# A Survey of Blind Modulation Classification Techniques for OFDM Signals
## 3 Statistics-Based Approach to MC
### Maximum a Posteriori (MAP) Approach
The side information like the known frame structure, channel reciprocity, and the knowledge of total data transmission rate, which are typically available in wireless TDD systems are intensively utilized by the proposed classifiers. By utilizing this information, the proposed likelihood-based MC algorithms are highly effective for the short OFDM frames. Another MAP-based MC for OFDM systems with adaptive coding and modulation (ACM) is carried out in [53]. The proposed classifier for QAM schemes utilizes the channel reciprocity in TDD systems that requires knowledge about the joint probabilities of the subcarrier-wise bit efficiencies at the transmitter and receiver sides. In contrast to prior heuristic approaches [52], these probabilities are calculated analytically if the transmitter and receiver apply the same bit loading (BL) algorithm on their erroneously estimated channel state information. Furthermore, the performance of the proposed MC algorithm employing analytical results is comparable to the simulated joint probabilities. However, it is still somewhat superior due to the subsidiary-independent technique's sub-optimal approach [50]. Analytical and simulation results outperform the heuristic approach [52], especially at higher SNRs. Another modulation classification algorithm for wireless TDD-based OFDM systems with adaptive modulation and coding is analyzed in [54]. The proposed MAP-based classifiers use the distinct signaling bits that are transmitted along with the information symbol. Thus, these can be viewed as a hybrid of MC and a signaling-based transmission principle. According to the signal structure of the received data symbols, these classification algorithms are characterized as bit allocation tables, i.e., a list of modulation formats used on each subcarrier. These received bit allocation tables are explicitly transmitted auxiliary information. Numerical studies indicate that the reliability of the classifier can be significantly enhanced by the use of the specified auxiliary information in a standard indoor propagation environment. Moreover, the simulation results of effective spectral performance show that the proposed method can be a reliable alternative in pure signaling-based or MC schemes in adaptive OFDM transmission. It outperforms the non-adaptive OFDM transmission system. However, this algorithm works in the presence of known CSI, knowledge about the total number of loaded bits, and coding rate. An adaptive transmission algorithm for TDD-based wireless OFDM systems is carried out in [55]. In this technique, at the transmitter side, the BL algorithm and at the receiver side modulation classification algorithm are jointly optimized. To increase the effective data rate, a MAP modulation classification algorithm is applied in place of signaling the complete BAT to the receiver. The classification reliability is increased while preserving the enhanced link quality and low signaling overhead with this optimization on the BL algorithm. The idea behind this contribution is to maximize the effective bandwidth efficiency by this joint optimization of the BL algorithm at the receiver side and the modulation classification algorithm at the receiver side. Thus, the data rate loss caused by the signaling overhead is reduced. The simulations are performed in a typical indoor propagation scenario using burst transmission. It shows the enhancement of bandwidth and reduces the signaling overhead compared to the conventional methods. A reciprocity-based MC algorithm for adaptive OFDM transmission systems in TDD mode is studied in [56]. This proposed transmission technique used the BL algorithm at the transmitter and MC at the receiver. A MAP-based MC is proposed, which is already effective for short frames if channel reciprocity in TDD systems is assumed. In this contribution, the authors analyze the performance of an improved version of this algorithm in a more realistic scenario.