Function approximation based energy detection in

Intelligent Automation & Soft Computing

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Function approximation based energy detection in cognitive radio using radial basis function network Barnali Dey, A. Hossain, A. Bhattacharjee, Rajeeb Dey & R. Bera To cite this article: Barnali Dey, A. Hossain, A. Bhattacharjee, Rajeeb Dey & R. Bera (2017) Function approximation based energy detection in cognitive radio using radial basis function network, Intelligent Automation & Soft Computing, 23:3, 393-403, DOI: 10.1080/10798587.2016.1217632 To link to this article: http://dx.doi.org/10.1080/10798587.2016.1217632

Published online: 16 Aug 2016.

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Date: 18 August 2017, At: 06:06

Intelligent Automation & Soft Computing, 2017 VOL. 23, NO. 3, 393–403 https://doi.org/10.1080/10798587.2016.1217632

Function approximation based energy detection in cognitive radio using radial basis function network Barnali Deya, A. Hossaina, A. Bhattacharjeeb, Rajeeb Deyc and R. Berad a

Department of Electronics & Communication Engineering, National Institute of Technology, Silchar, India; bDepartment of Computer Science and Engineering, National Institute of Technology, Silchar, India; cDepartment of Electrical Engineering, National Institute of Technology, Silchar, India; d Department of Electronics & Communication Engineering, Sikkim Manipal Institute of Technology, Sikkim, India

KEYWORDS

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ABSTRACT

In this paper an attempt has been made to evolve a computationally intelligent energy detection method for spectrum sensing in Cognitive Radio (CR). The proposed method utilizes the function approximation capability of radial basis function (RBF) network to learn the threshold function for a pre-determined range of probability of false alarm and number of samples. The receiver operating characteristic (ROC) results obtained by the proposed method have been compared with the conventional energy detection scheme. It is validated from the results that, the proposed method provides enhanced probability of detection in some cases compared to the conventional one due to its inherent shortcoming in terms of computational intelligence.

1. Introduction The issue of spectrum scarcity has given birth to the concept of cognitive radio (CR) (Haykin, 2005; Mitola & Maguire, 1999). In CR the unlicensed user or otherwise called secondary users (SU) are allowed to use a PU frequency band provided a spectrum hole is detected in terms of time, frequency and space (Yucek & Arslan, 2009; Wang et al, 2011). This coroneted Spectrum Sensing (Yucek & Arslan, 2009) as a major research direction in the operation of Cognitive Radio Technology as other cycles of CR is dependent on it. Conventional Spectrum sensing techniques may be broadly classified as Energy detection (Mahmood & Hussein, 2012), matched filter detection (Fatty, Maged, Ihab, & Ibrahim, 2014), cyclostationary detection (Dandawate & Giannakis, 1994), and wavelet detection (Tian & Giannakis, 2006). The present work focuses on improving Energy Detection as a method of spectrum sensing, which has the following merits: (i) less computational complexity for different types of wireless channels, (ii) does not depend on a priori information about PU characteristic. However, it is not an optimal detector under low SNR condition (Atapattu, Tellambura, & Jiang, 2010, 2014; Mercedes, Plataa, & Reátiga, 2012). We present brief review on energy detection based spectrum sensing to give an insight on the issues concerning the research in this direction. In YingChang, Zeng, Peh, & Hoang, 2008 sensing throughput tradeoff problems in energy detection sensing techniques has been dealt. Better performance measure for energy detection techniques have been discussed in Atapattu et al., 2010 and Haykin, 2005. Improvement of energy detection for random signal in Gaussian noise by replacing the squaring operation by suitable positive power has been discussed in Atapattu & Tellambura, 2010 and Chen, 2010). In Umar, Sheikh, & Deriche, 2014, it is brought out that there exist ambiguities in deciding the test statistics like ED approximates the PDF (probability density CONTACT Rajeeb Dey © 2016 TSI® Press

[email protected]

