Levenberg marquedet lion based artificial neural network for cooperative spectrum sensing in cognitive radio

Abstract

Cognitive Radio (CR) is a promising wireless communication system that allows the user in wireless environment to communicate with wide band of frequencies. Spectrum sensing is the most vital function of CR that plays significant role in identifying the available channel in CR environment. Hence, this work introduces the novel cooperative spectrum sensing approach based on the proposed optimal fusion score that enhances spectrum sensing performance. The optimal fusion score finds the required channel availability by training the proposed Levenberg Marquedet (LM), and the Lion Optimization Algorithm (LOA) based Neural Network (LML-NN) classifier and the fuzzy classifier. The inputs for the classifier training are test statistics based on the Energy Detection (ED), and the Generalized Likelihood Ratio Test (GLRT). These test statistics are derived using the eigenvalues extracted from a received signal covariance matrix. The performance analysis of the system is done by varying the number of sensors in CR and threshold values. The system performance is quantified in terms of probability of detection, probability of false alarm and receiver operating curves. The simulation results confirm that proposed LML-NN algorithm has achieved an improved probability of detection and reduced false alarm rate as compared to the existing eigenvalue based CSS model.

Keywords

Cognitive radio cooperative spectrum sensing optimal fusion score levenberg marquedet lion optimization algorithm

1. Introduction

Cognitive radio (CR) has emerged as one of the commonly used intelligent communication paradigm in the recent years. The radio systems used in the real time scenario must be able to communicate with a large number of users without any interference within between the spectrums band [1]. The major challenge in CR design is the scarcity of available bandwidth for communication. Hence, for each incoming user within the CR environment, the channel allocation for the communication is a challenging task. The design of the CR system for wireless environment tries to solve the spectrum scarcity problem through better utilization of the spectrum. The CR connects various devices through wireless medium and the communication between the devices take place by reconfiguring the electromagnetic parameters [15]. The CR model has two types of users which are primary users called as licensed user, and the secondary user called as unlicensed user. The sensors present in the CR receive data samples sent by each primary users, and the fusion centre collects the data samples from each sensors. The fusion center present in the CR environment takes the decision regarding the channel availability and based on this decision the spectrum can be allocated to each incoming user for the communication purpose. Thus, effective design of the CR faced difficulties in the following sectors such as spectrum sensing, dynamic spectrum access, spectrum sharing, spectrum management, Secondary user’s (SU) transmission, etc. [18].

From the literature review it is being observed that a number of spectrum sensing algorithms are implemented, like, eigenvalue based CSS [2, 3, 21], matched filter detectors (MFD), energy detectors (ED) and cyclostationary feature detectors (CFD) for the cooperative spectrum sensing (CSS) [4, 8]. The performance of the MFD based spectrum sensing is good, but it requires the knowledge of the fading channel coefficients of the channel in the CR. The CFD based model for the CSS improves the spectrum sensing with the use of the cyclostationary features. The CFD model has more complexity than the other CSS models since the sensing interval of the CFD is high. The CSS based on the ED has gained more popularity due to its simple nature [12]. The implementation complexity of the ED based techniques is very low. Recently machine learning is gaining lots of interest in CR. Many authors have used machine learning technique for CSS [15]. Machine learning treats the spectrum sensing as a signal classification problem. The various features like energy values and cyclostationary feature values of the received signal at different SUs are used to train the various classifiers to check the channel availability. Some of the recent work based on machine learning techniques for spectrum sensing observed in literature is as follows.

Xue and Gao [13] used machine learning approach for CSS based on sample covariance matrix of received signal from multiple sensors. They used K-means clustering and SVM classifiers which are trained using eigenvalues based features obtained from a sample covariance matrix to check spectrum availability. Sobabe and Song [11] Suggested unsupervised learning approach for CSS. They used eigenvector and eigenvalues of the received signal as a feature to K-means clustering and Gaussian mixture model classifier to detect the PU. Han et al. [9] Presented novel approach of CSS using a convolution neural network (CNN). They used cyclostationary feature and energy feature of the received signal to train CNN to detect the presence of the primary user. They claimed good detection probability under low SNR value. Maity et al. [19] have presented the Fuzzy C-means clustering approach for sensing the available spectrum in the CR. The suggested methodology combines selection combining (SC) and optimal gain combining for addressing the reliability problem present in the CR. This system reduces the power consumption during the channel allocation. But, the suggested method fails to detect the scattered primary users present in the long distance. Mohammadi and Taban [5] have suggested the Fuzzy membership functions based model for the spectrum sensing. This model determines the existence of primary user within the CR environment and achieves uniform quantization. The shadowing environment in the CR affects the performance of the proposed model.

