Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels

ISA Transactions xxx (xxxx) xxx

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Research article

Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels ∗

Ahmed K. Ali a,b , , Ergun Erçelebi a a b

Department of Electrical and Electronics Engineering, University of Gaziantep, 27310 Gaziantep, Turkey Department of Electrical Engineering, University of Mustansiriyah, Baghdad, Iraq

article

info

Article history: Received 24 May 2019 Received in revised form 16 February 2020 Accepted 2 March 2020 Available online xxxx Keywords: AMC AWGN Higher-order cumulants Low SNR processing Thresholding technique Pattern recognition

a b s t r a c t In this paper, we present a unique modulation classification method that is based on determining an attractive relation between higher-order cumulants (HOCs) using a decision tree-classifier to improve the extracted features employed for the recognition of modulation schemes, such as phase shift keying (PSK) and quadrature amplitude modulation (QAM). A threshold algorithm is applied to the proposed classifier, which consists of sub-classifiers, each comprising a single feature, and each being capable of distinguishing the modulation types individually. In this work, a high-accuracy classifier system is utilized to recognize modulation schemes, such as QAM (16, 32, 64, 128, and 256) and (2, 4, and 8) PSK at a low signal-to-noise ratio (SNR). In this study, 1000 signals are studied for each SNR of –5 dB to 30 dB. The most prominent results of the classifier decisions range from 88% to 100% with regard to distinguishing the same types of PSK and QAM. In the long run, the proposed classifier module will be advantageous in terms of accuracy and computational complexity relative to the other classifiers in the literature. The results demonstrate that the proposed algorithm has a significantly better classification accuracy in comparison with the previously proposed ones. © 2020 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction Wireless communication systems are becoming increasingly complex, which serves as a major inspiration for communication engineers to develop more intelligent modulation approaches, primarily for the accurate recognition of modulation signal types. Additionally, classification methods have become more challenging, especially for signal-to-noise ratio (SNR) less than zero. In non-cooperative communication channels, entire communication systems are designed based on the concept of automatic modulation classification (AMC), which enables the receiving system to distinguish between the modulation schemes of the received signals prior to the signal detection and demodulation processes. The identification of the modulation type is a critical task, and it is important to develop algorithms that have high accuracy with respect to identifying the modulation signals under various SNR ranges [1]. While many algorithms have been published in this field, their main limitation is that they are focused on cases with SNR values < 0 [2]. AMC plays a critical role in various applications in both military and civil fields; it is one of the essential blocks in electronic warfare receivers and cognitive radio systems. The most ∗ Corresponding author. E-mail addresses: [email protected], [email protected] (A.K. Ali).

common civilian applications include spectrum administration, signal affirmation, software radios, network traffic management, and intelligent modems, while in military applications, it can be used in interference identification, electronic surveillance, and monitoring [3]. It also plays a significant role in spectrum management, enabling the efficient utilization of the available spectrum and achieving higher data transfer speeds [4,5]. Previously, a large number of studies have focused on the performance of hierarchical tree classifiers to recognize high-order modulation signals [6– 8], whereas very few studies have focused on the behavior of high-order QAM under the effect of low SNR. Recently, the investigation conducted in [9] confirmed that natural logarithmic functions can be utilized to improve the extracted features, and that such statistical features of the signal provide a high classification rate in the recognition of high-order QAM signals. Based on the logarithmic classifier described in the previous work, the current work focuses on a new approach to distinguish between groups of modulation formats, which include phase shift keying (MPSK), as well as six quadrature amplitude modulation (MQAM) schemes. The proposed pattern recognition model is comprised of chosen groups of higher-order cumulant (HOC) parameters extracted from the generated signals. The extracted features are improved by using the properties of a natural logarithmic function. The new feature formats are used as classification features because of their attractive noise immunity. The threshold

https://doi.org/10.1016/j.isatra.2020.03.002 0019-0578/© 2020 ISA. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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A.K. Ali and E. Erçelebi / ISA Transactions xxx (xxxx) xxx

algorithm technique has been implemented to combine the features calculated at each individual node, as well as to generate an overall decision regarding the modulation type of the unknown signal. This creates a new generation of cumulant-based classifiers, known as logarithmic classifiers. The main benefactions of this work can be summarized as follows: (1) A complete theoretical analysis of the performance of cumulant-based decision multiple binary tree classification frameworks for M-PSK and M-QAM modulation schemes under the effect of additive white Gaussian noise (AWGN) channel. (2) A new hierarchical classification framework for a particular set of digital modulation schemes. (3) Performance analysis of the decision-tree classification framework for different types of correlated modulation schemes. (4) This work provides a new framework based on-logarithmic functions as classifier features. The proposed framework makes the feature distribution curves less sensitive to variations in SNR, even with a value less than zero. Additionally, the complexity of the classification is reduced because the stability of the features is improved by the properties of the logarithmic functions. (5) An investigation into the performance of the logarithmic classifier in recognizing nine modulation signals (2, 4, 8)-PSK and (8, 16, 32, 64, 128, 256)-QAM. The modulation signals were equipped with random row data that were generated to evaluate the overall performance. (6) The simulation results demonstrate that the combination of multiple sub-classifiers significantly enhances the correct classification rate of the classifier, even for low ranges of SNR. It is also shown that the proposed multiple tree classifier can provide a classification accuracy of up to 99.66% at SNR = −3 dB. When the SNR > 5 dB, the accuracy becomes higher than 99.8%. The remainder of this paper is arranged as follows: Section 2 presents some related work, while Section 3 presents the communication system model and introduces AWGN. Section 4 explains the AMC module, and Section 5 presents details of the proposed AMC-algorithm. Sections 6–8 describe the performance evaluation of the proposed AMC-algorithm, which is followed by the results and discussion. The conclusion is given in Section 9. 2. Background of related work AMC-algorithms can be classified into two main types of methods: likelihood-based (LB) formations and feature-based (FB) formations. LB-approach is considered AMC as a multiple compound-hypothesis testing that estimates the maximum likelihood ratios of a determined received signal and prior identified template signals. Then, the decision is made by comparing this ratio among the predefined threshold. This typically gives an optimal predicted in a Bayesian sense but includes significant complexity reported in [10]. Many LB-algorithms were proposed by Dobre et al. 2007 [11] and Wang et al. 2010 [12]. The FB-approach usually considers several features that are extracted, and a signal prediction is made based on their computed values along signals. The FBapproach has been extensively used in practical applications. Although the FB-approach might not be best one, it is generally still less complexity and easy to designing, and offers an excellent classification performance, especially if it is designed with high accuracy. The main parameters of the FB-methods are (1) feature extraction and (2) decisions that are usually made by the classifier. The extracted features are adopted to identify the properties of the modulation signal to simplify classification. Subsequently, the features of the modulated signal are computed. These features usually applied to a certain recognizer (limits of decision classifier) to make the decision for identifying the type of received modulation signal. The compatibility between the selections of suitable features with the appropriate classifier is usually based on accomplishing the highest probability