Words; Cognitive-radio (CR); Spectrum sensing; Energy-detection; Function approximation; Radial basis function (RBF) network; Neural network

function) for decision using Gaussian distribution based on central limit theorem, which is valid for large sample size (N), ambiguities in decision due to noise uncertainties and fading characteristics of the wireless channels has been pointed out in Digham, Alouini, & Simon, 2007. The decision regarding the largeness of the value of N is yet not clearly defined as different researcher proposes different values of N (Arshad, Imran, & Moessner, 2010; Urkowitz, 1967; Zeng, Liang, & Zhang, 2010). The use of intelligent or machine learning and decision techniques are being used to solve the spectrum sensing and learning problem of CR or CR systems to alleviate some of the computational issues of conventional techniques. In Tang, Zhang, & Lin, 2010 authors have attempted to sense the spectrum using ANN combining the energy and cyclostationary feature information gathered from the RF environment, spectrum prediction for CR using MLP (Multi-layer Perceptron) to predict the channel state with minimum error probability is considered in Tumuluru, Wang, & Niyato, 2010, a Multiple feed-forward NN(MFNN) has been used as a function approximation to evaluate the communication performance of the CR system in Baldo & Zorzi, 2008, Tsagkaris, Katidiotis, & Demestichas, 2008, and Bkassiny, Li, & Jayaweera, 2013 discuss the need of machine learning using ANN in assisting the CR functionalities, in Muhammad, Tarhuni, & Assaleh, 2012 learning based energy detection for spectrum sensing using classification approach has been dealt. Intelligent Fuzzy rule base has been used in Kaur, Uddin, & Verma, 2010 and Taghavi & Abolhassani, 2011 for spectrum sensing of CR, Fuzzy hypothesis based GLRT for energy detection can be found in Font-Segura & Wang, 2010, Ejaz, ul Hasan, Azam, & Kim, 2012 and Subhedar & Birajdar, 2013 various traditional spectrum sensing has been used for local sensing, which is further fed to Fuzzy rule base to take decision on the presence of PU, Fuzzy rule based Co-operative spectrum sensing can be found in Ejaz, ul Hassan, Aslam, & Kim, 2011 and Ejaz et al.,


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2012 and references therein, whereas the traditional method of cooperative spectrum sensing can be found in Unnikrishnan & Veeravalli, 2008. It is convincing from the above discussion that there still exist vast opportunity to try different techniques in order to improve the detection performance of energy detection based CR. In this note an attempt has been made to address the issue of detection performance of energy detection in spectrum sensing using artificial neural network (ANN) as a function approximator for the first time. The proposed scheme of spectrum sensing utilizes underlying concept of traditional energy detection in Kalamkar & Banerjee, 2013 and Ying-Chang et al., 2008 and references therein. Here the radial basis function network (RBFN) is used as function of probability of false alarm (PFA) and the number of samples (N). This is later used to compute the probability of detection (PD), probability of miss detection (PMD) and subsequently determines the ROC of the detection scheme for a pre-assigned PFA and SNR value. The numerical simulation is carried out for AWGN channel and the results are presented in the appropriate section below. The result validates the fact that neural network approximated threshold function can attain the result under low SNR condition as obtained by the traditional method in Ying-Chang et al., 2008. The proposed method is found to be more robust than that of the traditional method when the number of samples (N) varies. The proposed method has significant role in CR technology as the knowledge acquired about the threshold function for a predetermined range of parameters can later be used as a look up table for deciding the presence of PU. This reduces the computation time as threshold computation need not be carried out every time. The organization of the paper is as follows: after introduction, we discuss traditional energy detection for spectrum sensing in CR under AWGN channel condition, a brief discussion on radial basis function network and its function approximation capability are presented next, then we discuss the proposed computational model followed by numerical simulation results and in the last section one can find the conclusions and future direction of work.

2. Problem formulation for energy detection We present the background for the conventional energy detection in CR environment and further based on this theoretical background we will present our proposal on intelligent energy detection scheme in succeeding sections. 2.1. System model The system consists of one PU and one SU. The problem here is that, SU is trying to detect the presence of PU transmitted signal in certain frequency bands. SU (or called as CR) will then utilize the unused PU channel. To accomplish this task there is a need for sensing the spectrum by CR (or SUs), which is a continuous process carried out by the SUs. It is worth mentioning at this stage that, in this mechanism the location of PU is not known by the CRs (or SUs). The detection of PU transmitted signal by SU is usually based on Binary Hypothesis testing problem (Atapattu et al., 2010; Giucai, Chengzi, Antian, & Xi, 2012; Kalamkar & Banerjee, 2013; Mercedes et al., 2012; YingChang et al., 2008) that is stated as follows {

y(n) =

( ) w(n), Hypothesis 0 H0 = PU Signal Absent ( ) h(n) x(n) + w(n), Hypothesis 1 H1 = PU Signal Present