Senthilkumar and Geetha Priya [20] have used the Hidden Markov Model (HMM)-based Channel Selection Framework for the CSS.Here authors have used the HMM model for the channel sensing. They have also introduced the Time-Slot based optimal routing mechanism to find the spectrum band suitable for the communication. The given methodology has reduced running time, energy consumption and the average delay. But the performance of this system gets affected due to the complexity of the algorithm. Thilina et al. [15] have introduced the methodology for the effective pattern classification. In this work authors have used the machine learning approaches for finding the channel availability. The advantage of this model is the low training time for the classification. Their presented algorithm has reduced performance in the spectrum environments with the abrupt changes. Li and Xu [10] investigated the VMP based Bayesian hierarchical model. It estimates sparsity of the CR in both the frequency and space domain. This model has sparsity-inducing penalization terms leading to sparser solutions compared with typically norm based ones. This system suffers from the larger error value. Through a literature survey, it is observed that the field of CSS for finding the suitable channel for the communication suffers the challenges, like higher power dissipation and the presence of the noise in the channel affect the spectrum sensing. The noise uncertainty and absolute SNR wall affect performance of the channel detection. The algorithm used in [4] has the inability to differentiate the frequency bands between the primary and the secondary users. This will induce the interference in spectral sensing. The spectral utilization ratio gets affected due to the interference in the system [12]. Eigenvalue based spectrum sensing approaches like MME, MED that uses recent random matrix theory for threshold calculation gives better performance without prior information of signal, channel and noise power, but this asymptotic thresholds may not be accurate in practice [2, 11, 21]. In [5], fuzzy membership function was used for predicting the spectrum by formulating the optimal fusion score. This work does not make use of any learning algorithm for predicting the spectrum due to the unsupervised procedure of fuzzy membership function. The supervised models are more suitable for the time series based model prediction as the spectrum sensing is time dependent. So the combination of ANN and fuzzy can be explored to check the possibility of performance enhancement.

1.1 The major contributions

The literature survey exhibits that some existing approaches [2, 5, 21] have some issues as mentioned in Section 1. So taking consideration of those issues of existing approaches, this work introduces an innovative CSS scheme for detecting the available spectrum in the CR environment. The presented cooperative spectrum sensing (CSS) approach utilizes the test statistics to create a proposed optimal fusion score. In this system the channel availability is detected by providing the test statistics as input to the fuzzy classifier and the modified Levenberg Marquedet lion based neural network. This LML-NN uses the Levenberg Marquedet (LM) and lion optimization algorithm (LOA) for the training. The fusion center present in CR system gathers the information from CSS model and establishes the communication link based on the channel availability. Hence, the major contribution of this work is to introduce the optimal fusion score to find the channel availability using eigenvalue based test statistics along with fuzzy membership function and the design of LML-NN classifier based on LM and LOA optimization algorithm to enhance the sensing performance under low SNR condition.

The remaining of this work is organized as follows: Section 2 introduces the CSS model with the optimal fusion score and the LML-NN classifier. Section 3 briefs the results obtained from the proposed work for the various setups. Section 4 concludes the work with the summary and future work.

Table 1
List of abbreviation

Abbreviations/acronyms	Explanation
CR	Cognitive radio
LM	Levenberg marquedet
LOA	Lion optimization algorithm
LML-NN	Levenberg marquedet lion-based neural network
ED	Energy detection
GLRT	Generalized likelihood ratio test
CSS	Cooperative spectrum sensing
UHF	Ultra high frequency
SU	Secondary user
MFD	Matched filter detectors
CFD	Cyclostationary feature detectors
PSD	Power spectral density
FAR	Fast fourier transform average ratio
CFAR	Constant false alarm rate
AWGN	Additive white gaussian noise
SC	Selection combining
HMM	Hidden markov model
VMP	Variational message passing
SVM	Support vector machine
MOCSO	Multi-objective cat swarm optimization
PU	Primary user
MIMO	Multiple input multiple output
MLE	Maximum likelihood estimate
MMED	Maximum-minimum eigenvalue detection
MED	Maximum eigenvalue detection