of correct rate to identify the modulation type. Several features have been adopted in previous literature, including features that extract the received signals, such as instantaneous amplitude, phase, and frequency [13], as well as transform features, such as wavelet [14] and Fourier [15] transforms. Numerous algorithms that are based on HOCs and high-order moments (HOMs) easily process the received signals in different ways; these processes were documented by Liu and Xu 2006, Han et al. 2012, and Su 2013 [16–18]. Recently, some studies used the fourth, sixth-and eight-orders of cyclic cumulants (CCs) with hierarchical classifier structure for QAM, PSK and ASK signals classification, similar to that used the very high-order statistics (VHOS) to classify PSK between QAM which documented [6,16]. Additionally, constellation diagrams considered good representation for the modulation signals. The constellation diagram was extracted as a modulation signal feature in [17,18]. One crucial method that can perform the AMC functionality is higher-order statistics (HOS), which can be used to estimate the modulation factors [16]. In the other hand, using different cyclic moments and HOC to formulate a modulation recognition algorithm for PSK, QAM, and pulse-amplitude modulation (PAM) signals were described by Ghauri et al. 2014 [19]. In this study, the work is divided into two modules. First, we focus on the extraction of features using HOCs. These features are approximately parallel curves, and are relative to the SNR-axis for each type of modulated signal. The features that are identified based on the moments and cumulants are selected, taking into consideration the PAM and QAM modulations. This is conducted using a hybrid intelligent classification algorithm based on bee’s algorithm (BA) for chosen of the most useful features prior than applied to the classifier. Further described are documented in [20]. The selection of suitable features depends primarily on the types of modulation that are needed. The next step in the classification method is to decide what type of modulation was used on the signal based on the features that were calculated. The selected features that mainly deem positively contribute for classification are analyzed via a machine-learning classifier to identify the modulation scheme of the received data. Numerous models of classifiers have been utilized for this purpose, such as artificial neural networks (ANN), which were described by Popoola and Olst in 2011 [21]. This model of classifier is not only used for the classification of modulation formats, but also for the estimation of SNR in wireless networks [22]. The support vector machines (SVM) classifier was considered to classify the modulation signals in [23]; additionally, clustering algorithms and K-nearest neighbors (KNNs) were considered by Zhu et al. 2014 [5], and the polynomial classifier (PC) was considered by Abdelmutalab et al. 2016 [24]. The decision-theoretic classifiers method utilizes multiple compound-hypothesis testing arguments to represent the identification crisis [25,26], while the linear classifiers are more efficient in pattern-identification methods that do not need careful computation. Linear classifiers are simple to realize, whereas non-linear classifiers need complex and highly efficient training algorithms, as well as a large amount of data for the training process [27]. An appended factor that restricts a classifier efficiency is the condition of the transmission medium through which the modulated signal is transmitted. While many papers have focused on AMC systems, most of them have focused on AWGN channels, such as [5,28], while others have taken a more realistic approach for the channel models by considering the effect of multipath fading [29]. Certain modulation types, such as {8, 16, and 32}QAM signals, are more easily distinguished in comparison with modulation formats of dense constellations, such as {64,128, and 256}-QAM. In both cases, the ability of classifier for signals classification is affected by the signal length and positively participate from extracted features against SNR variations. Increasing the

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 1. Communication scheme model.

constellation symbols may decrease the classifier performance owing to the unpredicted residual frequency offset and phase offset, which are investigated briefly in the simulation performance section in this work. 3. Typical communication system model The main merit of the high-performance communication system is the transmission of information signals through a communication channel without the loss of any information at the receiving end. Information signals suffer from many types of degradation due to the effect of unwanted signals, such as noise, distortion, and attenuation, which affect the signal quality while traveling through a channel. Additionally, the signal loses some of its energy, which causes attenuation due to the effect of channel impedance. This causes tangible damage to the transmitted signal [30]. Moreover, the shape of the signal transmitted through the channel is vulnerable to distortion when the receiver receives more than one signal with close frequencies simultaneously. Random noises are unwanted signals, and because they are unpredictable, they are classified as random signals originating from unreal or natural sources; however, they still cause a palpable weakness in the transmitted signal. This is considered an important point by researchers who work in the field of transmission impairments in telecommunication systems. Owing to the presence of these retrogressions while transmitting a signal through a channel, it becomes difficult for the receiver to distinguish the type of modulation signal that carries the information signal. Fig. 1 illustrates a simple communication system model. The receiver comprises an automatic modulation classifier, which can be further split into two main sub modules, namely, the received signal pre-processing and classifier modules. The function of the pre-processing block is to measure the synchronization parameters, such as the frequency offset, timing recovery, and signal power, of the received signal. Furthermore, it helps the classifier module in selecting a satisfactory classification algorithm for modulation recognition. 3.1. Signal and channel model To study the behavior of any communication system, the transmission channel is typically assumed to be an ideal model; based on this assumption, the transmitted signals are usually weakened by AWGN, which includes all unwanted random signals present in nature, such as sky noise and fulgurite. This channel model is based on the idea of a normal distribution of random variables with zero mean, and has a constant power spectrum density, which gives a good description of the performance of the communication system and reflects their main

Fig. 2. Channel model.

characteristic. Therefore, this study focuses on a transmitted signal that has been corrupted by random noise, which is commonly used in AWGN-channel models to account for the deterioration in the transmitted signal when traveling from the transmitter site to the receiver site [17]. According to this assumption, the noise is sufficiently limited to demonstrate the robustness of the classification. Fig. 2 depicts the AWGN model. Other types of noise signals are beyond the scope of this article. The received signal is expressed as y (t) = S (t) + N(t)

0 ≤ t ≤ m,

(1)

where y (t) is the baseband envelope complex signal that is corrupted by noise at the receiver side, S (t) is the transmitted modulation signal that carries the information signal, and N (t) is the AWGN, m = nTs . n is the number of symbols transmitted, and Ts represents the time. Eqs. (1) and (2) have been derived from Azzouz and Nadi 1995 [31]. The general representation of the discrete baseband signal with zero mean is as follows: s (n) = Ae−i(ω0 nTS +θn ) k=∞

∑

×

s (L) h(nTS − kTS + εTs TS )

ω0 = 2π f0 (2)

k=−∞

S(n) is a complex conjugate of the mapping signal, and is expressed as follows: S = I + jQ

(3)

Here, S(L) is the starting input symbol, which can be expressed as M points of the symbols of familiar constellations, and it might be not critical that the symbols taking equal probabilities. A is the magnitude of the modulated signal, ω0 is the residual carrier frequency or frequency offset, which is constant, θn is the phase offset from one symbol to another, h (. . . , ) represents the channel impact (e.g., due to incomplete equalization), and εTs is the error that occurs in time or the timing jitter.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 3. Constellation points obtained after the AWGN channel at an SNR of 30 dB for the PSK and QAM modulation schemes.

Fig. 3 illustrates the constellation points obtained at the receiver site for different PSK and QAM modulation signals under an SNR of +30 dB, and the number of transmitted symbols is 4096. A unique algorithm for the identification between (2, 4, 8)-PSK and (8, 16, 32, 64, 128, 256)-QAM schemes is proposed and discussed in the next section.

an obvious confusion in the classification algorithm for the modulation signals. Therefore, it is necessary to eliminate this part before signal processing and determine that the received signals are normalized to have zero mean and unit variance before being passed to the feature extraction step. The first moment of a continuously random variable y is defined as [25].

∫ 4. AMC - module

∞

y. fx (y) dy

µy =

(4)

−∞

This section describes the pre-processing and selection of the desired features for classification. The pre-processing techniques and features used in the feature-based tree (FBT) were concisely presented by Salibian and Lampe, 2016 [32].

Here, µy is the first moment of variable y and fy (y) is the probability density function (PDF), which is the same as that for the random signals y (t). To remove the signals that have a mean value from the received signal, the expression of the received signal becomes [33]

4.1. Pre-processing block

µy(t) = lim Owing to the influence of the receiver at the receiving end, it may generate a signal that has a non-zero mean value. This directly influences the feature extraction process, and also creates

τ →∞

1

τ

τ

∫

y (t) dt

0

y (t) = y′ (t) − lim

τ →∞

1

τ

τ

∫

0 ≤ t ≤ τ, y (t) dt,

(5) (6)

0

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 4. Proposed decision tree classifier, which is based on the multi-tree and logic status.