(1)

where, y(n) is the PU transmitted signal received by SU, and w(n) is the additive white Gaussian noise signal, x(n) is the PU licensed signal and h(n) denotes channel gain. There are different choices of noise nature due to the presence of various practical radio environment available in wireless communication and thus different models of Eq. (2) can be obtained (Atapattu et al., 2014; Ying-Chang et al., 2008), but in our work we invoke following assumptions about noise and the licensed PU signal for the hypothesis in Eq. (1), • Noise w(n) is AWGN and independent and identically distributed[ (i.i.d) random process with zero mean and ] variance E |w(n)|2 = 𝜎w2 . • The primary signal x(n) is also independent and identically distributed [ (i.i.d) ]random process with a zero mean and variance E |x(n)|2 = 𝜎x2. • The primary signal x(n) is independent of the noise w(n) i.e., they are uncorrelated. In view of the first assumption highlighted above, h(n) = 1 and thus Eq. (1) can be rewritten as, { ( ) w(n), H ( 0) y(n) = (2) x(n) + w(n), H1 2.2. Conventional energy detection For detection of PU signal by CRs (or SU) using energy detection method a test statistics is to be constructed by collecting the samples of y(n) at different time indices as indicated below,

Ted =

N 1 ∑| 2 y(n)|| N n=1 |

(3)

where, N is the number of samples and Ted is the test statistics or average energy in the received samples (Umar et al., 2014). The probability density function (PDF) for test statistic is central Chi-Square distribution with N degrees of freedom under hypothesis H0 (Ying-Chang et al., 2008) and non-central ChiSquare distribution under hypothesis H1 with same degrees of freedom as H0. Degrees of freedom are taken to be N as both w(n) and x(n) are considered to be real-valued signals in the proposed work. The test Statistic Eq. (3) is compared with predetermined threshold to make the decision on the presence or absence of the PU transmitted signal by CR (or SUs). The performance metrics for energy detection are PFA (Probability of False Alarm), PMD (Probability of Miss detection) and PD (Probability of detection) that are stated as, ( ) • H1 is true in case of presence of PU signal, i.e., Pr H1 |H1 is known as probability of detection (PD). ( ) • H0 is true in case of presence of PU signal, i.e., Pr H0 |H1 is known as probability of miss- detection (PMD).( ) • H1 is true in case of absence of PU signal, i.e., Pr H1 |H0 is known as probability of false alarm (PFA). The relationship between the first two hypothesis can be obtained as PD = (1 − PMD ). For AWGN as sample mean is zero, so received SNR for the different type of signal models considered in (Atapattu et al., 2014) have the same expression 𝜎2 and is assumed as, SNR = 𝛾 = 𝜎x2 , where 𝜎w2 is noise variance w and 𝜎x2 is the signal average power. In this note compute PD (instead of PMD) and PFA will be computed for obtaining the detection performance.


There are broadly two distinct ways of computing PDFs of test statistics under hypothesis H0 and H1, they are (i) exact (Altrad & Muhaidat, 2013; Atapattu et al., 2014; Umar et al., 2014) and references therein (ii) approximate distribution (Atapattu et al., 2010, 2014; Giucai et al., 2012; Mercedes et al., 2012; Umar et al., 2014; Ying-Chang et al., 2008). The proposed work focuses on the approximate evaluation of PD and PFA based on the work of (Ying-Chang et al., 2008).


