# A Survey of Blind Modulation Classification Techniques for OFDM Signals
## 3 Statistics-Based Approach to MC
### FB Approach
The estimated parameters include the number of subcarriers, the length of the OFDM symbol, and the CP length. Using these parameters, traditional modulation classification techniques may be used to identify the linear modulation format on each OFDM subcarrier. The analytical distribution function-based Gaussian test technique is shown to differentiate OFDM from SC modulations effectively, and the correlation test is shown to estimate the cyclic prefix length effectively. A fast Fourier transform (FFT) is used to effectively estimate the number of subcarriers. The simulation findings show that the proposed technique provides classification performance of more than 90% for SNR greater the 15 dB. In the paper [70], a Bayesian inference-based MC technique for the MIMO-OFDM signal is used. This technique uses the Gibbs sampling convergence approach on a latent Dirichlet model as a baseline. However, the inference-based technique has a significant computational overhead, and it also needs perfect synchronization at the receiver. In the paper [71], an MC algorithm for the MIMO-OFDM system is analyzed under the unknown frequency-selective fading channels and SNR. This work is an extension of the achievements in MAP-based MC [50; 51] by adding a new constraint to the framework. The classification problem is presented as a Bayesian inference task, with solutions provided based on Gibbs sampling and mean-field variational inference. The Gibbs sampling method yields the best Bayesian result. It is shown that after multiple iterations, switching to the mean-field variational inference technique improves classification accuracy for the small length of the received signal. However, most of the existing MC consider channels as flat fading when the number of receiving antennas exceeds the number of transmitting antennas. However, under more general circumstances, the proposed algorithm works quite well. It is shown that the proposed Bayesian methods outperform existing non-Bayesian techniques based on independent component analysis (ICA). However, this inference-based technique is quite difficult, and it also necessitates perfect synchronization at the receiver. A tree-based blind MC method for asynchronous MIMO-OFDM is developed in [72]. It extracts unique features for different modulation schemes using normalized fourth-order and sixth-order cumulants. It then performs a threshold-based classification using the likelihood ratio test to determine the modulation format of the received signal. The number of subcarrier \(N=128\), CP length \(N_{cp}=N/4\), number of channel tap \(L=4\), number of OFDM symbol 50, normalized CFO \(-0.5<\epsilon<0.5\), symbol timing offset \([-N/2,N/2]\), sampling sampling rate 50 Msamples/s, symbol rate 1 Msymbols/s, and Rayleigh channel are considered the simulation parameters for this technique. The classification performance of this algorithm is validated by using the RF testbed in a realistic scenario. The authors consider the higher number of transmitting and receiving antennas in the simulation process. However, the actual experimental systems in this paper only contain at most two transmitter antennas and two receiver antennas. In the paper [112], signal parameter estimation, modulation classification, and synchronization are carried out for the OFDM signal. At the first stage, the cyclic cumulant is used to estimate the number of subcarriers, symbol length, useful symbol length, CP length, and oversampling factor. At the second stage, the elementary cumulant is used to classify the BPSK, QPSK, OQPSK, MSK, and 16-QAM modulation scheme over the Rayleigh fading channel. After that, a modified maximum likelihood technique is used to estimate the CFO and STO for the OFDM system jointly. After correction of the CFO and STO, recovery of the constellation diagram of modulation schemes and BER analysis is performed. The BER is found approximately \(8.5\times 10^{-3}\) and \(6.5\times 10^{-2}\) at 20 dB SNR for QPSK and 16-QAM modulation schemes, respectively.