ψ (s) = ln[ϕ (s)]

or y (t) = y′ (t) − µ {y (t)} ,

(7)

where µy(t) is the mean value of the signal, τ is the length of the signal vector, y′ (t) is the received signal that carries the raw-data, and y (t) is the received signal after eliminating the signal that has zero mean.

In a typical block of the AMC system (depicted in Fig. 1), the first task is preprocessing. After that, raw datasets are normally reduced in dimension before then are fed into the classifier. Such dimensional reduced data are commonly known as features stocks distinctive attributes about the original-datasets. The extraction of appropriate features is significant owing to the possible inability to utilize the received original datasets. The advantages of features extraction they not only enable the classifier to recognize more and higher-order modulation signals, but they further help in simplifying the arithmetical operation of the classifier. The signal processing method based on HOCs has the ability to suppress AWGN in the communication signal. Additionally, it can perform signal recognition at a low SNR with good performance, and is extremely effective at signal analysis. The HOC is extracted from the modulated signal that carries information as raw data to the receiver site. Subsequently, it is applied as an input feature to the proposed classifier. It is well-known that HOCs are comprised of functions of the signals’ auto-moments, and that they are subjected to an imitation of the stationary random process for a random variable y. Moreover, the α order moment was defined by Valipour et al. 2012 [23]. We assume a zero-mean discrete baseband signal sequence format as follows: (8)

Here, y∗ is defined as the complex conjugate of baseband signal y.β and α represents the value raised to the base of the conjugated terms and the value raised to the base of the nonconjugated terms of signal y, respectively. α − β is the momentorder and k = 1, 2, 3. . . M. To express on the cumulants-order to any a random variable having a zero-mean value. Here case, assume that y represents a random variable has zero-mean, the first ϕ (s) and second ψ (s) characteristic function can be expressed as follows [12]:

ϕ (s) =

∫

−∞

f (y)esy dy ∞

The nth-cumulant of y is defined as the nth derivative of Eq. (9), and is evaluated at s = 0:

λn =

dψ (s)n

(11)

dsn

The paradigmatic for the α-order of the cumulant is defined as:

⎡

4.2. Pattern identification and feature extraction

yk = {ak + jbk } Mαβ = E yα−β .(y∗ )β

(10)

(9)

⎤

Cαβ = cum ⎣ y, . . . ., y , y∗ , . . . ., y∗ ⎦

⎢

⎥

   

(α − β)term



β term

(12)



The cumulant of the random variable y is expressed as Cx,α.β (y). Even though the non-linear summation of ordered moments can produce the cumulants, the numerical values are complicated and cannot be measured practically [34]. Nevertheless, when the signal length is reduced, the effectivity of cumulants in the separation among signals is deteriorated. Feature normalization is crucial for machine-learning algorithms to work fitly; moreover, the HOCs are rescaled for normalization [25]. Similarly, one recent work confirmed that the properties of the natural logarithm can be used to improve the extracted statistical cumulant features. This provides a high classification rate at a low SNR [9]. 5. Algorithm evaluation and computational details 5.1. Classifier structure The binary decision tree classifiers were developed more than 20 years ago, and they are now commonly used in the pattern recognition process. Although there are many classifiers that use non-parametric techniques (such as non-linear classifiers), the binary decision tree requires a minimal memory size, has a considerably small training time, and does not require a high processing power. It is capable of handling difficult problems where parametric methods fail, even with the multi-class distribution of categories [35]. A combination of multi-tree decisions with tree classifiers provides one possible solution at the output of the classifier; each decision tree uses one feature or a combination of features to arrive at its decision. The sequential operation of the multiple trees of the binary decision tree classifier is depicted in Fig. 4, which shows the proposed classifier in which each binary decision tree works individually.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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A.K. Ali and E. Erçelebi / ISA Transactions xxx (xxxx) xxx Table 1 Theoretical values of M-QAM and M-PSK for logarithmic features (L11 , L22 , L33 , L44 ) and (L40 , L51 ). Parameters

B-PSK

Q-PSK

8-PSK

8-QAM

16-QAM

32-QAM

64-QAM

128-QAM

256-QAM

L11 L22 L33 L44 L40 L51

0.00 0.30 1.20 2.39 0.30 0.30

0.00 0.00 0.60 1.26 0.00 −2.55

0.00 0.00 0.60 1.23 −2.31 −1.67

0.67 1.17 2.32 3.95 1.41 −1.03

1.00 1.85 3.34 5.23 1.84 0.38

1.30 2.45 4.24 6.43 1.90 1.09

1.62 3.03 5.12 7.88 3.04 1.23

1.91 3.65 6.04 8.95 3.07 2.20

2.23 4.24 6.92 10.34 4.24 2.68

5.2. Implementation of the classification algorithm The signals considered in this work are {2, 4, and 8}-PSK and {8, 16, 32, 64,128, and 256}-QAM types with a signal length of N = 10,000 symbols. All the experiments were simulated in a computer-based environment. Native MATLAB functions were invoked to implement the random raw data and channel effects. The sets of modulation signals comprised random row data that were generated to evaluate the overall performances. Each modulated signal was generated 1000 times for each SNR (−10 to 20 dB) by considering the mean value. The group of HOCs that were improved by natural logarithmic functions was extracted. The extracted features were considered for the training stage, and were used to estimate the threshold values empirically in each node of the tree. After tuning the thresholds in each node, 1000 modulated signals were applied again for each SNR (−5 to 20 dB) to test the classifier. The proposed classification algorithm can be implemented using the following steps. (a) Test the cumulants for the best classification using C11, C22, C33, and C44 to discriminate QAM signals, and C40 and C51 to recognize the inter class of PSK formats. The extracted cumulant is optimized by the natural logarithmic properties. The selected cumulants for our proposed algorithm can be written as follows: C11 = cum y (n)∗ = M11

(

)

C22 = cum y (n) , y (n) C33

(

∗

∗

(

∗

∗

(13) 2

)

= M22 − M20 − 2M11 ) = cum y (n) , y (n) , y (n)∗

2

= M33 − 6M20 M31 − 9M22 M11

(14)

(15)

+ 18 (M20 )2 M11 + 12M11 3 C40 = cum (y (n) , y (n) , y (n) , y (n)) = M40 − 3M20 2 (16) C51 = cum y (n) , y (n) , y (n) , y (n) , y (n)∗

(

)

= M51 − 10M20 M31 − 5M11 M40

(17)

+ 30 (M20 ) M11 2

C44 = cum y (n) , y (n) , y (n)∗ , y (n)∗

(

)

= M44 − M40 2 − 18M22 2 − 16M31 2 −54M20 4 − 144M11 4 − 432M20 2 M11 2 +12M40 M20 2 + 96M31 M20 M11

(18)

+144M22 M11 2 + 72M22 M20 2 + 96M31 M20 M11 Then, according to these equations, six logarithmic features have been proposed. L11 = log10 [|C11 |]

(19)

L22 = log10 [|C22 |]

(20)

L33 = log10 [|C33 |]

(21)

L44 = log10 [|C44 |]

(22)

Table 2 Threshold levels of the M-QAM and M-PSK multi-hierarchical logarithmic classifier based on the features (L11 , L22 , L33 , L44 ) and (L40 , L51 ). M-QAM classifier