2.3. Approximated probability distribution function When the number of samples N are large enough then using Central Limit Theorem (CLT) one can approximate the distribution of the test Statistics as Normal Gaussian Distribution from Chi-square distribution under the binary hypothesis introduced above (Mercedes et al., 2012), (Ying-Chang et al., 2008), (Umar et al., 2014) and references therein. The approximated Probability of false alarm (Giucai et al., 2012; YingChang et al., 2008), can be expressed as,

PFA = Pr (Ted where, Q(x) =

⎛ ⎞ ⎜ 𝜆d − 𝜎w2 ⎟ > 𝜆d |H0 ) = Q⎜ � ⎟ 2 4 ⎜ ⎟ 𝜎 w N ⎝ ⎠

𝛼 −u2 1 √ ∫e 2 2𝜋 x

(4)

approximated Probability of Detection (PD) for real-valued signals (both w(n) and x(n)) for AWGN channel with N degrees of freedom can be written as (Atapattu et al., 2014; Giucai et al., 2012; Ying-Chang et al., 2008),

PD

(5)

where, γ is the received SNR of the signal. The probability of false alarm (PFA) depends on time-bandwidth (N = T × W) product and the threshold as seen from Eq. (4) thus one can find based on PFA as, ) ( √ ( ) 2 −1 2 +1 𝜆d = 𝜎w Q PFA (6) N The expression for threshold based on Eq. (6) is known as constant false alarm rate (CFAR) or sometimes referred in literature as Neyman-Pearson criterion (Giucai et al., 2012; Mercedes et al., 2012; Poor, 1994). One can also consider another similar approach of computing decision threshold 𝜆d from the expression of PD in Eq. (5) and this is referred in Giucai et al., 2012 as constant detection rate (CDR), however in the proposed work CFR approach has been used. The minimum number of samples required for spectrum sensing using energy detection method can be computed using the relation in Eqs. (4)–(5) for a given or specified PD and PF can be found for the considered case following (Giucai et al., 2012; Ying-Chang et al., 2008) as,

( ) ]2 2 [ −1 ( ) N = Q PF − Q−1 PD (1 + SNR) 2 SNR 𝛾 10

To capture this complex relationship between PD, PFA, 𝜆d and N we propose the concept of function approximation using NN of the threshold function for a given number of samples N (as they are independent of each other) and later use this knowledge of the threshold function energy detection utilizing lesser number of N in the test statistics thereby reducing the sensing time (as it directly dependent on N) and enhancing the sensing performance. However it is worth mentioning at this stage that, the number of samples ‘N’ is not chosen to be too small such that it violates CLT. As stated in Atapattu et al., 2014, Article num 2.5.2, the selection of ‘N’ is also an optimization problem. In this work we have allowed ‘N’ to vary within a range without any need of computation such that the minimum number of samples ‘N’ still satisfies CLT. The novelty of the work lies in the fact that while the RBFN has been trained for maximum number of samples, it still allows correct threshold approximation to a significantly lower value of N, thus improving the system latency and simpler detection.

3. Radial Basis Function Network

du is the Gaussian Q-function. The

⎛ ⎞ � 2� ⎜ 𝜆d − 𝜎w (1 + 𝛾) ⎟ = Q⎜ � � 2�⎟ 2 ⎜ 𝜎w ⎟ + 𝛾) (1 N ⎝ ⎠

395

(7)

where, SNR = (10) is expressed in linear scale whereas SNR in dB is given by γ. It is apparent from Eq. (7) that number of samples necessary for computing detections or specifically PD is not dependent on threshold rather on the SNR values, again PD and PF in turn depends on threshold.

The network architecture of RBFN as described in Demuth & Beale, 2001 is explained below for clarity of understanding of implementation and interpretation of results. Fig. 1 shows the architecture of RBFN. The nomenclatures of the architecture are placed in the Table 1 below. There are two different types of implementations of the architecture of RBFN depending upon the number of hidden layers neurons added to the network they are, a) Exact RBFN: In this case the numbers of RB neurons are exactly similar to the number of input elements. b) RBFN with fewer neurons: In this case the numbers of RB neurons are fewer than that of the number of input elements. In the present work we have designed an RBFN with fewer hidden layer (radial basis layer) neuron as the function approximation capability of such network is efficient than that of the former one (Demuth & Beale, 2001). The outputs of the various layers of the RBFN shown in Fig.1 are described below. Considering first the input to radial basis layer output which is given by,

a1 = �(||wki1 − xk ||)

(8)

where, the radial basis function used in this work is a Gaussian function and it is of the form,

) ( w1 − X || �(w, x) = exp −|| 2𝜎 2

(9)

and σ is the spread factor of the Gaussian function and it influences the smoothness of the approximating function. The output from the hidden to output layer of the RBFN is given by,

y = f (X) =

p1 ∑

) ( wi2 � ||wki1 − xk ||

(10)

i=1

where, k = 1, 2, …..N is the index of input and i = 1, 2, …..p1 is the index of hidden neurons, with. It is clear from Fig. 2, as the distance between w1 and X decreases the probability of firing the output out of radial basis neuron increases. The radial basis network is created here by adding one hidden neuron at a time. The addition of the network are done

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Figure 1. Architecture of RBFN.


