Automatic Modulation Classiﬁcation for Adaptive Wireless OFDM Systems

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).


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. 1 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 1 The BAT contains the information about the modulation schemes on each subcarrier.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).can be modeled by where s n,k and H n denote the transmitted data symbol and the transfer function value on the n-th subcarrier of the k-th OFDM block, respectively.We consider a propagation scenario with slowly time-variant channels, typical for indoor communications.Thus the channel transfer function does not change significantly during one transmission frame, i. e. it holds: The additive white noise exhibits a complex Gaussian distribution: v n,k ∼CN(0, σ 2 v ).Due to the multicarrier principle, low-data rate signals are transmitted via flat-fading subchannels.This enables a simple frequency domain channel estimation (CE) and equalization (EQ) shown in Fig. 2.
In OFDM systems using adaptive modulation, symbols on different subcarriers can emanate from different symbol alphabets.Without loss of generality, we restrict ourselves to the digital modulation schemes with maximum bandwidth efficiencies 6 bit/symbol according to Table 1.In Fig. 3, the respective signal constellations are depicted.

Adaptive modulation
Due to the frequency-selective nature of the radio propagation channel, some subcarriers exhibit good channel conditions whereas others suffer from a low signal-to-noise power ratio 383 Automatic Modulation Classification for Adaptive Wireless OFDM Systems www.intechopen.com(SNR).The overall system performance in terms of the raw bit-error ratio is dominated by the poor subcarriers.
The idea of adaptive modulation is to distribute the total amount of data bits among all subcarriers in an optimal way.If the subcarrier SNR is high, more bits than the average are loaded and higher-order modulation schemes are used.If the subcarrier SNR is low, less or even no bits are loaded such that the bit-error ratios on different subcarriers are evened out.
Using this principle, either the average bit-error ratio can be decreased at the same data rate or the data rate can be increased at the same target bit-error ratio.Since the knowledge about the data rate turns out to be an important feature of the AMC, the first approach with a fixed data rate is investigated here.
A huge amount of research on adaptive modulation algorithms has been carried out during the last twenty years (Campello, 1998;Chow et al., 1995;Czylwik, 1996;Fischer & Huber, 1996;Hughes-Hartogs, 1987).In the following, we focus on algorithms that utilize the bit metric: where γ and γ n denote the average signal-to-noise power ratio and the SNR of the n-th subcarrier.This bit metric b n is motivated by the channel capacity formula which takes the SNR gap (Starr et al., 1999) into account.As an example of adaptive modulation, the magnitude of the channel transfer function |H n | in a typical indoor propagation scenario (dashed line) and the corresponding bandwidth efficiencies (solid line) are shown in Fig. 4.There are two challenges involved in the application of AM in practical systems: • Channel knowledge at transmitter side In order to be able to apply AM, the transmitter must know about the subcarrier SNRs.
There are two ways to obtain this knowledge: 1) via feedback from the receiver or 2) using reciprocity in time-division duplex systems.Here, the focus is on TDD systems.

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Wireless Communications and Networks -Recent Advances www.intechopen.com In our analysis, the channel transfer factors H n are therefore obtained by a preamble-based channel estimation in the receive mode.
• BAT knowledge at receiver side In order to be able to decode the transmitted information, the receiver must know about the bit allocation table which includes the assignment of modulation schemes to subcarriers.Either this information is transmitted via a signaling channel or it is automatically classified.b) Based on the received preamble, the base station (BS) estimates the channel Ĥn,k 1 ,UL and calculates the optimal bit allocation table B Tx using an AM algorithm.

Problem formulation
2a) In the downlink (DL), the BS transmits a frame composed of training symbols and payload according to B Tx .
b) Based on the received preamble, the MS estimates the channel Ĥn,k 2 ,DL and calculates the optimal bit allocation table B Rx using the same AM algorithm as the BS. ...
In order to decode the payload that has been sent by the base station, the mobile station requires the knowledge about B Tx .Since we assume that the BAT information is not signaled, the receiver must automatically classify the modulation schemes on each subcarrier solely based upon the received signal.In this analysis it is shown that utilization of side information that is typically available in wireless communication systems can significantly boost the classification reliability.More specifically, the AMC algorithms can exploit: • channel correlation in frequency direction (e. g. subcarrier grouping) • channel correlation in time direction (fixed modulation order on subcarriers and/or subgroups for entire frame)

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• channel reciprocity in TDD mode
• knowledge about overall data rate (total number of loaded bits)