2. Cooperative spectrum sensing model with the optimal fusion score and the levenberg marquedet lion-based neural network classifier

The architecture of the CSS model with the optimal fusion score and LML-NN classifier is as shown in Fig. 1. The CR contains many sensors for interacting with the primary users (PU). Here CR shares the frequency of the spectrum with each PU in the system. The CR system tries to split the frequency bands to the each primary user without frequency overlap. The fusion center collects the information from the secondary users and provides it to the CR base station. The CR tries to figure the availability of spectrum within the radio range when the new user enters the environment. The presented CSS model finds the available channel through the proposed optimal fusion score. The optimal fusion score is the combination of the test statistics such as GLRT and ED. The suggested optimal fusion score finds the channel availability by training the fuzzy classifier and the LML-NN classifier. The test statistics are provided to the LML-NN and fuzzy classifier as the training features. The proposed NN classifier is trained with the LM [14, 16] and the LION [6, 17] algorithm. For the each incoming test statistic, the weights are updated. Based on the optimal fusion score of the channel, the classifier declares the channel to be occupied or vacant. Then the fusion center present in the CR sends the channel availability information to the CR base station. Then, if the channel is vacant, the communication link is established.

Figure 1.

Architecture of the cooperative spectrum sensing model with the proposed optimal fusion score.

2.1 Fusion test statistics for the cooperative spectrum sensing

This work introduces an optimal fusion score scheme for checking the availability of the channels in the cognitive radio network. This fusion score is created using eigenvalue based test statistics extracted from a received signal covariance matrix. The optimal fusion score is the combination of the eigenvalue based generalized likelihood ratio test (GLRT), and the energy detection (ED) of [3, 7]. To obtain these test statistics a MIMO radio environment is considered with $p$ number of primary transmitters and cognitive radio with $m$ number of sensors. The $p$ transmitters in the radio environment try to communicate with the sensors of the CR through the radio channels. During sensing period the CR searches for the available channels under two hypothesis. $H_{0}$ -hypothesis indicating absence of signal and $H_{1}$ -hypothesis indicating presence of signal on channel. The $m$ sensors present in the CR receive $n$ data samples from the transmitters. The matrix $Y$ is constructed based on the samples received by the sensors from the transmitter and is given as $Y$ in Eq. (1).

$\displaystyle Y=[y_{ik}]_{mxn}$ (1)

Where, the term $y_{ik}$ represents the $k^{th}$ data sample received by the $i^{th}$ sensor present in the CR. The term $m$ represents the total sensors present in the CR, and the term $n$ represents the data samples received by the sensors. The value of $i$ and $j$ varies between $1\leqslant i\leqslant m$ and $1\leqslant j\leqslant n$ respectively. The matrix $Y$ can be constructed with the various values such as signals transmitted by the transmitter, channel gain, and the thermal noise. The $P$ transmitters present in the radio environment sent various signals to the CR. The signals transmitted by the $p$ transmitters are arranged in the matrix $X$ . The transmitted signal matrix is shown as in Eq. (2).

$\displaystyle X=[x_{jk}]_{p\times n}$ (2)

Where, the term $x_{jk}$ represents the signal transmitted by the $j^{th}$ transmitter. The value of the $j$ ranges between $1\leqslant j\leqslant p$ . The transmitters and the sensors communicate via the radio channels. The channels present in the radio environment is represented in the channel matrix $H$ , and it is represented as Eq. (3),

$\displaystyle H=[h_{ij}]_{m\times n}$ (3)

Where, the term $h_{ij}$ represents the channel gain between the $i^{th}$ sensor and the $j^{th}$ transmitter. The signals transmitted through the radio channels get affected due to the thermal noise present in the radio environment. Hence, the thermal noise also needs to be considered while constructing the matrix $Y$ . The thermal noise matrix is represented as,

$\displaystyle N=[N_{ik}]_{m\times n}$ (4)

Where, the term $N_{ik}$ represents the thermal noise in the channel in which the data samples are received by the $i^{th}$ sensor. The Eq. (1) representing the matrix $Y$ is modified by substituting the value provided by the Eqs (2–4). The matrix $Y$ is expressed by Eq. (5).

$\displaystyle Y=[H\ast X]+N$ (5)

The proposed optimal fusion score requires a construction of the covariance matrix $V$ from the data samples matrix $Y$ . The construction of the covariance matrix from the samples matrix $Y$ requires the application of the binary hypotheses test. Thus, Eq. (6) gives the sample covariance matrix from the matrix $Y$ .