Table 1. Nomenclature of RBFN architecture. S. No 1 2 3 4 5 6 7 8 9 10

Notation X y W1 W2 B1 B2 p1 P2 Φ(x) a1

Meaning Input vector Output function Hidden layer weight matrix Output layer weight matrix Bias vector of hidden layer Bias vector of output layer Number of neurons in hidden layer Number of neurons in output layer Gaussian Basis function Output of hidden or radial basis layer

Dimension (Nx1) (p1xN) (p2xp1) (p1x1) (p2x1)

of learning only the exhaustive training data presented to the network. When the mean squared error is reduced over the training set to sufficiently low levels then network can predict outputs for unseen inputs giving better generalization of the approximated function. To accomplish this task of generalization the dataset for which function is to be approximated in the present problem has been divided into training and test sets. Further the network performance (MSE) when tested over the test data points have been found to be consistent. To avoid the problem of over fit and achieve a good generalization for the approximated function we tried to find the proper combination of number of hidden layer neurons, spread factor of the basis function and dividing the dataset into training and testing sets. The number of hidden neuron selection points towards the complexity of the network and to achieve a trade-off between good fit and good generalization there must be a limit to the complexity of the model as per bias-variance dilemma (Kumar, 2004) and references there in. 3.2. Design of RBFN

Figure 2. Gaussian basis function used in the hidden layer.

until the mean squared error (MSE), (which is the performance of the network) falls beneath a pre-specified error goal or maximum number of neurons have been reached. The output of the hidden layer is finally passed on through weighted pathways to linear output neuron, which is then summed up to generate final output of the network (f(X)). There is one hidden neuron for each basis function and each basis function has two design parameters; (i) center of a training data point for the Gaussian function and (ii) spread factor of the Gaussian function. The learning mechanism in this network involves finding the optimal weight of the network w2 by reducing the quadratic error function in least square sense. The quadratic error function is of the form, N )2 1 ∑( targetk − f (w, X) 2 k=1 p1 � � ∑ where, f (w, X) = wi2 � ��wki1 − xk �� .

𝜀=

(11)

i=1

3.1. Generalization capability of the network The present work focuses on the generalization capability of the RBFN to accomplish the function approximation task instead

The design of RBFN in the present work has been done using ‘newrb’ routine of neural network tool box of MATLAB (Demuth & Beale, 2001). The selection of number of neurons and the spread factor of the network has been selected by hit and trail by looking at the MSE, performance measure during training and the ability of the network to generalize the test data points (unseen data points) after the training phase of the network is over. For good fit and generalization of the threshold function, maximum numbers of hidden layer neurons are taken as 15, the spread factor of the Gaussian function is taken as 0.41 and error goal of zero is supplied to the network. The approximated threshold function by the network after training and testing phase are shown in the Fig. 3 below. The performance (MSE) minimization for 15 epochs during training of the network as shown in Table 2 and Fig. 4 signifies that the network reached the pre specified error goal as well as the maximum number of neuron before the training ceases. Fig. 5 explains the degree of smoothness of the approximated threshold function with that of the original function in (6) in terms of the variation of squared error w.r.t the output of RBFN to the unseen data presented to the trained network. It can be observed from the Fig. 5 that network could well generalize the function with insignificant amount of error for the unseen data points. The approximated function can be further smoothened by adopting some iterative heuristic algorithm to optimize the


397


Figure 3. Approximation of threshold function using 2 g RBFN for N = 1,000 samples.

