Optimized Polynomial Classifier for Classification of M-PSK Signals

Optimized Polynomial Classifier for Classification of M-PSK Signals

Nooh Bany Muhammad Mubashar Sarfraz Sajjad A. GhauriSaqib Masood 

Department of Computer Science & Information Systems, American University of Kuwait, Kuwait City 13034, Kuwait

Department of Electrical Engineering, National University of Modern Languages, Islamabad 44000, Pakistan

Department of Electrical Engineering, ISRA University, Islamabad 44000, Pakistan

Corresponding Author Email: 
dr.sajjadghauri@gmail.com
Page: 
575-582
|
DOI: 
https://doi.org/10.18280/mmep.080410
Received: 
29 March 2021
|
Accepted: 
7 May 2021
|
Published: 
31 August 2021
| Citation

OPEN ACCESS

Abstract: 

Automatic modulation classification (AMC) is the emerging research area for military and civil applications. In this paper, M-PSK signals are classified using the optimized polynomial classifier. The distinct features i.e., higher order cumulants (HOC’s) are extracted from the noisy received signal and the dataset is generated with different number of samples, various SNR’s and on several fading channels. The proposed classifier structure classifies the overall modulation classification problem into binary sub-classifications. In each sub-classification, the extracted features are expanded using polynomial expansion into higher dimension space. In higher dimension space numerous non-linearly separable classes becomes linearly separable. The performance of the proposed classifier is evaluated on Rayleigh and Rician fading channels in the presence of additive white gaussian noise (AWGN). The polynomial classifier performance is optimized using one of the famous heuristic computational techniques i.e., Genetic Algorithm (GA). The extensive simulations have been carried with and without optimization, which shows relatively better percentage classification accuracy (PCA) as compared with the state of art existing techniques.

Keywords: 

automatic modulation classification, higher order cumulants, polynomial classifier, M-PSK, genetic algorithm

1. Introduction

From past few decades, automatic modulation classification (AMC) application in communication systems has been an intriguing area for the researchers. AMC is a process to classify the modulation technique employed in the transmitted signals. AMC is conceded between the detection and demodulation of the received signal [1, 2]. AMC is generally divided into two categories:

  1. Decision-Theoretic Approach (DTA)
  2. Pattern Recognition Approach (PRA)

The decision-theoretic approach also termed as the likelihood-based approached in which the probability of correct decision is maximize via utilizing prior information. Even though the approach is optimal and high computational complexity. The decision theoretic approach provides optimal solution by calculating the likelihood function of the received signal. After having the likelihood function there are several tests to detect the modulation format such as: average likelihood ratio test (ALRT), generalized likelihood ratio test (GLRT), hybrid likelihood ratio test (HLRT), quasi-likelihood ratio test (Q-ALRT), kullback-leibler divergence test (KLDT) and the detailed explanation of decision theoretic approach can be found in [3-6].

In pattern recognition approach the received signals characteristics are exploited and various parameters are extracted. After extracting the parameters, feature selection is carried out. While comparing to the decision-theoretic approach, feature-based approach is sub-optimal, but with the advantage of reducing computational complexity [7]. The works [8-22] related to feature-based pattern recognition approach have been listed in Table 1. In the literature, authors have been utilized various classifier structures to classify the modulation formats [23, 24]. The classifiers are based on hidden Markov model (HMM), neural network based, support vector machine based, convolutional neural network based, recurrent neural network based, deep neural network based and Gabor filter network [25-28].

In this research, M-PSK signals are considered for classification using polynomial classifier. The polynomial classifier (PC) is optimized using one of the evolutionary computational techniques i.e., Genetic Algorithm. The PC transforms the feature space into higher dimension space (HDS). Various classes in low dimension space are non-linearly separable while in HDS it becomes linearly separable. The performance of PC is evaluated on various channel model and compared with the optimized PC (OPC).

