# A Survey of Blind Modulation Classification Techniques for OFDM Signals
## 3 Statistics-Based Approach to MC
### LB Approach
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Author(s)** & **Classifier(s)** & **Modulation(s)** & **Parameter(s)** & **Channel** & \begin{tabular}{l} **Average PCC** \\ **at 20 dB SNR** \\ \end{tabular} \\ \hline [PERSON] [45] & Sub-optimum algorithm & BPSK, QPSK, 16-QAM and 64-QAM & Imperfect noise variance & AWGN & 99.9\% \\ \hline [PERSON]. [PERSON] [46] & \begin{tabular}{l} Quasi-log-likelihood Ratio \\ Test based classifier \\ \end{tabular} & BPSK, QPSK, 16-QAM and 64-QAM & Known channel correlation between adjacent subchannels & AWGN & 98.50\% \\ \hline [PERSON] [47] & \begin{tabular}{l} ALRT, HLRT and \\ Energy-based detector \\ \end{tabular} & BPSK, QPSK, 8-PSK and 16-QAM & Known CSI, Known noise variance and unknown CSI & Rayleigh & 97.40\% \\ \hline [PERSON] [48] & \
\begin{tabular}{l} Expectation maximization \\ block-quasi HLRT \\ (EM-Block-QHLRT) \\ \end{tabular} & BPSK, QPSK, 16-QAM & Unknown CSI and unknown noise power & Acoustic Rayleigh & 100\% \\ \hline [PERSON] [49] &
\begin{tabular}{l} Iterative EM-based MC \\ algorithm, bit-interleaved \\ coded modulation iterative \\ decoding (BICM-ID) scheme \\ \end{tabular} & QPSK, 64-QAM, 1024-QAM and 8194-QAM & Presence of synchronization error and known and unknown CSI & Rayleigh & 99\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of LB approaches for OFDM signals. CP length \(N_{cp}=15\), number of channel tap \(L=5\) and Rayleigh channel are considered the simulation parameters. The simulation results revealed that with an increment in the observed data, the classification accuracy of MC with unknown CSI is near the MC with known CSI. Furthermore, a numerical analysis of MC for OFDM and OFDM-IM shows that OFDM-IM has less classification accuracy than the OFDM. It illustrates that OFDM-IM would have less MC efficiency than OFDM because of the identification of the additional parameter, i.e., the number of active subcarriers that would be necessary for OFDM-IM. In [48], a MC for OFDM signal underwater acoustic multipath channel is studied. It works in the presence of unknown channel impulse response (CIR) and noise power. Channel is first estimated by the EM block. If the number of blocks in EM increases, the channel estimation increases accordingly. Then, the QHLRT method is used to classify the subcarrier modulations. The EM-block-QHLRT method is compared with the EM-QHLRT. The number of subcarrier \(N=1024\), CP length \(N_{cp}=N/4\), sampling frequency 48 kHz and acoustic Rayleigh channel are considered the simulation parameters for this technique. It is observed that after 5 dB SNR, the classification rate achieved by EM-block-QHLRT is higher than 90%, which shows a higher accuracy compared to the EM-QHLRT-based classifier. In [49], an iterative EM-based MC algorithm is used for OFDM-SDR systems. The soft information provided by the channel decoder of bit-interleaved coded modulation iterative decoding (BICM-ID) scheme is utilized as a priori information to the proposed classifier. Simulation is done for the perfect CSI and imperfect CSI for higher-order modulations over the Rayleigh fading channel. The results show a slight difference between the perfect CSI and imperfect CSI, which shows the robustness of the suggested method. The suggested method improves significantly with iterations and outperforms traditional uncoded algorithms. The suggested method obtained acceptable classification performance in the presence of synchronization error, i.e., timing, frequency, and phase offset with reduced processing time. Furthermore, as the constellation size increases, the identification performance degrades. This is because of the less reliable soft information provided by the channel decoder.