Table 2. MSE profile during training. NEWRB, neurons = 0, MSE = 0.00160506 NEWRB, neurons = 4, MSE = 9.83927e-06 NEWRB, neurons = 7, MSE = 7.39243e-07 NEWRB, neurons = 10, MSE = 1.40473e-07 NEWRB, neurons = 13, MSE = 4.7359e-08

NEWRB, neurons = 2, MSE = 8.78078e-05 NEWRB, neurons = 5, MSE = 2.82191e-06 NEWRB, neurons = 8, MSE = 5.74707e-07 NEWRB, neurons = 11, MSE = 1.40721e-07 NEWRB, neurons = 14, MSE = 4.68714e-08

Figure 4. Mean Squared Error (MSE) minimization during training.

spread factor the network, this part will be treated as a future scope of this work.

4. Main results The importance of approximating some of the important Gaussian PDFs used in communication theory has been highlighted in George & Lioumpas, 2007 and references therein due to the difficulty in numerical computation of complicated analytical results. In Nam & Cong, 2003 and Wu, Wang, Zhang, & Du, 2012 and references therein, several attempts have been made towards function approximation using artificial neural network (ANN) to approximate unknown nonlinear and evaluation of derivatives of functions. In this note an attempt has been made for the first time to use the concept of function approximation using ANN to approximate threshold function for energy detection in cognitive radio. The computation of

NEWRB, neurons = 3, MSE = 8.72548e-05 NEWRB, neurons = 6, MSE = 2.42433e-06 NEWRB, neurons = 9, MSE = 1.46114e-07 NEWRB, neurons = 12, MSE = 1.41905e-07 NEWRB, neurons = 15, MSE = 4.68151e-08

threshold function depends directly on inverse Q-function of PFA and inverse of the square root of N, thus the approximation turns out to be the approximation of inverse Q-function, which is accomplished here using RBF network. The motivation behind the proposed work is multi fold, (i) to achieve the same accuracy in the performance receiver operating characteristic (ROC) of spectrum sensing using RBFN based function approximation as compared to the numerical approximation methods of Gaussian PDFs (ii) to achieve the robustness in the approximation results when the number of samples (N) vary within Nmin to Nmaxn without violating the CLT and (iii) to inculcate the philosophy of computational intelligence and memory (knowledge base) while taking decision for the presence or absence of the PU signal. The computational flow chart for the proposed work is shown in the Fig. 6 below for clarity of understanding the proposed technique. The proposed computational scheme is applicable for detection of real valued Gaussian signal model discussed in preceding section. Once the threshold function is learnt by the RBF network it is further used to detect the presence of PU signal using binary hypothesis indicated in equation Eq. (2). To verify the computed PD from Eq. (5) further Monte-Carlo simulation is carried out for 10,000 observations and simulated probability of detection is expressed as, PDsim =

Count of number of detections Number of observations of Monte - Carlo simulation

(12) Computation of ROC is carried out after the probability of detection is computed from (7) for the proposed computational scheme. 4.1. Contributions The major drawback of conventional energy detection under low SNR condition is that of the sample complexity problem


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Figure 5. Squared error variation for the approximated function for unseen data.

The proposed method deploys trained RBFN for approximating threshold within a range of N (Nmin < N < Nmax) satisfying the (6), (7) and (8) according to CLT alleviates the above mentioned drawbacks. We present below the justification of the contributions, (a) The proposed sensing technique as highlighted in Fig. 6 used RBFN for approximating the threshold function in (6) for N (in this case 1,000) > Nmin (as per equation (7)). The approximated λd by RBFN (for N = 1,000) is used for computing PD using (5) for (i) nominal case, N = 1,000 and (ii) reduced number of samples (reduction of 15, 40 and 60% in N are considered) without violating CLT. It is observed from the simulation and statistical results that, following the philosophy of the proposed method, percentage variation of standard deviation (SD) and variance (VAR) of PD is less with reduced N compared to conventional method thereby increasing the PD at low SNR and PFA. Thus the proposed method is robust to the sample complexity of energy detection due the use of pre-trained RBFN within a range of N.

Figure 6. Computational flow chart for ROC using RBF network.

which is of the order of O (1/SNR2) as seen from (7). This results into following consequences, (i) Reduced detection performance under low SNR condition even for low PFA. (ii) At low SNR for better detection performance more number of samples are required, thereby increasing system overall latency.