The rest of the paper is organized as follows: In section 2 system model is presented with the extracted features and polynomial classifier structure. Proposed classifier algorithm and the optimization is discussed in Section 3. The detailed simulation is carried out in section 4. In the end, the paper is concluded.

2. System Model

The system model for classification of M-PSK signals is shown in Figure 1. The signals have been considered for classification are PSK-4, PSK-8, PSK-16, PSK-32, and PSK-64. The modulated signal is transmitted over the faded channel (Rayleigh and Rician) with the addition of white gaussian noise. Higher order cumulants (HOCs) are selected as a feature set extracted from the received signal. In the first approach, these features are fed to the polynomial classifier, while in the second approach these features are optimized using Genetic Algorithm and fed to the polynomial classifier structure. The general expression of the received signal can be written as:

$r_{n}=s_{n}+g_{n}$                    (1)

where, rn is the received signal, gn is AWGN and sn is the modulated signal.

Figure 1. System model of the proposed algorithm

Table 1. Some existing feature-based techniques

Ref.

Classifier Algorithm

Modulation Formats

Channel

Features

[1]

Genetic Algorithm

QAM and PSK

AWGN

Spectral

[2]

Combined GP and KNN

BPSK, QPSK, QAM16, QAM64

AWGN

Cumulants

[8]

MAP

OFDM

AWGN, Fading

HOC

[9]

Pattern

M-PSK

Fading

HOC

[10]

ML

BPSK, QPSK, 8PSK, 16QAM

Rayleigh Fading, AWGN

High order cyclic cumulants

[11]

Hierarchical Classifier

M- ASK, FSK, PSK

AWGN

Instantaneous Spectral Feature

[12]

Linear and non-linear classifier

BPSK, 4PAM, QPSK, 16QAM, 64QAM

Multipath flat fading

HOC

[14]

Support Vector Machine

FSK, ASK, PSK

Fading

HOC

[15]

Pattern Recognition

M-PSK

M-QAM

Flat Fading,

HOC

[16]

Artificial Neural Network

FSK, PSK, PAM, QAM

Rayleigh Flat Fading and AWGN

High Order Statistics, Spectral

[17]

Genetic Programming with KNN

BPSK, QPSK, 16QAM, 64QAM

AWGN

HOC

[18]

Artificial Neural Network

PSK, FSK, ASK, AM, FM, DSB

AWGN

Statistical, Spectral

[19]

Pattern Recognition (MLP)

M-PAM, M-PSK, M-FSK, M-QAM

AWGN, Rayleigh Flat Fading,

Cyclo-stationary

[20]

Pattern Recognition(MPL)

M-PAM, M-PSK, M-FSK, M-QAM

AWGN, Rayleigh Flat Fading, Rician Flat Fading

Spectral

[21]

Hierarchical Classifier

M-PSK

AWGN

HOC

2.1 Feature extraction

From the received signal as in Eq. (1), the higher order cumulants are extracted as features set. For this, the pth order moment is defined as: -

$M_{p a}=E\left[r^{p-q}\left(r^{*}\right)^{q}\right]$             (2)

The second order, forth order, sixth order cumulants and 8th order cumulants expressions are expressed as follows [14]:

$\mathrm{C}_{20}=\mathrm{M}_{20}=\mathrm{E}\left[\mathrm{r}^{2}(\mathrm{n})\right]$                   (3)

$\mathrm{C}_{21}=\mathrm{M}_{21}=\mathrm{E}\left[|\mathrm{r}(\mathrm{n})|^{2}\right]$                 (4)

$\mathrm{C}_{40}=\mathrm{M}_{40}-3 M_{20}^{2}$                      (5)

$C_{41}=M_{40}-3 M_{20} M_{21}$                     (6)

$C_{42}=M_{42}-\left|M_{20}\right|^{2}-21 M_{21}$                   (7)

