# NC-OFDM Satellite Communication Based on Compressed Spectrum Sensing
## 4 Subcarrier Power Allocation Algorithm
### The Description of Power Allocation Problem  
In these 69 subcarriers, as shown in Table 2, 57 data subcarriers, 6 pilot subcarriers, and 6 protective subcarriers are allocated. According to Figure 3, the noise temperature of each spectrum hole is different, and the difference between the highest and the lowest value is about 6 dB. The demodulation threshold of BPSK modulation plus convolution code used in satellite communication is about 5 to 7 dB. Thus, we set the SNR of NC-OFDM subcarriers as 7-13 dB, as shown in Table 3.  
The problem solved by the power allocation algorithm is how to allocate and optimize the subcarrier power to achieve maximum system throughput within limited total power, known occupancy of authorized user frequency bands, and noise temperature constraints. The authors of [27] proposed a distributed power allocation scheme, which is suitable for resource allocation under multi-user and multi-channel conditions, but little consideration is given to the interference problem of authorized users. In [28], a distributed resource allocation scheme was proposed, which proved that the Particle Swarm Optimization (PSO) algorithm and the dual Lagrangian optimization method have similar performance and acceptable computational complexity. The authors of [29] proposed a method of combining the PSO algorithm and the case-based reasoning method for power allocation, which can speed up the convergence, but the case library samples require time and cost accumulation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Spectrum Hole Number** & **Start Frequency (MHz)** & **Cut-Off Frequency (MHz)** & **Bandwidth (MHz)** & **Assign Sub-Carrier Number** \\ \hline
1 & 12,325 & 12,395 & 70 & 7–23 \\ \hline
2 & 12,445 & 12,465 & 20 & 36–39 \\ \hline
3 & 12,475 & 12,510 & 35 & 43–50 \\ \hline
4 & 12,568 & 12,582 & 14 & 66–68 \\ \hline
5 & 12,615 & 12,700 & 85 & 77–96 \\ \hline
6 & 12,728 & 12,800 & 72 & 106–122 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spectrum holes extracting and subcarrier allocation. Figure 3: Spectrum sensing results of Ku-band satellite. In view of the high complexity of the current NC-OFDM sub-carrier power allocation algorithms, a sub-optimal power allocation method based on Hybrid Genetic Particle Swarm Optimization (HGAPSO) algorithm is proposed in this paper. The NC-OFDM sub-carrier power allocation scheme is converted into an optimization problem, and the maximum overall throughput of cognitive users in the system is taken as the goal of the optimization. The input optimization algorithm of the power allocation scheme was derived, and the scheme was optimized according to the output analysis of the target. The total number of cognitive users is taken as the optimized objective function according to the transmission rate, which is expressed as Formula (8):  
\[\max_{P_{i}}\sum_{i=1}^{N}\log_{2}\left(1+\frac{\left|h_{i}^{SS}\right|^{2}P_{ i}}{\sigma^{2}+J_{i}}\right). \tag{8}\]  
The constraint conditions of the objective function are shown in Equation (9):  
\[\sum_{i=1}^{N}P_{i}\leq P_{\max},\sum_{i=1}^{N}I_{i}(P_{i})\leq I_{th}, \tag{9}\]  
where \(P_{i}\) is the power of the \(i\)-th sub-carrier, \(h_{i}^{SS}\) is the channel gain coefficient between the subcarriers, and \(\sigma_{2}\) is the variance in Gaussian noise. \(J_{i}\) is the interference noise power of the authorized user to the \(i\)-th subcarrier:  
\[J_{i}(PU)=\int_{f_{i}-\Delta f/2}^{f_{i}+\Delta f/2}\frac{1}{2\pi N}\int_{- \pi}^{\pi}\Phi_{PU}(f)\Bigg{(}\frac{\sin(\frac{N}{2}(2\pi f-\Phi))}{\sin(\frac {1}{2}(2\pi f-\Phi))}\Bigg{)}d\Phi, \tag{10}\]  
where \(\Phi_{PU}(f)\) is the power spectral density function of the authorized user, \(f_{i}\) is the center frequency of the authorized user, and \(\Delta f\) is the bandwidth of the cognitive user.