(b) In addition to the improvement in detection performance with reduction in sample size, it also helps in minimizing the system overall latency as less number of samples (N) may be used as per this scheme to compute PD unlike in conventional method. As reduction of sample size affects the computation of λd which in turn affects PD values. (c) A sensing algorithm with low computational complexity can always achieve high PD with minimum number of samples (N) (Muthumeenakshi & Radha, 2014). The proposed method is computationally simpler and robust than conventional sensing method due to reason highlighted in (a) and thus validates the improvement. (d) The requirement for CR is to learn, adapt and store knowledge and thereby take decisions which are



399

Figure 7. ROC curve for scenario 1.

fulfilled by the use of RBFN in the proposed method, whereas in conventional technique such features are not present. (e) The proposed scheme can carry out sensing even for fading (Rayleigh) channel using approximated λd by pre-trained RBFN for an AWGN channel, but degradation in sensing performance can be observed as these data comes from a separate probability distribution.

5. Simulation results In this section, we present our numerical results to describe the Neural Network based Energy Detector with function approximation capability. We quantify the receiver performance by depicting the ROC i.e., PD Vs PFA for the different situations of interest. First we compare the probability of detection and probability of false alarm calculated from Monte Carlo simulations. In this paper we have considered 10,000 Monte Carlo simulations. The sample size N has been considered as 1,000 for nominal situation and then progressively 15%, 40% and 60% reduction in the number of samples (N) are considered for showing the efficacy of the proposed intelligent energy detection scheme. The sensing performances for the reduced number of samples are carried out using pre-trained RBFN for 1,000 samples. For a given low values of SNR, we vary the range of PFA to obtain the threshold and hence compute PD Vs the considered PFA range and obtain the ROC at a low SNR value. The different scenarios considered are as follows:

function approximated threshold function via RBFN is shown in Figure 7. It is clear from the figure that the RBF network has learnt the function appropriately. Thus we obtain exactly similar sensing performances in both the cases, i.e., conventional energy sensing and Neural Network based sensing. 5.2. Scenario 2 Next, we consider 15% reduced number of samples (than that of nominal case, N =1,000), SNR is taken to be -10 dB and Monte Carlo Simulations for 10,000 realizations is carried out, the range of PFA is swept from 0.01 to 1. In this scenario pre-trained RBFN for N = 1,000 samples is used for detection with 15% reduced sample size. The proposed scheme need not calculate the threshold again for the reduced sample size and the knowledge stored in the pretrained RBFN for the approximated threshold for nominal case (N =1,000) can be used for detection purpose. It is worthy to mention here that, this philosophy cannot be implemented in a Conventional Energy Detector using (5) and (6) as the computation of the threshold has to be carried out for the reduced samples before the detection is performed. The ROC curve for this scenario is shown in the Fig. 8, which depicts better sensing performance of NN based sensing compared to conventional sensing. This scenario is a direct consequence of adverse conditions of the transmission channel, or intentional assumption of less number of samples being transmitted in an attempt to reduce the sensing time [N =T ×W (T =time and W = Bandwidth)]. 5.3. Scenario 3

5.1. Scenario 1 Here we consider number of sample, N as 1,000, SNR as -10 dB and Monte Carlo Simulation is carried out for 10,000 realizations. RBFN is trained for the range of PFA from 0.001 to 0.99 to approximate threshold function for considered N, we refer this case as a nominal situation. Under this scenario, the ROC curve obtained through simulation using (5) and using the

The condition considered in scenario 3 depicts the sensing performance for IEEE 802.22 WRAN standard for which the range of PFA is purposefully taken as 0.01 to 0.1. The pre-trained RBFN (for N =1,000) is used for detection with 15% reduced number of samples (N) for SNR of −30 dB. Figure 9 shows the comparison in the sensing performance between Conventional and Neural Network based sensing.