L11

L22

L33

L44

Main ηxx

0.7

0.85

1.7

4

Thresholds levels

ηLow

0 1 2 3 4 5

0.9 1.2 1.6 1.8 2.2

M-PSK classifier

L40

Thresholds levels

ηLow

0 1 2

–0.4 0.1

ηHigh 0.9 1.2 1.6 1.8 2.2 4

ηLow

ηHigh

1.5 1.5 2 2 2.8 2.8 3.3 3.3 4 4 7

ηLow 2.8 4 4.8 5.3 6.5

ηHigh 2.8 4 4.8 5.3 6.5 8

ηLow 5.2 6.2 7.7 8.5 15

ηHigh 5.2 6.2 7.7 8.5 9.7 15

L51

ηHigh –0.4 0.1 0.5

ηLow 0.4 1

ηHigh 0.4 1 1.5

L40 = log10 [|C40 |]

(23)

L51 = log10 [|C51 |]

(24)

1. Theoretical values: The theoretical values of the cumulants-based on a logarithmic function of various signal constellations of considered are defined by calculating the mean averages over the ideal noise-free constellation. Table 1 lists the theoretical values of the cumulant-based logarithmic function. The values of {L11 , L22 , L33 } are the same for the 4-PSK and 8-PSK modulated signals. However, table row-wise shows a better separation boundary for all orders of QAM modulation. Figs. 5(a, b, and c) illustrates the distinct values of these features against SNR for various types of PSK and QAM modulation signals. (b) Eqs. (19), (20), (21), (22), (23), and (24) were used to create five logarithmic classifiers and five threshold levels for M-QAM. Similarly, three thresholds were created for MSPK. The proposed threshold values are empirically computed based on the results in Figs. 5(a, b, and c), and are listed in Table 2. (c) By comparing the threshold levels with the features depicted in the flowchart tree in Fig. 6, the decision tree proceeds according to the following steps: 1. The main parameters are calculated (L11 , L22 , L33 , L44 , L40 , and L51 ). 2. The comparisons are made sequentially by using (L11 , L22 , L33 , L44 ) for the M-QAM logarithmic classifier and (L40 , L51 ) for the M-PSK logarithmic classifier. If any classifier Lxx weakly identifies the signal in both cases of SNR — greater than or less than 0 dB, the other classifiers boost the accuracy before

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 5a. Distinct values of L22 , L33 against SNR, utilized to recognize {8, 16, 32, 64, 128, and 256}-QAM modulation signals.

Fig. 5b. Distinct values of L11 , L44 against SNR, utilized to recognize {8, 16, 32, 64, 128, and 256}-QAM modulation signals.

Fig. 5c. Distinct values of L40 , L51 against SNR, utilized to recognize {2, 4, and 8} PSK modulation signals.

deciding the correct modulation that these compar-

Finally, we plot the results demonstrating the relationship be-

isons show in Fig. 6. Based on the proposed criteria,

tween SNR and capability of the correct identification rate with

a high-precision classifier can be created.

respect to the constellation shapes.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 6. Hierarchy of the threshold levels of the logarithmic classifier. ‘‘non’’ refer to undefined signal.

6. Evaluation of classifier performance

6.1. Results and discussion

In this section, we manifest the results of the simulation executed. The performance of the proposed strategy for AMC is tested under an AWGN-channel, and is compared with that of the current algorithms in the literature. The simulation involves the generation of 1000 different realizations of (2, 4, and 8)-PSK and (8, 16, 32, 64,128, and 256)-QAM signals to estimate six selected features. Each signal is comprised of 10,000 symbols. To perform the testing, the range of signal-to-noise power ratio was selected to be −5 to 20 dB. All simulations were performed using a PC.

Remarkable results were obtained when the proposed classification algorithm was tested under low values of SNR, and they are shown in Figs. 7 and 8 and Tables 3–7. Most of the classifier methods in the literature exhibit poor accuracy in identifying the modulation schemes when the SNR is less than 0, and it is often difficult to implement them owing to their complex structures. However, our approach has six classifiers that work sequentially. To discriminate between M-PSK and M-QAM, the main four logarithmic cumulants classifiers have been utilized, and subsequently, they are used to discriminate between the internal classes of the QAM formats (8, 16, 32, 64, 128, 256)-QAM.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Table 3 Classification performance in terms of confusion matrix for each modulation type with a signal sample length of 10,000 for SNR > 5 dB. Actual modulation

Predicted classifier B-PSK

Q-PSK

8-PSK

8-QAM

16-QAM

32-QAM

64-QAM

128-QAM

256-QAM

B-PSK Q-PSK 8-PSK 8-QAM 16-QAM 32-QAM 64-QAM 128-QAM 256-QAM

100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 100.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 100.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 100.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0

Percentage performance

100.0%

Table 4 Classification performance in terms of confusion matrix for each modulation type with a signal sample length of 10,000 for SNR of 1 dB. Actual modulation

Predicted classifier B-PSK

Q-PSK

8-PSK

8-QAM

16-QAM

32-QAM

64-QAM

128-QAM

256-QAM

B-PSK Q-PSK 8-PSK 8-QAM 16-QAM 32-QAM 64-QAM 128-QAM 256-QAM

100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 100.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 100.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 100.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0

Percentage performance

Similarly, the other two sub-classifiers are used to classify (2, 4, 8)-PSK. The results are focused on SNR values that are less than 0 dB. Tables 3–6 list the rates of recognition as a confusion matrix for both the QAM and PSK modulations with various SNRs. The best rate of identification was 100% of the highest value for SNR values equal to −1 dB and > 5 dB as presented in Tables 3 and 4, respectively. With respect to the same modulation formats and data length, in case of SNR values equal to −1 dB, the accuracy of classification was 99%, as listed in Table 5. Table 6 illustrations decrease in the accuracy to 88% when the SNR value is equal to −3 dB. similarly, the average value of the correct classification rate (% vs. SNR) for all modulation formats at a signal data length of 10,000 symbols approached 100% at an SNR of +1 dB, as can be observed in Fig. 7(a and b). In Fig. 7b, the correct recognition rate of all the signals of interest was greater than 99% when the SNR value was greater than 0 dB. Table 7 presents the comparison of the classification rate in other similar investigations with various signal sample lengths (500, 1000, 1024) at an SNR of 3 dB. Similarly, Figs. 8(a, b, and c) illustrate the classification accuracy percentages for different values of SNR. The signal sample lengths are 256, 512, 1024, 2048, and 4096, and the SNR values range from −3 to 20 dB. Under similar conditions, the classification method demonstrates good stability even with data lengths of 1024 and 512. It can be observed that the recognition rate reaches almost 100% for SNR values exceeding 3 dB. Additionally, the recognition rate of QAM is found to be the best. 6.2. Performance of different classifiers The recognition of 64 QAM and 8-PSK was slightly inferior at low SNR, but it improved when the SNR was slightly increased. Generally, most of the literature focuses on high SNR ranges, and few of them have discussed SNR values less than 0 dB. In our work, two major aspects were investigated: SNR values less than 0 and the creation of a logarithmic threshold level