Automatic modulation classifier
In this section, automatic modulation classifiers that are based on different levels of knowledge are introduced.Denote the group of M possible digital QAM schemes by (1 ≤ m ≤ M) where L (m) is the constellation size (number of constellation points) of the m-th modulation scheme and S (m) i denote the complex constellation symbols.
After collecting the received symbols where K is the data frame length, the following M hypotheses are tested for each subcarrier n: = the used modulation scheme of the received data symbols d n was I (m) .
Based upon these symbols, the underlying modulation scheme is to be detected. .Whereas it seems obvious that the symbols emanate from a 16QAM scheme if a large number of symbols is available, it becomes much more difficult to classify the underlying modulation scheme if only a small number of symbols is available.Hence, the exploitation of additional information turns out to be a key aspect for a robust and reliable classification.

Maximum-likelihood (ML)
The maximum-likelihood (ML) approach chooses the hypothesis whose likelihood-function is maximum: The probability density function of the received symbols under the condition that the m-th modulation scheme was used (hypothesis Each symbol within its constellation is equiprobable, i. e. p(S . Since v n is assumed to be Gaussian distributed, it holds: n ) is given by: The log-likelihood function is: Neglecting irrelevant terms for the maximization, the ML-based classifier can be formulated as: An example for the probability of correct classifications is given in Fig. 7.At the transmitter, the bandwidth efficiencies from 0 to 6 bit/symbol have been loaded by the AM algorithm in (Chow et al., 1995).

Maximum-a-posteriori (MAP)
One major drawback of the ML algorithm is that it cannot take into account that the hypotheses under test are not equally likely.Depending on the current channel status, however, some modulation schemes will be used more frequently than others.The ML algorithm is therefore not suitable for OFDM-based systems with adaptive modulation.
A first step to improve the performance is to maximize the a-posteriori probability p(H The main difference can be seen by using the Bayes theorem: n |d n ), the MAP classifier can be formulated as: The a-priori information about the occurence probabilities p(H n ) is utilized.2But still, the MAP algorithm in its current form is not able to sufficiently consider the specific characteristics of adaptive modulation.

MAP algorithms exploiting channel reciprocity (MAP-R)
One key feature to increase the classification reliability is the utilization of channel reciprocity in TDD systems.Under ideal conditions (perfect channel reciprocity, channel time-invariance and channel state information (CSI)), the receiver can perfectly reconstruct the transmit BAT by applying the same AM algorithm based on the propagation channel in the receive direction.In that case, the bit allocation table B Rx equals B Tx .To be more realistic, we assume that the channel is time-variant and CSI is taken from a data-aided channel estimation.This causes B Tx and B Rx to be different but still correlated.Both the channel transfer functions as well as the BATs differ for the transmitter and receiver, respectively.However, they are very similar which an AMC algorithm can take advantage of.
Two different concepts to benefit from this channel reciprocity are discussed now.

Receive bit allocation table (MAP-RQ)
Let Ĥn,Rx be the modulation scheme for the n-th subcarrier in B Rx which was computed by the AM algorithm.The method in (11) is extended by the knowledge about Ĥn,Rx .The modified approach which exploits channel reciprocity in terms of the quantized information Ĥn,Rx can be written as: 389 Automatic Modulation Classification for Adaptive Wireless OFDM Systems www.intechopen.com By applying the Bayes theorem and then neglecting irrelevant terms, we obtain: = arg max Since p((A, B)|C)=p(A|(B, C)) • p(B|C), it holds: The simplification p( n ) turns out to be reasonable for increasing correlation between B Tx and B Rx .We set: Taking the logarithm and using p( Ĥn,Rx , H n ), the MAP classifier based on the receive BAT is: The joint probability p( Ĥn,Rx , H n ) could be numerically determined in advance and stored in look-up tables.Simulation results have shown that a coarse knowledge of these values is sufficient to achieve a significant performance improvement compared to the conventional ML algorithm.However, the probabilities p( Ĥn,Rx , H (m) n ) are usually not available in practice and, moreover, strongly depend on the transmission system and the propagation scenario.In order to overcome this disadvantage we present a heuristic approach to obtain these values.The classification performance is similar to the optimal one.

