# A Survey of Blind Modulation Classification Techniques for OFDM Signals
## 3 Statistics-Based Approach to MC
### Maximum a Posteriori (MAP) Approach
Simulations are carried out to validate the accuracy of the MC algorithm in the presence of imperfections caused by channel time-variance, channel estimation errors, and non-reciprocal transceiver filters. Simulation setup investigations are focused on indoor propagation scenarios typical for WLAN. For calibrated transceivers, the simulations show superior performance of the proposed adaptive transmission scheme with MC compared to a non-adaptive transmission in a typical indoor propagation scenario. It also has superior classification performance as compared to the signaling-based technique. A simplified MAP-based MC is analyzed in [57]. An adaptive OFDM based on an IEEE 802.11a system is simulated. The system occupies a bandwidth of 20 MHz, which is split into \(N=64\) subcarriers. Among these subchannels, \(N_{d}=48\) subchannels are used for data transmission: 4 are reserved for channel tracking and synchronization purposes and the remaining 12 are unused. Throughout this paper, they have assumed perfect time and frequency synchronization, which they consider to be a typical indoor scenario. The number of multipath components is assumed to be 16 such that the length of the guard interval is set to be 16 too. The maximum Doppler frequency is assumed to be \(f_{d}=55\) Hz corresponding to a speed of 3.33 ms, and the Doppler spectrum follows Jakes' model. The correlation is very strong in the considered system due to the quantized structure of the effective channel. The quantization is a result of adaptive power allocation. In the context of this paper, a MAP-based MC approach is investigated in wireless local area network (WLAN) based OFDM systems with adaptive modulation. The receiver has to estimate the channel, which is modeled by a slowly varying multipath Rayleigh fading channel and AWGN. The performance of the MC algorithm is measured in terms of the end-to-end packet error rate (PER). Package errors occur due to data detection errors and MC classification errors. The PER of the proposed MC algorithm is almost identical to the PER of an error-free MC algorithm. This exemplifies the potential of MC applications in real-time scenarios. Another MAP-based MC for the TDD-based OFDM system is studied in [58]. This paper proposes a channel prediction approach for improving the efficiency of the MC used in the adaptive OFDM scheme. To achieve an acceptable prediction performance, effective noise reduction and interpolation techniques are used. The channel is supposed to be frequency-selective, with Rayleigh fading coefficients and a power delay profile decided by the standard indoor environment for IEEE 802.11a models. For time correlation, Jakes' Doppler spectrum is presumed, with the maximum Doppler frequency \(f_{d}\) set to 20 Hz by default. Finally, simulations for the channel modeled with the Gaussian Doppler spectrum are carried out to explore the robustness of the proposed approach to the channel model. The probability of incorrect classification for both Jakes' and Gaussian Doppler spectrum is compared, in the case \(f_{d}=20\) Hz. In this case, it can be shown that the proposed technique is sufficiently robust to the model of the channel's time variance. The importance of adaptive modulation for effective usage of channel capacity in the OFDM system is shown in [59]. The need to transfer the information about modulation to the receiver is abolished by the MC algorithm, and thus, these algorithms are a very useful method to increase the channel capacity. However, in practice, two different sets of pilot symbols are used for the identification of the modulation type and for the estimation of the channel impulse response. The author proposes only one set of pilot symbols to find the information about the modulation type as well as the channel in this paper. As the pilot symbols are related to the modulation type, so they are named \"adaptive pilots\". The identification of the modulation type is successfully done with the help of these adaptive pilots without affecting the performance of the channel estimation.