100.0%

to accurately distinguish between modulation types to increase the classifier prediction ratio. Six logarithmic features were proposed, i.e., (L11, L22 , L33, L44 ) and (L40, L51 ) based on the number of associated statistical cumulant orders. The logarithmic-based algorithm exhibits good performance with respect to distinguishing between internal classes of both signal formats, namely QAM and PSK. This is achieved by the sequentially working strategy, wherein if any classifier fails to identify the modulation type, the other remaining classifiers intercept the signal according to the threshold limits. In this sequence, the overall classification accuracy rate is recovered. Eventually, this unique method improves the system and achieves high efficiency in comparison with the published works in [5,24,38], and [40]. Fig. 9 depicts the comparison of the logarithmic classifier with the traditional sixthorder cumulant-based classifier. The logarithmic classifier has an extremely good average classification rate, even at low values of SNR. This enhancement is a result of the efficiency of the natural logarithmic function, which directly optimizes the distribution curve of the features. 6.3. Complexity details The commonly used engineered classifying method for 16QAM and 64-QAM signals involves using many cumulant-order values of the fourth-order (C40, C41 , C42, ) or values of the sixthorder (C60, C61 , C62, C63 ) for SNR values ranging from +5 to 20 dB, as explained by Zhu et al. 2014 [5]. Alam et al. 2010 [38] used the same cumulant-order design, but achieved a better classification rate than Zhu et al. 2014 [5]. This was achieved by efficiently classifying the (16,64)-QAM and (2,4)-PSK signals, with the same SNR of +5 dB, also in [24]. Therefore, these classifiers are considered to be complex in comparison with our proposed classification algorithm. However, according to [40], traditional cumulant-orders are replaced by (C11 , C22 , C33 , C44 ) to enable the classifier to identify QAM (16 and 256) at a low SNR (−4 to 20 dB). While this would make it an efficient classifier, this is not the case

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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A.K. Ali and E. Erçelebi / ISA Transactions xxx (xxxx) xxx Table 5 Classification performance in terms of confusion matrix for each modulation type with a signal sample length of 10,000 for SNR of −1 dB. Actual modulation

Predicted classifier B-PSK

Q-PSK

8-PSK

8-QAM

16-QAM

32-QAM

64-QAM

128-QAM

256-QAM

B-PSK Q-PSK 8-PSK 8-QAM 16-QAM 32-QAM 64-QAM 128-QAM 256-QAM

100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 100.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.1 99.9 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.2 99.8 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 4.2 95.8 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 3.3 96.7 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 100.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.7 98.3

Percentage performance

98.9%

Table 6 Classification performance in terms of confusion matrix for each modulation type with a signal sample length of 10,000 for SNR of –3 dB. Actual modulation

Predicted classifier

B-PSK Q-PSK 8-PSK 8-QAM 16-QAM 32-QAM 64-QAM 128-QAM 256-QAM

B-PSK

Q-PSK

8-PSK

8-QAM

16-QAM

32-QAM

64-QAM

128-QAM

256-QAM

96.9 3.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 92.9 7.1 0.0 0.0 0.0 0.0 0.0 0.0

0.0 13.5 86.5 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 100.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 12.0 88.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.9 23.7 75.4 0.0 0.0 0.0

0.0 0.0 0.0 0.1 2.9 21.0 76.0 0.0 0.0

0.0 0.0 0.0 0.0 0.3 1.6 5.3 92.8 0.0

0.0 0.0 0.0 0.0 0.0 0.1 0.6 20.0 79.3

Percentage performance

87.6%

Table 7 Classification performance (average percentage) for different signal sample lengths for each modulation scheme at SNR ≥ 5 dB. References

Signal sample data length

Classification rate (%) B-PSK

Q-PSK

8-PSK

16-QAM

32-QAM

64-QAM

[36] [37] [38] [39]

500 1000 1024 2048

100 100 1 #

100 100 <97 100

100 9.6 # 100

65 0 <82 87

0 0 # 70

10 0 <20 85

Proposed classifier

500 1000 1024 2048

99.9 100 100 100

100 100 100 100

100 100 100 100

99.9 100 100 100

99 100 100 100

99 100 100 100

‘‘#’’ not included in the reference.

with certain types of modulations (only QAM) and weak signals (SNR less than 0 dB). It is obvious that it is extremely difficult to make a fair comparison of the presented algorithm and previous works in the field of AMC owing to some random parameters. Therefore, to guarantee a fair comparison, the simulation scenario is performed by applying the same parameters, particularly the channel type and length of signal. The results are presented in Table 8. It is clear that the implementation logarithmic classifier requires a logarithm operation in comparison with conventional cumulant-based classifiers. However, the complexity of the proposed classifier is significantly reduced because the number of cumulants used for the classification is less than the sixth-order. Meanwhile, the complexity of the proposed classifier can be summarized based only on the implementation of the logarithmic functions, which is mainly used while the algorithm is running. The complexities of several existing approaches reported in the literature are presented in Table 8. Moreover, this table summarizes the degree of variations of our classifier system, as well as those of the others. Additionally, in Table 8, it can be seen

that the proposed method has a more reliable classification accuracy in comparison with the existing algorithm [6], even under extremely difficult conditions (SNR = −2 dB in AWGN channel). 6.4. Details of mathematical operations required for different classifiers The number of mathematical operations of the modulation classifier is an important part of the real-time implementation. In some applications, the priority for modulation schemes that can be classified against the complexity of mathematical operations and hardware design. However, for applications that require fast classification and less computational time, but have some determinants in the platform specifications, classifiers that require a few mathematical operations are preferred. Therefore, the number of mathematical operations required for cumulantbased classifiers is presented in Table 9. This table compares the proposed classifier and other conventional cumulant-based

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 7. Correct recognition ratio of signals vs. SNR. Each has a data length of 10,000 symbols. (a) Overall classification rate of signals for all modulation formats. (b) Recognition accuracy rate for all signals.

Table 8 Comparison of the proposed classifier with other systems in the literature at a signal length of 4096 symbols. lm represents the total magnitude of the cumulant’s order (number of elements in the feature vector). References

Classifier structure Features

[5]

[38]

C40 , C41 , C42 , C60, C61 , C62, C63, C40 , C41 , C42 , C60, C61 , C62, C63,

Modulation type

System performance

lm

Complexity cumulant order

M-QAM

M-PSK

SNR (dB)

Accuracy (%)

7

{(3)4th, (4)6th} -High

16,64

4

–3 0

# # 78.4%–100%

{(3)4th, (4)6th}-High

16,64

7

C20 , C21 , C40 , C41, [6]

C42 , C60, C61, C62,

14

{(2)2th, (3)4th, (4)6th, (5)8th}-High

≥ +5

16,64,256

2,4

4

{(1)1th, (1)2th, (1)3th, (1)4th}-Medium

16–256

{(2)2th, (3)4th, (4)6th}-High

16,64,256

No

C42 , C60, C61, C62,

9

2–8

L11 , L22 , L33 , L44

, L40 , L51

0

# 98.6%

–3 0 –3 0

≥ +5

C63 Proposed

#

≥ +5

C20 , C21 , C40 , C41, [24]

–3

≥ +5

C83 , C84 C11 , C22 , C33 , C44,

≥ +5

# # 89.8%–100%

2,4,8 and others

C63 , C80 , C81, C82, [40]

–3 0

6

{(1)1th, (1)2th, (1)3th, (2)4th, (1)5th}-Medium

8–256

2–8

–3 0

≥ +5

Simulation tool

MATLAB functions are used to implement and evaluate performance

98.33% 100% 100% # 77.6% 99.96% 88% 100% 100%

Abbreviations: ‘‘–’’ refer from M-Signal to M-Signal, ‘‘,’’ M-Signal and M-Signal.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 8(a). Recognition accuracy rate vs. SNR for different modulation formats {B-PSK, Q-PSK, 8-PSK} under different signal length scenarios.

classifiers in the literature. Furthermore, the mathematical operations required for the complete classification of the MN class of modulation has been studied as a measure of the total number of mathematical operations. The proposed classifier requires 82 MN operations to compute the logarithmic cumulants of the modulated signal, whereas the number of mathematical operations of the conventional cumulant-based classifiers ranges from 60 MN to 178 MN . For example, in the sixth-order cumulants, the number of basic operations required was 51 MN , which involves addition, subtraction, and multiplication, whereas the number of eight-order cumulants was 145 MN . In the same context, the

logarithmic cumulants require 54 MN cumulants, which is still not very complex. Finally, based on the above discussion, it can be concluded that the logarithmic classification algorithm is not the best one. Nevertheless, it simplifies the classification paradigm of high-order QAM schemes [9]. However, the drawback of the classifier established on logarithmic thresholds levels that it is a channel-based model. In other words, any changes in the type of noise (colored vs. AWGN), number of transmitted samples, or type of possible modulation schemes. That will be demanded a modification an overhaul of all four of the tree thresholds levels.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 8(b). Recognition accuracy rate vs. SNR for different modulation formats {8-QAM, 16-QAM, 32-QAM} under different signal length scenarios.

