**1. Introduction**

The flexible adaption of the transmission scheme to the current channel state becomes more and more a key issue in future communication systems. One efficient solution in multicarrier systems like Orthogonal Frequency Division Multiplexing (OFDM) has been proven to be adaptive modulation (AM) where the modulation scheme is selected on a subcarrier-basis or group of subcarriers. A lot of research has been carried out on AM or bit loading algorithms (Campello, 1998; Chow et al., 1995; Czylwik, 1996; Fischer & Huber, 1996; Hughes-Hartogs, 1987).

A basic disadvantage, however, is that the receiver requires the knowledge about the selection of the modulation schemes to decode the transmitted data. The conventional measure is to transmit the so-called bit allocation table (BAT) via a signaling channel.<sup>1</sup> This leads to a considerable reduction of the effective data rate. In contrast to wired communication links like the digital subscriber line (DSL) in which AM is already well-established, the time-variance of mobile radio channels usually necessiates a continuous and fast update of the BAT. Even sophisticated signaling schemes using state-dependent source coding of signaling bits reduce the throughput by 3 − 4% for short packets (Chen et al., 2009). If the channel statistics are not known, the signaling overhead is significantly larger.

In order to lower the amount of the signaling overhead and to obtain more flexibility, the BAT can be automatically detected at the receiver side. Such automatic modulation classification (AMC) algorithms have already been explored intensively since several decades, primarily for military applications but not for civil radio communication systems. The classifiers can be categorized into two types: likelihood-based (Boiteau & Martret, 1998; Long et al., 1994; Polydoros & Kim, 1990; Sills, 1999; Wei & Mendel, 2000) and feature-based methods (Dobre et al., 2004; Hsue & Soliman, 1989; Nandi & Azzouz, 1998; Swami & Sadler, 2000). While likelihood-based approaches arise from a defined optimality criterion, feature-based methods are usually heuristically motivated using e. g. higher-order moments. On the other hand, likelihood algorithms tend to require a higher complexity. A comprehensive overview of existing AMC algorithms is given in (Dobre et al., 2007).

In this book chapter, we will highlight the classification of digital quadrature amplitude modulation (QAM) schemes in wireless adaptive OFDM systems using the likelihood principle (Edinger et al., 2007; Huang et al., 2007; Lampe, 2004). We particularly focus on

<sup>1</sup> The BAT contains the information about the modulation schemes on each subcarrier.

Fig. 1. Block diagram of an OFDM transmitter

Fig. 2. Block diagram of an OFDM receiver

time-division duplex (TDD) systems in which the channel can be regarded as reciprocal. In contrast to other research work, a lot of new constraints are taken into account. Namely, many parameters are known by the receiver that can be utilized to enhance the classification reliability (Häring et al., 2010a; Häring et al., 2010b; 2011).