$\displaystyle V=E[Y.Y^{+}]$ (6)

where, the term $E[.]$ represents the expected value operator. The term $Y^{+}$ represents the conjugate and transpose of the sample matrix $Y$ . The covariance matrix is obtained by modifying the expected value operator with the maximum likelihood estimate (MLE). The modified covariance matrix is given as follows,

$\displaystyle V=\frac{1}{n}[Y.Y^{+}]$ (7)

From the covariance matrix constructed from the Eq. (7) two test statistics are derived. These test statistics are based on the GLRT, ED. The GLRT based test statistics [7] is expressed as follows,

$\displaystyle Z_{\textit{GLRT}}=\frac{\lambda_{1}}{\frac{1}{m}\sum\limits_{i=1% }^{m}{\lambda_{i}}}=\frac{\lambda_{1}}{\frac{1}{m}tr(V)}$ (8)

The ED based test statistics [7] is represented as,

$\displaystyle Z_{\textit{ED}}=\frac{\left\|Y\right\|_{F}^{2}}{m\times n\times% \sigma^{2}}=\frac{1}{m\times\sigma^{2}}\sum\limits_{i=1}^{m}{\lambda_{i}}$ (9)

where, the term $\|Y\|_{F}^{2}$ represents the forbenius norm of the matrix $Y$ , and the term $tr(V)$ represents the trace norm of the matrix $Y$ . The term $\sigma^{2}$ represents the thermal noise power and $\lambda$ is the eigenvalue. The optimal fusion score is constructed from the GLRT and the ED based test statistics along with the fuzzy membership function [5]. The optimal fusion score provides the information about the channel availability in the CR environment. The proposed optimal fusion score is represented as follows,

$\displaystyle Z=\alpha\ast Z_{\textit{net}}+\beta\ast Z_{\textit{fuzzy}}$ (10)

where, the term $Z$ represents the optimal fusion score which provides the information regarding the availability of the channel. The term $Z_{\textit{net}}$ expresses the channel availability from the proposed LML-NN algorithm. The term $Z_{\textit{fuzzy}}$ expresses the channel availability from the existing the fuzzy classifier [5]. The term $\alpha$ and $\beta$ expresses the fuzzy membership function from the [5]. The test statistics based on the GLRT and the ED have the similar characteristics. The GLRT and the ED require the eigenvalue for the construction of the test statistics. The use of the fuzzy membership function along with the test statistics improves the detection of the presence of the energy in the communication channel. The value of the fuzzy membership function is expressed as follows,

$\displaystyle\alpha=\frac{Z_{\textit{GLRT}}}{Z_{\textit{GLRT}}+Z_{\textit{ED}}}$ (11) $\displaystyle\beta=\frac{Z_{\textit{ED}}}{Z_{\textit{GLRT}}+Z_{\textit{ED}}}$ (12)

The optimal fusion score detects the channel availability in the radio environment by analyzing the energy along the channel. The channel availability based on the LML-NN classifier is expressed as follows,

$\displaystyle Z_{\textit{net}}=\textit{net}\,[Z_{\textit{GLRT}},Z_{\textit{ED}% },\alpha,\beta]$ (13)

where, the term net expresses the NN function. The feature vectors are provided as the input to the LML-NN classifier. To train the classifier the more values of the test statistics are required. Hence, a database is created with 200 random events. For the each event, the value of the system/channel availability is calculated for the various values of $Z_{\textit{GLRT}}$ and $Z_{\textit{ED}}$ . The channel availability based on the fuzzy classifier is expressed in the following Eq. (14).

$\displaystyle Z_{\textit{fuzzy}}=\textit{fuzzy}\,[Z_{\textit{GLRT}},Z_{\textit% {ED}},\alpha,\beta]$ (14)

Figure 2 represents the proposed optimal fusion score, in which the results of the LML-NN classifier and the fuzzy classifier are fused. Initially, the test statistics are provided to the LML-NN classifier and the fuzzy classifier separately. The channel availability determined by the LML-NN classifier is denoted as $Z_{\textit{net}}$ , and the channel availability determined by the fuzzy classifier is denoted as $Z_{\textit{fuzzy}}$ . Then, depends on the results of both classifiers the optimal fusion score is generated.

Figure 2.