$\mathrm{C}_{60}=\mathrm{M}_{60}-15 \mathrm{M}_{20} \mathrm{M}_{40}+30 \mathrm{M}_{20}{ }^{3}$                (8)

$C_{61}=M_{61}-15 M_{21} M_{40}-10 M_{20} M_{41}+30 M_{20}^{2} M_{21}$                (9)

$C_{62}=M_{62}-6 M_{20} M_{42}-8 M_{21} M_{41}-M_{22} M_{40}$$+6 M_{20}^{2} M_{22}+24 M_{21}^{2} M_{22}$                   (10)

$C_{63}=M_{62}-9 M_{21} M_{42}+12 M_{21}^{3}-3 M_{20} M_{43}$$-3 M_{22} M_{41}+18 M_{20} M_{21} M_{22}$                     (11)

$C_{80}=M_{80}-35 M_{40}^{2}-28 M_{60} M_{20}$$+420 M_{40} M_{20}^{2} 630 M_{20}^{4}$                     (12)

From the Eqns. (3)-(12), the distinct features are extracted and higher order cumulants have been served as feature set. The features are extracted for different number of samples, different modulation formats, various SNR’s and channel conditions i.e. Rician and Rayleigh.

2.2 Polynomial classifier

The crux of the polynomial classifier is to expand the original features set space into higher dimensional space, where various classes become linearly separable [20]. Generally, there are two stages of PC:

1) Training of PC

2) Testing of PC

2.2.1 Training stage of polynomial classifier

In the training stage, the received signal with known modulation type is used to find the weight vectors. The extracted features are transformed into higher dimensional space using polynomial expansion method to yield more distinct features. This expansion of the features vector allows us the linear separation of the modulation formats. The order of the classifier is same as the dimension of the expanded feature space. Higher order classifiers can be used, but for simplicity and due to ease of implementation generally lower order classifiers have been utilized, however, in this research, the second order polynomial classifier is used. In the second order polynomial classifier, the original extracted features plus the product of these features and squared values of these features have been found. Let Ci is the vector that contains input features which are higher order cumulants [21].

$C_{i}=\left[C_{i, 1}, C_{i, 2}, C_{i, 3}, \ldots C_{i, K}\right]$            (13)

The feature vector Ci is expanded using polynomial expansion and the resulting expanded feature vector Pi is given below:

$P_{i}=\left[C_{i, 1}, C_{i, 2}, C_{i, 3}, \ldots, C_{i, K}, C_{i, 1} \times C_{i, 2}, \ldots, C_{i, 1} \times, C_{i, 2}\right.$$\times C_{i, 3}, \ldots, C_{i, 2} \times C_{i, K}, \ldots, C_{i, K-1}$$\left.\times C_{i, K}, C_{i, 1}^{2}, C_{i, 2}^{2}, \ldots, C_{i, K}^{2}\right]_{1 \times R}$          (14)

The dimension of the expanded feature space is denoted by R, and K represents the total number of the features i.e., HOC. Expansion of features vectors for all N number of classes will result in a matrix G that is produced by concatenating all Pi. For N feature vectors, the expanded feature vectors are $P_{1}, P_{2}, \ldots, P_{N}:$-

$P_{N}=\left[C_{N 1}, C_{N 2}, C_{N 3}, \ldots, C_{N M}\right]$                    (15)

$G=\left[P_{1}, P_{2}, \ldots, P_{N}\right]$                 (16)

$\mathrm{X}=\mathrm{G}^{\prime} \times \mathrm{G}$              (17)

In the next step, optimized weights are selected to reduce the minimum mean square error as: -

$\mathrm{W}=X^{-1} \times G$             (18)

where, W is the weight vector. The weight is used in the testing stage to recognize the modulation type of the received signal. The block diagram of the training stage of polynomial classifier is shown in Figure 2.

