equitable and efficient resource allocations among stations, thereby enhancing resource management and user experience. Using the Shapley value as a resource optimization strategy in an IBOC transmission scheme in FM presents several advantages. Firstly, it facilitates the fair and equitable evaluation of each node's relative contribution to the final outcome, particularly useful in systems with multiple agents like the 12 transmission stations in this case. Secondly, it aligns with fairness and justice concepts by assigning value to each node based on its marginal contribution to the system, reducing potential conflicts among nodes with different interests. However, linear programming optimization also has advantages, offering precise and computationally efficient solutions when constraints and objectives are well defined. It allows explicit modeling of problem constraints, ensuring compliance with technical or regulatory requirements. To assess the efficiency of the Shapley value in resource optimization compared to linear programming, a comparative statistical analysis was conducted for the proposed scenario. Table 9 presents the optimal bandwidth values for linear programming (\(BW_{O}\)), Shapley value (\(BWSh\)), as well as the differences (X1 and X2) between the bandwidth requested by each node (\(d_{i}\)) and the bandwidth assigned through linear programming and Shapley, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Node \(i\)**} & \multirow{2}{*}{**BW Requested \(d_{i}\)**} & \multicolumn{4}{c}{**Logic Channels BW [kbps]**} \\ \cline{3-6}  & & \(BW_{O}\) & \(BWSh\) & \(X_{1}\) & \(X_{2}\) \\ \hline
1 & 98 & 77.8238 & 80.95 & 20.1762 & 17.05 \\ \hline
2 & 110 & 89.9117 & 90.88 & 20.0883 & 19.12 \\ \hline
3 & 124 & 104.3908 & 102.88 & 19.6092 & 21.12 \\ \hline
4 & 123 & 103.3451 & 102.02 & 19.6549 & 20.98 \\ \hline
5 & 125 & 105.4379 & 103.73 & 19.5621 & 21.27 \\ \hline
6 & 98 & 77.8238 & 80.95 & 20.1762 & 17.05 \\ \hline
7 & 149 & 130.8483 & 125.04 & 18.1517 & 23.96 \\ \hline
8 & 100 & 79.8156 & 82.60 & 20.1844 & 17.4 \\ \hline
9 & 110 & 89.9117 & 90.88 & 20.0883 & 19.12 \\ \hline
10 & 125 & 105.4379 & 103.73 & 19.5621 & 21.27 \\ \hline
11 & 125 & 105.4379 & 103.73 & 19.5621 & 21.27 \\ \hline
12 & 100 & 79.8156 & 82.60 & 20.1844 & 17.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimal BW-PL vs. BW-Shapley and differences in BW allocation according to channel state.