Approximation of joint probabilities
Suppose that Ĥn,Rx = I (μ) is the modulation scheme for the n-th subcarrier in B Rx .Due to the correlation between transmit and receive BAT, I (μ) is said to be more likely than the other M − 1 possible modulation schemes.Consequently, we set The proportional factor α is irrelevant for the metric maximization.The probabilities of all other hypotheses m = μ have been set equally to 1−w M−1 .Further numerical investigations have shown that distributing the "residual" probability 1 − w in a more sophisticated way does not lead to a significant advantage.
The optimal values of the weighting factors w depend on a multitude of effects: channel quality, channel estimation method, adaptive modulation algorithm etc.The more correlated 390 Wireless Communications and Networks -Recent Advances www.intechopen.comB Tx and B Rx are, the higher the value of w should be chosen.Unfortunately, the analytical search for the optimum seems to be intractable.
The simplicity of this heuristic approach appears attractive for a practical implementation.The receiver needs to calculate B Rx anyway for the application of adaptive modulation in the next transmission frame.
A general drawback of using the BAT in order to exploit channel reciprocity is the quantization of bandwidth efficiencies.

Receive channel state information (MAP-RS)
An even better way to incorporate the channel correlation in transmit and receive direction into the AMC algorithm is described now.We assume that the AM algorithm at transmitter and receiver side is based upon bit loading according to the widely used criterion (Chow et al., 1995) for the estimated bandwidth efficiency: in which k is adapted such that the target bit rate is achieved.The classification method that utilizes the soft channel information bn,Rx instead of the hard BAT information Ĥn,Rx can be formulated as: Following the same steps as in the previous section, the solution of ( 21) is: n , bn,Rx ) with Whereas the AMC algorithm based on the receive BAT in section 3.3.1 requires the knowledge about p( Ĥn,Rx , H n ), here the function p( bn,Rx , H n ) must be known.

Approximation of joint probability density functions
It is unrealistic to assume that the joint probabilities p( bn,Rx , H (m) n ) are available in practical systems.Again, we find approximations based on a heuristic approach: Suppose that the AM algorithm at the receiver has computed bn,Rx = b 0 for subcarrier n.Then it is obvious that those hypotheses which are "closer" to b 0 are more likely than others.We use the heuristic measure The more correlated the channels at transmitter and receiver are, the smaller σ should be chosen.Due to the complex influence of the AM algorithm, it seems to be intractable to find the optimal value σ analytically.
However, compared to the quantized information that is used in the MAP-RQ algorithm, the MAP-RS method benefits from the more reliable soft information leading to a higher classification performance.

Discussion
In Fig. 10, the classification error probability P ce = Pr{ BTx = B Tx } versus E S /N 0 for various AMC methods is shown.If already one modulation scheme in B Tx is incorrectly classified, the whole packet would get lost.Throughout the entire contribution, the performance discussion is based upon a common simulation scenario: The main parameters concordant with a WLAN IEEE 802.11a/n system (IEEE, 2005) are summarized in Table 2.The bandwidth efficiencies, however, vary between 0 − 6 bit/symbol.In average, 4 bit/symbol are loaded by the AM algorithm proposed in (Chow et al., 1995).Due to the fact that the subcarrier spacing is small compared to the channel coherence bandwidth, 2 neighbouring subcarriers are grouped without sacrificing significant system performance.The AMC algorithms utilize this It is assumed that the receiver has perfect knowledge about the total data rate since this single information can be protected against errors well by suitable channel coding.The design parameters for the reciprocity-based classifiers are set to w = 0.8 and σ = 0.3.First, we refer only to the ML algorithm (section 3.1) and the reciprocity-based methods MAP-RQ and MAP-RS: Due to the additional reciprocity information used, the reciprocity-based MAP algorithms outperform the classical ML algorithm significantly.With the soft information used in MAP-RS, the number of modulation classification errors can even be further reduced compared to MAP-RQ.Another step towards a higher reliability is to include even more side information in the modulation classification.