Figure 2. Training stage

2.2.2 Testing stage of polynomial classifier

In the testing stage, the received signals that have unknown modulation formats are applied to the polynomial classifier to recognize the modulation formats of the received signals. The ith feature vector Ci that contains higher order cumulants is extracted and then ith expanded feature vector Pi is determined using the Eq. (14). The second order polynomial expansion is used, and expanded vector Pi is multiplied with the classifier weights Wi to obtain the scores Si: -

$S_{i}=P_{i} * W_{i}$                 (19)

These scores present the new super features for the polynomial classifier and based on these scores, the modulated signal, modulation format is determined. The class identity of vector C is determined by the following rule: -

selected $\left\langle\right.$ class $\left._{i}\right\rangle=\arg \left(\underset{i}{\max }\left\{S_{i}\right\}\right)$                 (20)

For example, if there are two modulation types i.e., BPSK and QPSK, then there are two scores S1 and S2. If the score S1 is greater than the S2, then the modulation type is BPSK, otherwise the modulation type is QPSK. The block diagram shown in Figure 3, representing the training stage of polynomial classifier.

Figure 3. Testing stage

3. Optimization of Polynomial Classifier

Algorithm 1: GA based polynomial classifier

Inputs:

N → Number of samples

M → Modulation order

Ub → Upper bound of N

Lb → Lower bound of N

sn → Modulated signal

Cht → Channel type (Rician or Rayleigh)

snr → Signal to noise ratio

Outputs:

    return;

PCA → Percentage Classification Accuracy

Initialization:

Initialize;

  $\forall$ parameters

  $\forall$ variables

Main:

  1. for i=1 to N
  2.      $\forall$ M
  3.    if  Input_samples(i)= = (Ub, Lb)
  4.    continue
  5.        get  sn =input samples (i)
  6.   else
  7.       break
  8.   end if
  9. end for
  10. get  Cht
  11. apply snr
  12. while rounds $\leq$ max round
  13.       do
  14.       rounds++
  15.      features $\leftarrow$get
  16. // Apply GA to optimize features
  17.     while features ~ optimized
  18.       do 
  19.         Apply GA
  20.         generate dataset
  21.     end while
  22. end while
  23. if training == true
  24.    train polynomial classifier
  25. elseif testing == true
  26.    test polynomial classifier
  27.   evaluate PCA
  28. end if

Figure 4. Flow chart of GA

To optimize the classifier performance, the GA is used to optimize the features and to reduce the mean square error by finding the optimized weight vector. The figure of merit of the classification problem is percentage PCA (PCA) which is enhanced by using optimal values of the overexcited parameters. GS is used as global optimization due to their greater efficiency and is stochastic optimization algorithm which adopts the survival of the fittest theory of Darwin. GA is used to take the optimal features and classifier must reject the similar features means redundant features to reduce the computational complexity. The flow chart of the genetic algorithm for classification of modulation formats is shown in Figure 4. The pseudo code of proposed classifier structure is shown.

4. Simulation Results

The performance of polynomial classifier and optimized polynomial classifier have been evaluated for the classification of M-PSK signals. The figure of the merit of the considered problem is percentage classification accuracy (PCA). The simulation parameters are shown in the Table 2. The extensive simulations have been carried out with 512, 1024 and 2048 number of samples and different SNR’s of 0dB, 5dB and 10dB. Two fading channel models have been considered throughout the simulations i.e., Rayleigh and Rician.

Table 2. Simulation parameters

Parameters

Values

Candidate Solutions

10-50

Cross-over

Single Point

Selection

Roulette Wheel

Mutation

Adaptive

Classifier

Polynomial

Iterations

1000

SNR in dB

0-10

4.1 Case-1: Classification on Non-Fading Channel Model

The classifier performance is evaluated on non-fading channel i.e., only considered the AWGN. Tables 3-11 shows the PCA for AWGN channel model with different number of samples and SNR’s. From the Tables 3-5, the average PCA for the 512 number of samples is 87.5%, 89.46% and 91.94% at 0, 5 and 10 dB of SNR, respectively.