6.5. Evaluation of the speed of logarithmic classifier in signal recognition In this section, the recognition speed for interesting modulated signals using the proposed algorithm is evaluated. For the test, the algorithm is implemented on two computer platforms. The first simulation platform contains an Intel Core 2.3 GHz i5-4200U CPU and 12 GB RAM. With the second simulation platform, we used a PC with an Intel Core 2.8 GHz i7-7700HQ CPU and 16 GB RAM. Both computers ran under 64-bit Windows 10 operating system. Similarly, on a real-time platform, it is simple to obtain a DSP kit

with comparable execution, such as the Arria10 SoC Development Kit or the TMDSEVM6670LE. In practical applications, the speed of the algorithm when recognizing a signal is crucial to the complexity of the algorithm. Therefore, in this study, to measure the computational complexity of the proposed algorithm, the signal length was set at 10,000 symbols and the SNR was varied from −3 dB to 30 dB; 100 records from each modulation scheme were generated. Then, the average value was calculated to obtain better accuracy in the calculations. The results are depicted in Figs. 10 and 11, and it is apparent from Fig. 10 that the platform with the i7-7700HQ CPU achieves a higher performance speed

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 8(c). Recognition accuracy rate vs. SNR for different modulation formats {64-QAM, 128-QAM, 256-QAM} under different signal length scenarios.

in terms of the modulation signal recognition. If we exclude this superior speed in the recognition of (2, 4, and 8)-PSK modulation schemes, then the speed of the signal recognition of the proposed system has an advantage in terms of the recognition of M-QAM schemes, more precisely for the 64-, 128-, and 256-QAM schemes, as depicted in Fig. 10. This result indicates that the speed of the signal recognition is directly related to the specifications of the simulation platform, which can also observed in the second experiment with another simulation platform. In the second test, the simulation platform was comprised of a 2.3 GHz i5-4200U CPU and 12 GB of RAM. In this test, similar

signal settings were used, and the results are depicted in Fig. 11. As anticipated, the recognition speed clearly decreased. However, the performance was nearly equal in both scenarios. Therefore, according to these test scenarios, the speed of the signal recognition is directly related to the specifications of the execution platform. Furthermore, the time required to recognize a modulation scheme is subjected to the same imitations. However, the computing duration to each signal in second can be summarized in Figs. 12 and 13. As can be obviously seen the variance in performance between two platforms, the reason for this variation is due to the speed of components in each system.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 9. Comparison between the proposed logarithmic classifier and sixth-order cumulant-based classifier for overall signal classification with a signal length of 10,000 symbols.

Fig. 10. Speed of the modulation signal recognition of the proposed classifier for the simulation platform with an Intel Core 2.8 GHz i7-7700HQ CPU. Table 9 Mathematical operations required for different cumulant-based classifiers. The total number of candidate signals for classification is MN with a total of N number of samples. Cumulant based classifiers

C40 , C41 , C42 , C60, C61 , C62, C63,

Operations

Functions

Total mathematical operations

Subtractions

Additions

Multiplications

Logarithmic log10 x

Absolute|x|

x raised to n (x)n

13[MN ]

6[MN ]

32[MN ]

0

1[MN ]

8[MN ]

60[MN ]

30[MN ]

25[MN ]

90[MN ]

0

3[MN ]

30[MN ]

178[MN ]

12[MN ]

8[MN ]

28[MN ]

0

4[MN ]

14[MN ]

66[MN ]

13[MN ]

6[MN ]

32[MN ]

0

2[MN ]

8[MN ]

61[MN ]

12[MN ]

8[MN ]

34[MN ]

6[MN ]

6[MN ]

16[MN ]

82[MN ]

C20 , C21 , C40 , C41, C42 , C60, C61, C62, C63 , C80 , C81, C82, C83 , C84 C11 , C22 , C33 , C44, C20 , C21 , C40 , C41, C42 , C60, C61, C62, C63 L11 , L22 , L33 , L44 L40 , L51

Accordingly, it can be concluded that the type of CPU platform significantly influences the speed and duration of the execution of the algorithm.

with a fixed phase error are to be considered, the frequency and

7. Performance of logarithmic classifier with frequency and phase offset

with data lengths of 512 and 1024 symbols, and SNR values of

In this section, the performance of the logarithmic classifier is evaluated. In cases where the frequency offset and phase offset

phase offset are considered individually. We set two scenarios

−3, −1, +1, and > +5 dB; the signal realizations of 1000 samples were tested for each modulation format.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 11. Speed of the modulation signal recognition of the proposed classifier for the simulation platform with an Intel Core 2.3 GHz i5-4200U CPU.

Fig. 12. Duration of time required to recognize the modulation signal of the proposed classifier for the simulation platform with an Intel Core 2.8 GHz i7-7700HQ CPU.

Fig. 13. Duration of time required to recognize the modulation signal of the proposed classifier for the simulation platform with an Intel Core 2.3 GHz i5-4200U CPU.

7.1. Frequency offset In this subsection, we examine the effect of variations in the frequency offset, which causes rotations of the constellation diagram; this directly influences the distribution of symbol points. In scenario of the frequency offset, the normalized frequency offset was varied from 0 to 1 × 10−3 (congruent to a maximum rotation of 90◦ ) along with a fixed-phase offset and phase jitter. Fig. 14 depicts the variation of the average classification rate with the frequency offset. With a frequency offset ranging from 2 × 10−4 to 4 × 10−4 , the classification accuracy for a data length of 512 symbols decreased significantly, as depicted in Fig. 14a. It

can be observed that an acceptable performance is obtained at a frequency offset below 2 × 10−4 . Similarly, in Fig. 14b, when the degree of the frequency offset is increased to 2 × 10−4 , the classification performance decreases almost linearly to 80%. Nevertheless, it starts with a lower classification accuracy of 99.8% at a frequency offset of 1 × 10−4 , and reduces to 80% at a frequency offset of 2 × 10−4 . One of the reasons for this reduction in the classification rate is the modulation type being used, exclusively Q-PSK, 8-PSK and 64-QAM, 256-QAM. There is little space for any frequency offset. The other aspect pertains to the nature of the logarithmic classifier, which is based on the permanent threshold biases at each node. However, a larger amount of data would achieve linear performance, as can be seen in Fig. 14b. Although

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 14. Classification rate vs. frequency offset for each considered modulation scheme with signal lengths of a. 512 symbols and b. 1024 symbols.

