## 5 OFDM Signal Identification Based on Inherent Features
### Analysis of OFDM Signal Parameters Utilizing Cyclic Correlation Characteristics  
In Section 2.3, an analysis of the correlation properties of CP-OFDM has been conducted. Leveraging the correlation characteristics introduced by the CP to the OFDM signal, it is feasible to estimate the effective time length \(T_{\text{use}}\) of the OFDM symbol, the total symbol length \(T_{s}\), and the length of the cyclic prefix \(T_{\text{cp}}\) with minimal prior knowledge. Additionally, corresponding estimations can be made for the number of subcarriers \(K\) and the oversampling rate \(\rho\). The steps for estimating OFDM parameters are illustrated in Figure 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Signal** & \(d_{1}\) \\ \hline MPSK & 0.00 \\ MFSK & 0.00 \\ MQAM & 0.62–0.76 \\ OFDM & 2.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Theoretical \(d_{1}\) values for single-carrier and OFDM signals. Given that the sampling frequency \(F_{s}\) employed by the receiver is known, the accurate estimation of \(N_{s}\), \(N_{\text{use}}\), and \(N_{\text{CP}}\) allows for the straightforward determination of \(T_{s}\), \(T_{\text{use}}\), and \(T_{\text{CP}}\) by multiplying \(N_{s}\), \(N_{\text{use}}\), and \(N_{\text{CP}}\) by \(\frac{1}{F_{s}}\), respectively. Consequently, the most critical parameters to estimate initially are \(N_{s}\), \(N_{\text{use}}\), and \(N_{\text{CP}}\). According to Section 2.3, the second-order cyclic cumulant \(C[\alpha;\tau]\) is expressed as  
\[C[\alpha;\tau]=\frac{1}{N}\sum_{n=0}^{N}r[n]r^{*}[n+\tau]e^{-j2\pi\alpha n} \quad\tau=0,1,...,M. \tag{42}\]  
It follows that the cyclic correlation function possesses the following properties:  
\[C[n;\tau]=C[n+N_{s};\tau],C[n;\tau]=\frac{1}{N}\sum_{\alpha=0}^{N}C[\alpha; \tau]e^{j2\pi\alpha n}. \tag{43}\]  
The expression above denotes that \(N_{s}\) is the cyclic factor and also represents the length of a complete symbol period for the OFDM signal, which corresponds to the total symbol time duration. Therefore, within \(N_{s}\) samples, the correlation function satisfies the following property: \(C[n;\tau]=C[n+N_{\text{use}};\tau]\) for \(n\in N_{\text{CP}}\). This indicates that the cyclic cumulant exhibits a bipartite peak characteristic: one due to the cyclic nature at every \(N\)use points, and the other because of the cyclic nature at every \(N_{s}\) points. However, when \(\tau=N_{\text{use}}\), the peak caused by \(N_{\text{use}}\) vanishes, and at this point, the peaks of the cyclic cumulant \(C[\alpha;\tau]\) represent \(\pm k/T_{s}\), where \(k=0,1,2,\ldots\). The spacing between these peaks allows us to determine the number of samples corresponding to the total symbol time duration \(N_{s}\). Hence, it is necessary to first estimate the number of samples corresponding to the effective symbol time duration \(N_{\text{use}}\) using the maximum likelihood method. \[\hat{N}_{use}=\arg\max_{\tau}C[0;\tau]. \tag{44}\]  
Consequently, the effective duration of the associated OFDM symbol can be expressed as  
\[\hat{T}_{use}=\hat{N}_{use}\times 1/F_{s}. \tag{45}\]  
It can be derived that the total duration of the OFDM symbol can be estimated as  
\[\hat{T}_{sl}=\frac{1}{\arg\max_{\frac{1}{T_{\text{user}}+0.5}T_{\text{user}} \leq\alpha\leq\frac{1}{T_{\text{user}}}}C[\alpha;N_{\text{use}}]}. \tag{46}\]  
Figure 4: The steps for estimating OFDM parameters. Through the aforementioned estimation, the estimated value of the number of samples corresponding to the length of the cyclic prefix (CP) can be determined as  
\[\hat{N}_{CP}=\hat{N}_{s}-\hat{N}_{use}. \tag{47}\]  
Thus, the estimated value for the length of the cyclic prefix \(T_{\text{CP}}\) is determined as \(T_{CP}=N_{CP}\times 1/F_{s}\). In LEO satellite systems, the number of OFDM subcarriers is \(2^{k}\). Therefore, based on the signal bandwidth \(\hat{B}w\) and the effective symbol time duration, the number of subcarriers can be estimated.