Illustration of the proposed optimal fusion score.

2.2 Finding of the channel availability

Z_{\textit{fuzzy}}

based on the fuzzy classifier

This section explains the fuzzy classifier for finding the channel availability $Z_{\textit{fuzzy}}$ . The fuzzy classifier used in the work [5] uses the various test statistics to find the channel availability based on three important steps such as, fuzzification, fuzzy rule inference and defuzzification. Here, the two test statistics $Z_{\textit{GLRT}}$ , and $Z_{\textit{ED}}$ along with $\alpha$ , and $\beta$ are provided as the input to the fuzzy network. Then, the fuzzy network is trained with the test statistics value and thus, finally provides the channel availability value $Z_{\textit{fuzzy}}$ .

2.3 Finding of the channel availability $Z_{\textit{net}}$ based on the levenberg marquedet lion-based neural network

2.3.1 Architecture of the levenberg marquedet lion-based neural network to find $Z_{\textit{net}}$

The architecture of the LML- neural network with the fuzzy membership and the LM model is shown in Fig. 3. The test statistics functions along with $\alpha$ , and $\beta$ are provided to the neural network as the input. Thus the LML-neural network contains four input layers. Equation (15) provides the expression of the input layers.

$\displaystyle I=\{Z_{\textit{GLRT}},Z_{\textit{ED}},\alpha,\beta\}$ (15)

The size of the input layer and the hidden layer of the proposed LML-NN is 1 $\times$ 4. The hidden layers of the LML-NN provide the required weights for the computation. The hidden layers contain four weights corresponding to the inputs. The weights provided in the hidden layers are represented as in Eq. (16),

$\displaystyle W=\{W{}_{1},W{}_{2},W{}_{3},W{}_{4}\}$ (16)

The output layer contains a single layer which provides the value of the spectrum availability $Z_{\textit{net}}$ . The spectrum availability $Z_{\textit{net}}$ primarily depends on the optimal score and the weights in the hidden layer. The weights provided in the hidden layers are obtained through the training of the LML-NN network.

Figure 3.

Architecture of the NN with the proposed fusion test statistics.

2.3.2 Training of the neural network with the levenberg marquedet lion algorithm

The proposed LML-NN network is trained with the modified LM algorithm. The LM algorithm is modified with the lion optimization algorithm to train the LML-NN. The following steps provide the detailed explanation about the training phase of LML-NN classifier.

Step 1: Initialization of the weights in the hidden layer: The initial step in the training of the LML-NN is the initialization of the weights for the training. The learning rate and the delay rate of LM algorithm are also fixed in the initialization step. The weights of the proposed LML-NN is given as,

$\displaystyle W=\left\{{W_{1},W_{2},W_{3},W_{4}}\right\}\ \text{and}\ l=0.1,% \delta=0.1$

Where, the term $l$ represents the learning rate, and the delay $\delta$ represents the delay rate for the required training Phase.

Step 2: Find the output of the NN for the initialized weight: In the next step, the output of the LML-NN is found with the initialized weights and the inputs. The Eq. (17) provides the expression of the output of the proposed LML-NN,

$\displaystyle Z_{\textit{net}}(t)=\left\{{\begin{array}[]{ll}1;&W^{T}.I>\theta% \\ 0;&\textit{else}\\ \end{array}}\right\}$ (17)

Where, the term $Z_{\textit{net}}(t)$ indicates the system availability. The output of the LML-network $Z_{\textit{net}}(t)$ is the function of the input and the weights provided to the NN. Thus the system availability can also be indicated as $Z_{\textit{net}}(t)=F(W(t),I)$ . The term $F()$ indicates the NN function. The term $\theta$ indicates the threshold function. The output takes the value of 0 or 1 based on the input provided to the system.

Step 3: Determination of the error: The error of the LML-NN depends on the target output value. When the determined output deviates from the target output, then the error is produced. The Eq. (18) provides the expression of the error.

$\displaystyle Q(t)=Z_{\textit{net}}(t)-O(t)$ (18)

where, the term $Z_{\textit{net}}(t)$ indicates the output of the current iteration, and the term $O(t)$ indicates the original/target output. The error $Q(t)$ expresses the deviation of the current output value from the target.