MAP-R algorithms exploiting the knowledge about the data rate (MAP-R-D)
In communication systems, the overall data rate is typically signaled to the receiver via a control channel.Therefore, we can incorporate the available information about the total number of transmitted bits N b per OFDM block into the MAP-R algorithms. 3s an example, we describe the extension for the algorithm MAP-RS.The corresponding modifications in MAP-RQ are analogous.The scheme that jointly classifies the bandwidth efficiencies on all subcarriers can be formulated as: With the abbreviations for the hypotheses under test, the bandwidth efficiencies computed at the receiver, the classified hypotheses and the collected received data symbols on all subcarriers, we reformulate (24): Since the modulation schemes and data symbols on different subcarriers are independent from each other, it holds: and hence: The maximum search must be carried out over a set of all possible hypothesis candidate combinations H. Due to its high complexity, such a joint search is not feasible in practice.We investigate a trade-off between this joint algorithm and the subcarrier-independent methods instead.
First, we split the set of all subcarriers S = {1,...,N} into two subsets: • S rel := {n | reliable decision} including subcarriers for which reliable decisions are possible, and • S crit := {n | critical decision} = S\S rel including subcarriers with critical decisions.
The number of elements in S crit is denoted as N crit .The distinction is based upon an ordering procedure according to the absolute distance between the largest and second largest metric value of the subcarrier-independent metrics (18) or ( 22  The automatic modulation classification is performed for the two subsets in a different way: • For set S rel , we apply the subcarrier-wise MAP-R algorithms described in section 3.3, e. g.: Ĥn,MAP−RS−D = arg max • For set S crit , we apply the joint MAP algorithm following (31): ĤMAP−RS−D = arg max with H S crit and H S rel denoting the vectors that contain the hypotheses of all subcarriers in set S crit and S rel , respectively.
The choice of the design parameter N crit balances performance and complexity.

Discussion
We refer to Fig. 10 again.It shows, among others, the classification reliability of the MAP-RS-D algorithm for different values of N crit .A significant increase of the reliability can be seen, independent of the value of N crit .For N crit > 2, the performance improvement saturates whereas the complexity grows rapidly.In numerous cases at high SNR, only very few decisions are ambiguous.By incorporating additional information, the reliability of these vague decisions can be considerably improved.Against the background of a practical design, small values of N crit are an appropriate choice.

MAP algorithm with reduced complexity (MinMAP)
The complexity of all presented MAP methods is still rather high and may be prohibitive for real-time applications.In order to reduce the complexity, we take a closer look e. g. at the n ) with No exponential and almost no logarithm operations are needed in the classifier.This leads to an essentially decreased complexity.The algorithms MAP-RS-D, MAP-RQ and MAP-RQ-D are modified alike, i. e. denoted as MinMAP-RS-D, MinMAP-RQ and MinMAP-RQ-D.
Metric analysis for high SNR: It will be shown that the error caused by the simplification (37) tends to zero (under mild conditions) if γ → ∞.For simplicity reasons, we neglect all subcarrier, modulation and block indices.First, we analyze the sum: Here, we have sorted |Δ i | in a ascending order with |Δ 1 | being the minimum and |Δ L | being the maximum distance.Now, let us define the error ε between the optimal MAP and the simplified MAP metrics (K = 1):  An overview of the presented metrics is appended at the chapter end in Table 3.

Discussion
Fig. 13 shows the classification performance of the algorithm MAP-RS-D with and without the previously described metric simplification.It indicates that the influence of the metric simplification on the classification performance is minor.Only a small performance degradation is visible which will even decrease with increasing SNR.Obviously, the MinMAP-RS-D approach seems to be an proper tradeoff between performance and complexity.

QAM symbol rotation
Apart from the algorithm design of the receiver, also the transmitter can be factored into the modulation classification for performance improvements.A simple example is given here: Similar to pattern recognition, automatic classification becomes effective if the objects to discriminate are as different as possible and can therefore be easily separated.
However, especially the constellation sets of the higher-order modulation schemes are very similar.A large number of received symbols must be observed to judge safely from which set the symbols have been generated.As a first measure to achieve a better separation of the constellation sets we rotate all 16QAM symbols by 45 • as shown in Fig. 14 (right).Note that the optimal constellation modifications would take the rotation of all modulation schemes into account.

Discussion
The algorithms using the constellation modification at the transmitter side are denoted as ML-45 and MinMAP-RS-D-45, respectively.A slight performance improvement due to the algorithm is considerable and even overcompensates the benefit from adaptive modulation, the overall PER with perfect knowledge and classified BAT according to MinMAP-RS-D is very similar.The longer the frames, the smaller the influence classification errors on the PER will be.On the one hand, AMC benefits from more symbols to average.On the other hand, payload detection errors will occur more frequently with increasing frame lengths.By using the presented AMC approach, we can fully gain from adaptive modulation (at costs of a higher complexity) without loss in the effective data rate due to signaling of the BAT, also in wireless communication scenarios.