the frequency offset scenario is being promising, some practical blind frequency offset appraisal and compensation paradigms for QAM — formats were found to be scalable (e.g., in [41]), which could help in achieving the required level of frequency offset. 7.2. Phase offset The influence of the phase offset is tested in a pure AWGN channel. We utilized a range of 0–10◦ , which is also considered in some investigations, such as classifiers based on extended maximum likelihood (ML) in [42] and deep learning architecture [43]. The results are depicted in Fig. 15. With no frequency offset and phase error, the classification accuracy rate is theoretically insensitive to variations in the phase offset, which is constant over a realization, but changes randomly depending on the data length (512–1024 symbols) and the SNR values ranging from −3 dB to SNR > 5 dB. The variations were measured to be approximately 2% with respect to the assumed phase offset (in degrees, with values varying from 0 to 10). It is observed that there is no degradation, assuming a phase variance at SNR values of −3 dB or SNR values > 5 dB; similarly, the classification performance increases at SNR > 5 dB. 8. Performance of logarithmic classifier with various channels We focused on three types of channel models. The first channel type is a pure AWGN channel, which has always been the primary method employed in the literature to evaluate the performance of an AMC system. We considered the average classification accuracy of our proposed classifier with SNR values ranging from −3 dB to 20 dB. We set the signal data length

Table 10 Multipath-channel fading parameters. Parameter

Values

Sampling time: Ts Path gains Path delay (s)

2 × 10−7 [0, –2, –10] dB [0, 1.8, 3.4] Ts

Channel type

Rayleigh Ricean

Maximum doppler shift

4 Hz

K-factor: 0 K-factor: 3

to 4096 symbols. Following this, a total of 1000 samples were used to evaluate each modulation format. The performance curve of the AWGN channel is depicted in Fig. 16. It can be observed from the figure that the performance curve of the pure AWGN at an SNR of −3 dB has an advantage of approximately 75% in comparison with the curves of the other channels. It also shows that the logarithmic classifier exhibits a better performance in the AWGN channel, and the classification accuracy reaches 100% at SNR > 2 dB. In the second scenario (channel type), to evaluate the robustness against flat-Rayleigh and Rician fading, the focus was on the influence of multipath channels. In this case, similar settings were used as in the previous scenario. The detailed configuration of the multipath channels is summarized in Table 10. The results are depicted in Fig. 16. As anticipated, the performance dropped to approximately 55%. One of the main reasons for this performance degradation is that the threshold bias at each node was estimated for an AWGN channel. However, the logarithmic classifier does not fail to classify the modulation signals, and it exhibits an almost equal performance in the multipath channels.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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Fig. 15. Classification rate vs. phase offset for each considered modulation scheme consisting of signal lengths of a. 512 symbols and b. 1024 symbols.

Fig. 16. Performance of logarithmic classifier technique under different channels.

Finally, we focused on the performance degradation of our proposed classifier without any prior knowledge of the nature of the channel. In this scenario, similar parameters were used as before. The performance curve of the unknown transmission labeled as ‘‘unknown’’ is depicted in Fig. 16. It can be noticed from the figure that the performance curve under the unknown transmission environment has an advantage of approximately

20% in comparison with the curves for the multipath channels. The performance becomes almost equal to 63% at SNR > −2 dB. Nevertheless, this degradation in performance is acceptable for the logarithmic classifier because the structure of the classifier is based on the linearity in the separation between classes. However, the proposed classifier has a fixed threshold bias at each node.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

A.K. Ali and E. Erçelebi / ISA Transactions xxx (xxxx) xxx

9. Conclusion This study proposed a new generation of high-order cumulants, and presented a highly efficient algorithm to overcome the drawbacks of conventional AMC-algorithms, which are based on statistical features and pattern recognition criteria. The proposed method combines higher-order cumulants with threshold classifiers, and improves the cumulant features using the properties of a natural logarithmic function. The improved signal parameters are called logarithmic features (L11 , L22 , L33 , L44 ) and (L40 , L51 ), which make the classifier efficient with respect to decision-making. A high-accuracy classifier system was handled for the AMC of the M-PSK and M-QAM modulation schemes, even at low levels of noise ratios and channel fluctuation. The study used 1000 signals and SNR values ranging from −5 dB to high values 30 dB Optimum threshold levels were derived from the extracted signal features, and they were then applied to the proposed classifier. This resulted in identification rates of 88%, 99%, and 100% for identifying PSK (2, 4, and 8) and QAM (8, 16, 32, 64, 128, and 256) signals, with different numbers of data lengths (256, 512, 1024, 2048, 4096 symbols) under SNR values ranging from −3 to 20 dB. The results obtained for the identification of the same types of PSK and QAM ranged from 86.6% to 100%. The proposed classifier module was found to be advantageous in terms of accuracy and computational complexity in comparison with the other methods utilized in the literature. More importantly, the high efficiency of the proposed recognizer module was achieved with the selection of only six unique features. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] Ramkumar B. Automatic modulation classification for cognitive radios using cyclic feature detection. IEEE Circuits Syst Mag 2009;9:27–45. http: //dx.doi.org/10.1109/MCAS.2008.931739. [2] Yin C, Li B, Li Y, Lan B. Modulation classification of MQAM signals based on density spectrum of the constellations. In: Proc 2010 2nd int conf futur comput commun ICFCC 2010, Vol. 3. 2010, p. 57–61. http://dx.doi.org/10. 1109/ICFCC.2010.5497682. [3] Sherme AE. A novel method for automatic modulation recognition. Appl Soft Comput J 2012;12:453–61. http://dx.doi.org/10.1016/j.asoc.2011.08. 025. [4] Shermeh AE, Ghazalian R. Recognition of communication signal types using genetic algorithm and support vector machines based on the higher order statistics. Digit Signal Process A Rev J 2010;20:1748–57. http://dx.doi.org/ 10.1016/j.dsp.2010.03.003. [5] Zhu Z, Waqar Aslam M, Nandi AK. Genetic algorithm optimized distribution sampling test for M-QAM modulation classification. Signal Process 2014;94:264–77. http://dx.doi.org/10.1016/j.sigpro.2013.05.024. [6] Dobre OA, Bar-Ness Y, Su Wei. Higher-order cyclic cumulants for high order modulation classification. In: IEEE mil commun conf 2003 MILCOM 2003, Vol. 1. 2003, p. 112–7. http://dx.doi.org/10.1109/MILCOM.2003. 1290087. [7] Ghofrani F, Keshavarz-Haddad A, Jamshidi A. Internet traffic classification using multiple classifiers. In: 2015 7th conf inf knowl technol IKT 2015. 2015, http://dx.doi.org/10.1109/IKT.2015.7288772. [8] Dobre OA, Öner M, Rajan S, Inkol R. Cyclostationarity-based robust algorithms for QAM signal identification. IEEE Commun Lett 2012;16:12–5. http://dx.doi.org/10.1109/LCOMM.2011.112311.112006. [9] Ali A, Ergun E. An M-QAM signal modulation recognition algorithm in AWGN-channel. Sci Program 2019;17. http://dx.doi.org/10.1155/2019/ 6752694. [10] Hameed F, Dobre OA, Popescu DC. On the likelihood-based approach to modulation classification. IEEE Trans Wirel Commun 2009;8:5884–92. http://dx.doi.org/10.1109/TWC.2009.12.080883.