Step 4: Determination of the incremental weights for the LML-NN: For the each incoming inputs, the weights of the LML-NN need to be updated. The incremental weight required for the update of the LML-NN is represented below,

$\displaystyle\Delta W=[R^{T}R+l.I_{M}]^{-1}\cdot R^{T}\;Q(t)$ (19)

Where, the term $R$ expresses the Jacobian matrix, and the term $l$ represents the learning rate.

Step 5: Update the new weight based on the incremental weight: In this step, the weights obtained in the previous iteration are updated with the use of the incremental weights obtained in step 4. The weight update equation is given in the Eq. (20).

$\displaystyle W(t+1)=W(t)+\Delta W$ (20)

where, the term $W(t+1)$ expresses the updated weight value. At the each iteration the value of the $W(t+1)$ gets changed.

Step 6: Calculate the output based on the updated weight: In the next step, the equation of the output neuron also gets updated based on the new weights. The equation of the output neuron is indicated as follows,

$\displaystyle Z_{\textit{net}}(t+1)=F\left({W(t),\;I}\right)$ (21)

Step 7: Find the updated error: The LML-NN uses the LA to update the error equation. The error update equation is expressed as follows,

$\displaystyle W_{w}\left({t+1}\right)=\left\{\begin{array}[]{ll}W_{w}^{\textit% {LA}}\left(t\right);&\textit{if}\ w=t\\ W_{w}\left(t\right);&\textit{otherwise}\\ \end{array}\right.,w=1,2,3,4$ (22)

where, the term $W_{w}^{\textit{LA}}(t)$ expresses the updated weight equation based on the LA algorithm. The term $w$ expresses the each weight elements of the hidden layer. The LA equation updates the weight on certain conditions otherwise it retains the old weight. The weight update using the LA is expressed as follows,

$\displaystyle W_{w}^{\textit{LA}}\left(t\right)=\min\left\lfloor{W_{w}^{\max}% \left(t\right),\max\left({W_{w}^{\min}\left(t\right),\nabla(t)}\right)}\right\rfloor$ (23)

where, the term $W_{w}^{\max}\left(t\right)$ expresses the maximum weight value present in the $W_{w}^{LA}\left(t\right)$ , and the term $W_{w}^{\min}\left(t\right)$ expresses the minimum weight value present in the $W_{w}^{LA}\left(t\right)$ . The term $\nabla(t)$ expresses the required update. The update from the LA depends on the maximum and the minimum weight values. The weight values of the hidden neurons are updated based on the update $\nabla(t)$ . The update for the LA algorithm is expressed in the equation.

$\displaystyle\nabla(t)=\left\lfloor{W_{w}^{\textit{LA}}\left({t+1}\right)+% \left({0.1p_{1}-0.05}\right)\left({W_{w}(t)-p_{2}W_{w}^{\textit{LA}}(t+1)}% \right)}\right\rfloor$ (24)

where, the term $W_{W}^{\textit{LA}}\left({t+1}\right)$ expresses the weight in the current iteration, the term $W_{W}\left(t\right)$ represents the weight in the previous iteration, and the terms $p_{1}$ , and $p_{2}$ has the values of 0 and 1.

Step 8: Find the output of the LML-NN based on the updated weight: In this step, the output function and the error are recalculated. The following equations determine the expression for the output and the error of the LML-NN,

$\displaystyle Z_{\textit{net}}(t+1)=F\left({W_{w}(t+1).I}\right)$ (25) $\displaystyle Q(t+1)=Z_{\textit{net}}(t+1)-O(t+1)$ (26)

Where, the term $Z_{\textit{net}}(t+1)$ represents the updated output after the weight update by the LA and the term $O(t+1)$ represents the ground truth value.

Step 9: Termination: The algorithm concludes when the iteration $t$ reaches its maximum value. Until the Steps 3 to 8 are repeated.

2.3.3 Testing phase of levenberg marquedet lion based neural network classifier

In the testing phase, features of the optimal fusion score obtained from the test channel are provided as the input to the LML-NN classifier. The weights of the NN are updated with the LM and the LOA concerning the optimal fusion score. Based on the trained values, the LML-NN declares channel to be busy or vacant. The output of the proposed LML-NN classifier is given as follows,

$\displaystyle Z_{\textit{net}}=\left\{{\begin{array}[]{ll}1&\textit{Channel is% available}\\ 0&\textit{Channel is busy}\\ \end{array}}\right\}$ (27)

3. Simulation results and discussion

This section shows the simulation results of the implemented CSS model with the optimal fusion score and the LML-NN classifier. The experimentation is varied with the various simulation parameters.