Table 3. PCA on AWGN Channel at SNR of 0dB, N=512

PSK

4

8

16

32

64

4

84.3%

 

 

 

 

8

 

92.4%

 

 

 

16

 

 

83.8%

 

 

32

 

 

 

84.1%

 

64

 

 

 

 

93%

Table 4. PCA on AWGN Channel at SNR of 5dB, N=512

PSK

4

8

16

32

64

4

87.3%

 

 

 

 

8

 

93.5%

 

 

 

16

 

 

86.4%

 

 

32

 

 

 

87.1%

 

64

 

 

 

 

93%

Table 5. PCA on AWGN Channel at SNR of 10dB, N=512

PSK

4

8

16

32

64

4

88%

 

 

 

 

8

 

94.7%

 

 

 

16

 

 

88.8%

 

 

32

 

 

 

90.2%

 

64

 

 

 

 

98%

Tables 6-8, the PCA improves as number of samples increases from 512 to 1024. The average PCA at 10dB of SNR is 93.9% which is better that 91.94% for 512 number of samples.

Table 6. PCA on AWGN Channel at SNR of 0dB, N=1024

PSK

4

8

16

32

64

4

87.3%

 

 

 

 

8

 

93.4%

 

 

 

16

 

 

90.8%

 

 

32

 

 

 

85.1%

 

64

 

 

 

 

98.1%

Table 7. PCA on AWGN Channel at SNR of 5dB, N=1024

PSK

4

8

16

32

64

4

88.3%

 

 

 

 

8

 

94.4%

 

 

 

16

 

 

91.1%

 

 

32

 

 

 

89.4%

 

64

 

 

 

 

98.5%

Table 8. PCA on AWGN Channel at SNR of 10dB, N=1024

PSK

4

8

16

32

64

4

89.1%

 

 

 

 

8

 

95.2%

 

 

 

16

 

 

93.8%

 

 

32

 

 

 

92.22%

 

64

 

 

 

 

99%

Table 9. PCA on AWGN Channel at SNR of 0dB, N=2048

PSK

4

8

16

32

64

4

88.9%

 

 

 

 

8

 

95.1%

 

 

 

16

 

 

92%

 

 

32

 

 

 

89.2%

 

64

 

 

 

 

99.45%

Table 10. PCA on AWGN Channel at SNR of 5dB, N=2048

PSK

4

8

16

32

64

4

89%

 

 

 

 

8

 

97.2%

 

 

 

16

 

 

93.8%

 

 

32

 

 

 

92.1%

 

64

 

 

 

 

100%

Table 11. PCA on AWGN Channel at SNR of 10dB, N=2048

PSK

4

8

16

32

64

4

92%

 

 

 

 

8

 

98.7%

 

 

 

16

 

 

94.8%

 

 

32

 

 

 

96.2%

 

64

 

 

 

 

100%

Tables 9-11 shows the percent accuracy of classification with 2048 number of samples and average PCA is quite improved as compared with 512 and 1024 number of samples i.e., 96.34%.

4.2 Case-2: Classification on Rician Fading Channel

The classifier performance is evaluated on Rician channel model. Tables 12-20 shows the PCA for Rician channel model with different number of samples and SNR’s. From the Tables 12-14, the average PCA for the 512 number of samples is 86.4%, 88% and 88.26% at 0, 5 and 10 dB of SNR, respectively.

Tables 15-17, the PCA improves as number of samples increases from 512 to 1024. The average PCA at 10dB of SNR is 91.5% which is better that 88.26% for 512 number of samples. Table 18-20 shows the percent accuracy of classification with 2048 number of samples and average PCA is quite improved as compared with 512 and 1024 number of samples i.e., 94.1%.