19

[11] Dobre OA, Abdi A, Bar-Ness Y, Su W. Survey of automatic modulation classification techniques: classical approaches and new trends. IET Commun 2007;1:137–56. http://dx.doi.org/10.1049/iet-com:20050176. [12] Wang F, Wang X. Fast and robust modulation classification via Kolmogorov–Smirnov test. IEEE Trans Commun 2010;58:2324–32. http: //dx.doi.org/10.1109/TCOMM.2010.08.090481. [13] Assaleh K, Farrell K, Mammone RJ. A new method of modulation classification for digitally modulated signals. In: Mil. commun. conf. 1992. MILCOM’92, conf. rec. commun. command. control intell.. IEEE; 1992, p. 712–6. [14] Yuan Yabo, Zhao Peng, BoWang B. Hybrid maximum likelihood modulation classification for continuous phase modulations. IEEE Commun Lett 2016;20:450–3. http://dx.doi.org/10.1109/LCOMM.2016.2517007. [15] Fangjuan X, Chisheng L, Guojin W. An efficient and simple method of MPSK modulation classification. In: 2008 int. conf. wirel. commun. netw. mob. comput. WiCOM 2008. 2008, p. 1–3. http://dx.doi.org/10.1109/WiCom. 2008.339. [16] Su W. Feature space analysis of modulation classification using very highorder statistics. IEEE Commun Lett 2013;17:1688–91. http://dx.doi.org/10. 1109/LCOMM.2013.080613.130070. [17] Jajoo G, Kumar Y, Yadav SK, Adhikari B, Kumar A. Blind signal modulation recognition through clustering analysis of constellation signature. Expert Syst Appl 2017;90:13–22. http://dx.doi.org/10.1016/j.eswa.2017.07.053. [18] Chou Z, Jiang W, Xiang C, Li M. Modulation recognition based on constellation diagram for M-QAM signals. In: Proc. 2013 IEEE 11th int. conf. electron. meas. instruments, ICEMI 2013, Vol. 1. 2013, p. 70–4. http: //dx.doi.org/10.1109/ICEMI.2013.6743041. [19] Ghauri SA, Qureshi IM, Malik AN, TAC. Automatic recognition algorithm for linearly modulated signals under non-coherent asynchronous condition. J Korea Inst Inf Commun Eng 2014;18:2409–16. [20] Shermeh AE, Azimi H. Blind signal-type classification using a novel robust feature subset selection method and neural network classifier. Ann Telecommun - Ann Télécommun 2010;65:625–33. http://dx.doi.org/ 10.1007/s12243-010-0180-4. [21] Popoola JJ, Olst RV. Automatic classification of combined analog and digital modulation schemes using feedforward neural network. IEEE Afr 2011;13–5. http://dx.doi.org/10.1109/AFRCON.2011.6072008. [22] Khan FN, Teow CH, Kiu SG, Tan MC, Zhou Y, Al-Arashi WH, et al. Automatic modulation format/bit-rate classification and signal-to-noise ratio estimation using asynchronous delay-tap sampling. Comput Electr Eng 2015;47:126–33. http://dx.doi.org/10.1016/j.compeleceng.2015.09.005. [23] Valipour MH, Homayounpour MM, Mehralian MA. Automatic digital modulation recognition in presence of noise using SVM and PSO. In: 2012 6th int symp telecommun IST 2012. 2012, p. 378–82. http://dx.doi.org/10.1109/ ISTEL.2012.6483016. [24] Abdelmutalab A, Assaleh K, El-Tarhuni M. Automatic modulation classification based on high order cumulants and hierarchical polynomial classifiers. Phys Commun 2016;21:10–8. http://dx.doi.org/10.1016/j.phycom.2016.08. 001. [25] Swami A, Sadler BM. Hierarchical digital modulation classification using cumulants. IEEE Trans Commun 2000;48:416–29. http://dx.doi.org/10. 1109/26.837045. [26] Mirarab MR, Sobhani MA. Robust modulation classification for PSK / QAM / ASK using higher-order cumulants. In: 6th int. conf. information, commun. signal process.. 2007, http://dx.doi.org/10.1109/ICICS.2007.4449591. [27] Hsieh WW, Sci O. Neural networks and learning machines. 3rd ed.. Ontario, Canada: Pearson Prentice Hall; 1999. [28] Moazzeni T, Jiang Y, Chen TD. Data-classification-based SNR estimation for linearly modulated signals. Comput Electr Eng 2016;56:85–95. http: //dx.doi.org/10.1016/j.compeleceng.2016.09.017. [29] Ahmadi N, Berangi R. Modulation classification of QAM and PSK from their constellation using genetic algorithm and hierarchical clustering. In: 2008 3rd int conf inf commun technol from theory to appl ICTTA. 2008, http://dx.doi.org/10.1109/ICTTA.2008.4530242. [30] Forouzan Behrouz A. Data communication and networking. 4th ed.. Mc Graw Hill; 2007. [31] Azzouz EE, Nandi AK. Modulation, automatic of, recognition signals, communication. Kluwer Academic Publishers; 1995. [32] Lau K, Salibian-barrera M, Lampe L. International journal of electronics and communications (AEÜ) modulation recognition in the 868 MHz band using classification trees and random forests. AEUE - Int J Electron Commun 2016;1–8. http://dx.doi.org/10.1016/j.aeue.2016.07.001. [33] Zhou Q, Lu H, Jia L, Mao K. Automatic modulation classification with genetic backpropagation neural network. In: 2016 IEEE congr evol comput CEC 2016. 2016, p. 4626–33. http://dx.doi.org/10.1109/CEC.2016.7744380. [34] Wong MLD, Nandi AK. Automatic digital modulation recognition using artificial neural network and genetic algorithm. Signal Process 2004;84:351–65. http://dx.doi.org/10.1016/j.sigpro.2003.10.019. [35] Breiman L. Classification and regression trees. 1st ed.. New York: Routledge; 2017, http://dx.doi.org/10.1201/9781315139470.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.

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A.K. Ali and E. Erçelebi / ISA Transactions xxx (xxxx) xxx

[36] Li C, Xiao J, Xu Q. A novel modulation classification for PSK and QAM signals in wireless communication. In: ICCTA2011. 2011, p. 4. [37] Weber C, Peter M, Felhauer T, Peter M, Weber C, Peter M, et al. Automatic modulation classification technique for radio monitoring. Electron Lett 2015;51:794–6. http://dx.doi.org/10.1049/el.2015.0610. [38] Aslam MW, Zhu Z, Nandi AK. Automatic digital modulation classification using genetic programming with k-nearest neighbor. In: MILCOM 2010 mil. commun. conf. san jose. IEEE; 2010, http://dx.doi.org/10.1109/MILCOM. 2010.5680232, 1731–1736. [39] Tsakmalis A, Chatzinotas S, Ottersten B. Automatic modulation classification for adaptive power control in cognitive satellite communications. In: 2014 7th adv satell multimed syst conf 13th signal process sp commun work ASMS/SPSC 2014 2014. 2014, p. 234–40. http://dx.doi.org/10.1109/ ASMS-SPSC.2014.6934549.

[40] Hashim IA, Sadah JW, Saeed TR, Ali JK. Recognition of QAM signals with low SNR using a combined threshold algorithm. IETE J Res 2015;61:65–71. http://dx.doi.org/10.1080/03772063.2014.985263. [41] Serpedin E, Chevreuil A, Giannakis GB, Loubaton P. Blind channel and carrier frequency offset estimation using periodic modulation precoders. IEEE Trans Signal Process 2000;48:2389–405. http://dx.doi.org/10.1109/78. 852019. [42] Huang S, Yao Y, Wei Z, Feng Z, Zhang P. Automatic modulation classification of overlapped sources using multiple cumulants. IEEE Trans Veh Technol 2017;66:6089–101. http://dx.doi.org/10.1109/TVT.2016.2636324. [43] Ali A, Yangyu F, Liu S. Automatic modulation classification of digital modulation signals with stacked autoencoders. Digit Signal Process A Rev J 2017;71:108–16. http://dx.doi.org/10.1016/j.dsp.2017.09.005.

Please cite this article as: A.K. Ali and E. Erçelebi, Algorithm for automatic recognition of PSK and QAM with unique classifier based on features and threshold levels. ISA Transactions (2020), https://doi.org/10.1016/j.isatra.2020.03.002.