3.1 Simulation setup

The simulation results of the CSS model with the optimal fusion score are determined using the MATLAB R2016 tool run on Intel i5 quad core processor (2.66 GHz) with 4 GB RAM. Simulation results are obtained with one PU and multiple SUs also called as sensors. The number of samples taken to be 50 and SNR value set to be –20 dB. Table 2 shows the simulation parameters used for the experimentation of the optimal fusion score based CSS model.

Table 2
Simulation parameters used for the experimentation of the proposed CSS model

Simulation parameters	Variables	Values
Number of sensors	$m$	20, 40, 60
Number of transmitters	$p$	1
Data samples	$n$	50
Channel used for the communication	$H$	Rayleigh
Number of trials	–	200
SNR (dB)	–	$-$ 20 dB
Maximum value of threshold	–	1.2
Minimum value of threshold	–	0.8

3.2 Evaluation metrics

The performance parameters such as the probability of detection and the probability of the false alarm, define the usefulness of the proposed CSS model with the LML-NN classifier. The probability of detection of the channel defines ratio of total number of times channel detected correctly as busy channel to the total number of times the channel was busy in CR environment. The probability of detection metric must have a high value for the improved performance. The smaller value of the probability of false alarm indicates the better performance. The false alarm rate of the channel defines the ratio of total number of times channel detected as available channel to total number of times channel was busy.

3.3 Performance analysis

Figure 4.

Performance analysis of the proposed CSS model with 20 sensors.

This section briefs the simulation results obtained by the implemented CSS model with the LML-NN classifier. Various test statistic methods for the CSS are utilized in this work for the performance analysis. Models such as GLRT [7], MMED [7], and MED [7] models are used for the comparison with the proposed method. The performance of the each model is measured in terms of probability of detection and the probability of false alarm. The value of the performance metrics is measured against the gamma value (threshold values). The analysis is done by varying the number of sensors in the CR.

Figure 5.

Performance analysis of the proposed CSS model with 40 sensors.

3.3.1 Performance analysis of the CSS model with LML-NN for different number of sensors

The performance analysis of the suggested CSS model having 20 sensors for the communication purpose is as shown in Fig. 4. The performance of the system based on the probability of detection is shown in Fig. 4a for the gamma value of 1, the existing GLRT, MMED, MED has the values of 0.5, 0.31958, and 0.3186 for the probability of detection. The implemented CSS model has the improved probability of detection with the value of 0.55 for the gamma value of 1. For the gamma value of 1.2, the existing GLRT, MMED, MED has the values of 0 for the probability of detection. The implemented CSS system with the LML-NN classifier has the best probability of detection with the value of 0.33. The increase in the gamma value has reduced the probability of detection of the available channel for the communication. For GLRT, MMED and MED the probability of detection becomes zero, whereas the CSS model with LML-NN maintains a detection value of 0.33 for the larger value of the gamma. Figure 4b shows the performance analysis of the system based on the probability of the false alarm rate. The value of the false alarm rate must be as low as possible for improved performance. For the gamma value of 1, the existing GLRT, MMED, MED has the probability of false alarm rate values of 0.481481, 0.300971, and 0.192661. The CSS model with the LML-NN classifier has the improved probability of false alarm rate with the value of 0.192661 at gamma $=$ 1. For the gamma value of 1.2, the existing GLRT, MMED, MED has the values of 0 for the probability of false alarm rate. The proposed CSS system has the reduced probability of false alarm rate with the value of 0. The increase in the gamma value has reduced the probability of false alarm rate of the available channel for the communication. The CSS model with the LML-NN classifier maintains a false alarm rate of 0 for the larger value of the gamma. Figure 4c shows the ROC curve that is the graph of the probability of false alarm rate vs. probability of detection for various models with 20 sensors. From the graph it is observed that the performance of the CSS system with LML-NN is enhanced as compared to the existing methods.

Figure 6.

Performance analysis of the proposed CSS model with 60 sensors.