Table 12. PCA on Rician Channel at SNR of 0dB, N=512

PSK

4

8

16

32

64

4

83%

 

 

 

 

8

 

91.4%

 

 

 

16

 

 

83.7%

 

 

32

 

 

 

82.7%

 

64

 

 

 

 

91%

Table 13. PCA on Rician Channel at SNR of 5dB, N=512

PSK

4

8

16

32

64

4

85.3%

 

 

 

 

8

 

92.66%

 

 

 

16

 

 

84.3%

 

 

32

 

 

 

86%

 

64

 

 

 

 

92%

Table 14. PCA on Rician Channel at SNR of 10dB, N=512

PSK

4

8

16

32

64

4

86.9%

 

 

 

 

8

 

93.86%

 

 

 

16

 

 

86.34%

 

 

32

 

 

 

88.92%

 

64

 

 

 

 

95%

Table 15. PCA on AWGN Channel at SNR of 0dB, N=1024

PSK

4

8

16

32

64

4

86.4%

 

 

 

 

8

 

92%

 

 

 

16

 

 

88.2%

 

 

32

 

 

 

84.7%

 

64

 

 

 

 

92%

Table 16. PCA on AWGN Channel at SNR of 5dB, N=1024

PSK

4

8

16

32

64

4

87.1%

 

 

 

 

8

 

93.4%

 

 

 

16

 

 

89.9%

 

 

32

 

 

 

87%

 

64

 

 

 

 

95.2%

Table 17. PCA on AWGN Channel at SNR of 10dB, N=1024

PSK

4

8

16

32

64

4

88.22%

 

 

 

 

8

 

94%

 

 

 

16

 

 

90%

 

 

32

 

 

 

89.25%

 

64

 

 

 

 

96 %

Table 18. PCA on Rician Channel at SNR of 0dB, N=2048

PSK

4

8

16

32

64

4

87%

 

 

 

 

8

 

94.5%

 

 

 

16

 

 

90.7%

 

 

32

 

 

 

88%

 

64

 

 

 

 

95%

Table 19. PCA on Rician Channel at SNR of 5dB, N=2048

PSK

4

8

16

32

64

4

88%

 

 

 

 

8

 

95%

 

 

 

16

 

 

91.1%

 

 

32

 

 

 

89%

 

64

 

 

 

 

97%

Table 20. PCA on Rician Channel at SNR of 10dB, N=2048

PSK

4

8

16

32

64

4

90%

 

 

 

 

8

 

96.9%

 

 

 

16

 

 

92.33%

 

 

32

 

 

 

92%

 

64

 

 

 

 

98.9%

4.3 Case-3: Classification on Rayleigh Fading Channel

The classifier performance is evaluated on Rayleigh channel model. Tables 21-29 shows the PCA for Rayleigh channel model with different number of samples and SNR’s. The average PCA for 512, 1024 and 2048 number of samples at 10dB of SNR is 88.5%, 90.1% and 92.14%. The average PCA is slightly less at 5 dB and 0dB of SNR and can be seen from the tables 21-23, 24-26, 27-29.

Table 21. PCA on Rayleigh Channel at SNR of 0dB, N=512

PSK

4

8

16

32

64

4

81.98%

 

 

 

 

8

 

90%

 

 

 

16

 

 

81.7%

 

 

32

 

 

 

82%

 

64

 

 

 

 

90%

Table 22. PCA on Rayleigh Channel at SNR of 5dB, N=512

PSK

4

8

16

32

64

4

83.7%

 

 

 

 

8

 

91.5%

 

 

 

16

 

 

82.8%

 

 

32

 

 

 

85.7%

 

64

 

 

 

 

91.3%

Table 23. PCA on Rayleigh Channel at SNR of 10dB, N=512

PSK

4

8

16

32

64

4

84.8%

 

 

 

 

8

 

92%

 

 

 

16

 

 

84.3%

 

 

32

 

 

 

87%

 

64

 

 

 

 