Summary
In this contribution, a framework of likelihood-based automatic modulation classification algorithms for wireless orthogonal frequency division duplex systems with adaptive modulation has been presented.Instead of signaling the bit allocation table to the receiver, the bit allocation table can be efficiently detected solely based upon the received signal and side information which is available in time-division duplex communication systems.
It has been shown that the well-known maximum-likelihood algorithm does not offer a sufficiently high classification reliability in typical wireless communication scenarios.Therefore, an improved maximum-a-posteriori technique has been presented that utilizes additional information, i. e. a fixed bit allocation table per frame, channel reciprocity in time-division duplex systems and the information about the overall data rate.A metric simplification is possible which reduces the computational burden considerably without sacrificing much performance.
By using these advanced classifiers, there is almost no performance loss in terms of the packet error ratio compared to the case with perfect knowledge of the bit allocation table.Due to the moderate computational complexity and high classification reliability even for short 400 Wireless Communications and Networks -Recent Advances www.intechopen.com

Fig. 4 .
Fig. 4. Example of adaptive modulation Fig.5.TDD system structure Fig.5shows the signal flow at the initiation of adaptive modulation in downlink transmission of the considered time-division duplex system model: 1a) In the uplink (UL), the mobile station (MS) transmits a frame consisting of training information and payload.When establishing the link, the MS does not know the channel state.Hence, for the first frame transmitted, no AM can be applied.

Fig. 6 .
Fig. 6.Constellation diagrams of equalized 16QAM symbols at an average SNR of γ = 20 dB As a motivating example, random signal constellations of received (and equalized) 16QAM symbols d n,k / Ĥn at an average SNR of γ = 20 dB are shown in Fig.6.Whereas it seems obvious that the symbols emanate from a 16QAM scheme if a large number of symbols is available, it becomes much more difficult to classify the underlying modulation scheme if only a small number of symbols is available.Hence, the exploitation of additional information turns out to be a key aspect for a robust and reliable classification.

Fig. 7 .
Fig. 7. Classification probability of the ML algorithm versus E S /N 0 , frame length K = 10

Fig. 8 Fig. 8 .
Fig.8shows an illustrating example of the magnitudes of the channel transfer function at transmitter and receiver side and the corresponding BATs B Tx and B Rx at an SNR of γ = 10 dB, a frame duration of T fr = 0.1 ms and a Doppler frequency of f dop = 15 Hz.A typical preamble-based zero-forcing method to estimate the channels has been applied.
Fig. 9 depicts simulation examples of the joint probability density function p( bn,Rx , H

Fig
Fig. 10.BAT classification error probability P ce of AMC algorithms versus E S /N 0 , frame length K = 10 subcarrier grouping by additively combining the corresponding metric values.A zero-forcing channel estimation is carried out on 2 training OFDM blocks with a total length of 160 samples.It is assumed that the receiver has perfect knowledge about the total data rate since this single information can be protected against errors well by suitable channel coding.The design parameters for the reciprocity-based classifiers are set to w = 0.8 and σ = 0.3.

Fig. 11 .
Fig. 11.Signal flow of joint algorithm are mutually coupled -bandwidth efficiencies increase with increasing SNR.High-order modulation schemes like 64QAM are, however, more difficult to classify than low-order modulation schemes like BPSK.

Fig
Fig. 13.BAT classification error probability P ce of AMC algorithms versus E S /N 0 , frame length K = 10, N crit = 2

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Fig. 15.BAT classification error probability P ce of the MinMAP algorithm versus E S /N 0 , frame length K = 10, N crit = 2

Table 1 .
Considered digital modulation types

Table 2
)=2 bit/symbol and γ = 10 dB; the average bandwidth efficiency is 4 bit/symbol n ) and p( Ĥn,Rx , H n .Simulation set-up thus assuming a Gaussian distributed deviation with the design parameter σ.Here, the operator b(H) denotes the number of bits transmitted for hypothesis H; β is a proportional factor that is irrelevant for the maximization.
), respectively.Subcarriers with the largest absolute distances are inserted in S rel ; the remaining N crit subcarriers are included in S crit .In other words, decisions are said to be critical if the two largest metric values are similar.Surprisingly, ordering by subcarrer SNR values turns out to be unfavourable.Due to adaptive modulation in the considered OFDM systems, channel gains and modulation orders Numerical results have shown moderate deviations between the simplified and the optimal metrics already for practical SNR ranges.Assume that the received equalized symbols converge to their constellation points for high SNR.Then e. g. the special case|Δ 2 | = |Δ 1 | or |Δ 2 |≈| Δ 1 | thatwe excluded in our consideration so far can only occur if the hypothesis under test is incorrect.Since the neglect of terms in (37) lowers the metric value of this incorrect hypothesis, this condition can even have a favourable effect on the discrimination of the modulation schemes.