The performance analysis of the CSS model with LML-NN having 40 sensors for the communication purpose is shown in Fig. 5. The performance comparison of the suggested model based on the probability of detection is expressed in Fig. 5a. For the gamma value of 1, the existing GLRT, MMED, MED has the values of 0.52475, 0.32142, and 0.25 for the probability of detection. The presented CSS system with the LML-NN classifier has the improved probability of detection with the value of 0.54. For the gamma value of 1.2, the existing GLRT, MMED, MED has the values of 0 when the sensors increased to 40. The proposed CSS model with 40 sensors has the improved probability of detection with the value of 0.34. Figure 5b shows the performance of the model based on the probability of the false alarm rate. For the gamma value of 1, the existing GLRT, MMED, MED has the values of 0.434343, 0.19318, and 0.11363 for the probability of false alarm rate. The CSS model with LML-NN has the improved probability of false alarm rate with the value of 0.11363. Figure 5c shows the ROC curve for various models with 40 sensors. For the probability of false alarm rate value 0.6, the existing GLRT, MMED, and MED have the detection values of 0.59, 0.7, and 0.789. The proposed LML-NN classifier has overall increased the probability of detection value of 0.999.

Figure 6 shows the performance analysis of the CSS model with 60 sensors for the communication purpose. Figure 6a shows that initially, the comparative model has improved value of 1 for the probability of detection. The increase in the gamma value has decreased the probability of detection. For the gamma value of 1, the existing GLRT, MMED, MED has the values of 0.536363, 0.26, and 0.2268 for the probability of detection. The CSS model with the LML-NN classifier has the improved probability of detection with the value of 0.53636. The increase in the gamma value has made the detection values of the existing models as 0. But, the LML-NN model has maintained a constant value of 0.35 throughout the increase in the gamma value. Figure 6b shows that for the gamma value of 1, the existing GLRT, MMED, MED has the values of 0.31111, 0.19, and 0.1262 for the probability of false alarm rate. The suggested CSS model has the improved probability of false alarm rate with the value of 0.07. The increase in the gamma value has reduced the false alarm rate as 0 in the each comparative model. Also, the increase in the sensors to 60 reduced the false alarm rate. Figure 6c shows the ROC graph for various models with 60 sensors. For the probability of false alarm rate value 0.5, the existing GLRT, MMED, and MED have the detection values of 0.6, 0.65, and 0.65. The LML-NN classifier has overall increased the probability of detection value of 0.8997.

From the simulation result, it is observed that the proposed CSS system with LML-NN classifier performance is enhanced as compared to the existing eigenvalue based CSS system model [7]. Also, with the increase in the number of sensors the probability of detection is slightly improved and the probability of false alarm is reduced to zero.

4. Conclusion

This work introduced a novel CSS scheme for sensing the available channel in the CR. This CSS scheme generates the proposed optimal fusion score by combining the GLRT and ED test statistics. The presented model uses the fuzzy membership function and LML-NN classifier for finding the channel availability. The LML-NN algorithm uses the LM ANN and its training process is modified by embedding the LOA algorithm for weight optimization. The channel availability decision from both the classifier is combined with the constant to form the optimal fusion score. The optimal fusion score provides the final output regarding the channel availability more accurately even under low SNR condition. The information taken from the LML-NN classifier helps CR in decision making for the channel allocation. The performance of the CSS model is analysed by varying the number of sensors in the CR.The metrics such as the probability of detection and the probability of the false alarm rate determine the effectiveness of the proposed algorithm compared to various existing models. From the simulation results, it is evident that the proposed optimal fusion score provides improved value of the probability of detection and probability of false alarm rate. In future this work may be extended to explore the suitability of other classifiers to improve the system performance.

Footnotes

Authors’ Bios

Rajendra Yelalwar received the B.E. degree in Electronics and Tele communication Engineering from Amravati University, Amravati, India in 2001 and the M Tech degree from Pune University, India in 2008. He is pursuing his Ph.D. degree in Electronics & Telecommunication at the department of E&TC of Pune Institute of Computer Technology, SPPU University Pune, India.His current research interest include spectrum sensing for cognitive radio and machine learning techniques.

Y. Ravinder is currently working as Head and Professor in E&TC Engineering Department, Pune Institute of Computer Technology, Engineering College affiliated to S P Pune University, Pune. He received B.E. in Electronics Engineering from Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India in 1992. He obtained M.E and Ph.D. (Electronics and Communication Engineering) from Osmania University, Hyderabad, India 2000 and 2008 respectively. He worked as senior consultant for two years at Centre for Excellence in Microwave Engineering, University College of Engineering, Osmania University. He is member of IEEE, IET and IEI. His research areas include, Adaptive Antennas, Smart Antenna, Wireless Communications and Cognitive Radio.

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