94.5%

Table 24. PCA on Rayleigh Channel at SNR of 0dB, N=1024

PSK

4

8

16

32

64

4

85%

 

 

 

 

8

 

91%

 

 

 

16

 

 

86.9%

 

 

32

 

 

 

83%

 

64

 

 

 

 

91%

Table 25. PCA on Rayleigh Channel at SNR of 5dB, N=1024

PSK

4

8

16

32

64

4

85.56%

 

 

 

 

8

 

92%

 

 

 

16

 

 

87%

 

 

32

 

 

 

85.6%

 

64

 

 

 

 

93%

Table 26. PCA on Rayleigh Channel at SNR of 10dB, N=1024

PSK

4

8

16

32

64

4

86%

 

 

 

 

8

 

93.6%

 

 

 

16

 

 

88.96%

 

 

32

 

 

 

87%

 

64

 

 

 

 

95.1%

Table 27. PCA on Rayleigh Channel at SNR of 0dB, N=2048

PSK

4

8

16

32

64

4

85.5%

 

 

 

 

8

 

93%

 

 

 

16

 

 

88.9%

 

 

32

 

 

 

85%

 

64

 

 

 

 

91.8%

Table 28. PCA on Rayleigh Channel at SNR of 5dB, N=2048

PSK

4

8

16

32

64

4

86%

 

 

 

 

8

 

94%

 

 

 

16

 

 

90.6%

 

 

32

 

 

 

87%

 

64

 

 

 

 

95%

Table 29. PCA on Rayleigh Channel at SNR of 10dB, N=2048

PSK

4

8

16

32

64

4

88%

 

 

 

 

8

 

95%

 

 

 

16

 

 

91%

 

 

32

 

 

 

90%

 

64

 

 

 

 

96.7%

4.4 Case-4: Classification Performance Comparison

Table 30 shows the comparison of PCA of polynomial classifier and optimized polynomial classifier at 0dB of SNR. From the table, it is evident that after optimization, there is a significant improvement in PCA as compared without optimization. The PCA is 98% of OPC while 92.8% of PC for AWGN channel model at 2048 number of samples.

Table 30. PCA after Optimization Comparison at SNR of 0dB

 

Samples

SNR in dB

0

5

10

AWGN

512

89.3%

91%

92.5%

1024

93.6%

96%

97%

2048

98%

99.1%

99.8%

Rician

512

88.8%

90.1%

91.9%

1024

92%

93.5%

94.9%

2048

95%

96.7%

98.9%

Rayleigh

512

87%

88.6%

91%

1024

91.5%

95%

97.1%

2048

93%

95%

97%

Table 31. Comparison of proposed algorithm with the existing techniques

Samples

SNR (dB)

Native

SVM

GP-KNN

Without optimization

With optimization

512

0

63%

64%

65%

87%

89%

10

90%

91%

94%

91.9%

92.5%

1024

0

69%

70%

70%

90%

93.6%

10

94%

94%

97%

93%

97%

2048

0

76%

75%

95%

92%

98%

10

97%

97%

98%

96%

99.9%

In Table 31, the performance of proposed optimized polynomial classifier is compared with the well-known existing techniques and from the table, proposed OPC performs better in terms of percentage classification accuracy. The PCA is evaluated for different number of samples as well as different SNR’s. The PCA is around 98% even at lower SNR’s.

5. Conclusion

In this paper, an optimized polynomial classifier is employed to classify M-PSK signals. From the noisy received signal, HOCs are extracted and these feature vectors are fed into the polynomial classifier. The polynomial classifier expands the feature vector into a higher dimensional space in which various classes becomes linearly separable. The performance of the classifier is analyzed on Rician and Rayleigh fading channels in addition to white gaussian noise. The performance of classifier is also optimized using a Genetic Algorithm in conjunction with a polynomial classifier. From the extensive simulations, it is shown the supremacy of the proposed classifier as compared with the state of art existing techniques.

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