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5.4. Scenario 4 As in the case of scenario 3 we consider PFA = 0.001 to 0.1 as per the WRAN standard, number of transmitted samples is considered to be 40, 60 and 80% reduced compared to the nominal case (N =1,000) with a very low value of SNR = −30 dB. A family of ROC curves are presented in Fig. 10 to show the efficacy of the pre-trained RBFN (for N =1,000) to reduced number of samples and a very low value of SNR in terms of detection performance at a low value of probability of false alarm compared to conventional energy detection method. 5.5. Scenario 5 In this section we compare the ROC curve for detection through AWGN and Rayleigh fading channel as shown in Fig. 11. It can be observed that probability of detection falls considerably in case of Rayleigh fading channel when the approximated threshold for AWGN channel is used of

detection for same number of samples N and SNR = −10 dB. The threshold approximated by RBFN does not fail completely rather under low SNR condition the performance of detection will be degraded. The detection performance can be improved by using suitable threshold function for the Rayleigh fading channel as the data for this process comes from different probability distribution. The statistical parameter presented in Table 3 indicates that standard deviation and variance of the PD closely matches for both the cases even when detection for reduced N in the proposed method is carried out using pre-trained threshold function for N = 1,000, which is not the case of conventional technique. 5.6. Statistical validation of the proposed method The relation between PD and 𝜆d as indicated in (5) for a given SNR is depicted in Fig. 12. In the proposed method we train our RBFN with N =1,000 for approximating the threshold function and later use this same pre-trained RBFN to carry




Figure 11. Comparison of detection performance between AWGN and fading channel. Table 3. Statistical Variations of PD and 𝜆d. RBFN Variance and standard deviation of PD and 𝜆d N for 𝜆d computation 1,000 for 𝜆d approximation Standard deviation of PD 0.0545 Variance of PD 0.0030 Standard deviation of 𝜆d 0.0307 Variance of 𝜆d 9.4392e-04 Variance and standard deviation of PD computed by RBFN for 15% reduced N N for 𝜆d computation Pre-trained RBFN (N = 1,000) Standard deviation of PD 0.0591 Variance of PD 0.0035 Standard deviation of 𝜆d 0.0307 Variance of 𝜆d 9.4392e-04 Variance and standard deviation of PD computed by RBFN for 40% reduced N N for 𝜆d computation Pre-trained RBFN (N = 1,000) Standard deviation of PD 0.0716 Variance of PD 0.0051 Standard deviation of 𝜆d 0.0307 Variance of 𝜆d 9.4392e-04 Variance and standard deviation of PD computed by RBFN for 60% reduced N N for 𝜆d computation Pre-trained RBFN (N = 1,000) Standard deviation of PD 0.0784 Variance of PD 0.0062 Standard deviation of 𝜆d 0.0307 Variance of 𝜆d 9.4392e-04

Conventional 𝜆d for N = 1, 000 0.0544 0.0030 0.0305 9.3157e-04 𝜆d for N = 850 0.0671 0.0045 0.0331 0.0011 𝜆d for N = 600 0.0988 0.0098 0.0394 0.0016 𝜆d for N = 400 0.1311 0.0172 0.0483 0.0023

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Figure 12. Variation of PD with 𝜆d for different samples.

out the detection for reduced number of sample (15, 40 and 60%) thereby making the relation between PD and 𝜆d in (5) independent of N, whereas for conventional computation it is sensitive to N. The result presented in Fig. 12 validates that the pre-trained RBFN (for a given samples) can capture the relation well between PD and 𝜆d in (5) while the model was not trained to learn the function in (5). Further it can be observed from Table 3 that, the percentage change in standard deviation and variance of PD using the proposed method is lesser than that of conventional technique with the change in the value of N due to the philosophy of using pre-trained 𝜆d for N =1,000, which is not the case in the later case. This statistical parameter variations points towards robustness of the proposed technique and thereby improving the detection probability at low false alarm probability for reduced number of samples as shown in Fig. 12.

6. Conclusions A simple yet computationally intelligent energy detection scheme for sensing the PU signal by CR has been proposed in this work. The work focuses on the central theme of CR that has the ability to learn, adapt, acquire knowledge and take decision. To accomplish this task a RBFN has been used to learn the threshold function for a given range of PFA and number of samples N. After the neural network is trained to approximate the function, it is then used for sensing the spectrum. The inclusion of this feature makes the sensing more robust under the uncertain condition of number of samples being transmitted by deliberately transmitting less number of samples, in order to reduce the sensing time (as sensing time directly depends on the number of samples). Unlike conventional energy detection, the proposed intelligent energy detection scheme does not compute threshold every time by taking an input, rather it uses pre-trained knowledge of the learnt threshold function, depending on the minimum number of required samples for given PFA. As a future scope of work the proposed computational intelligent philosophy can be used straight forward to modify available computationally complex sensing techniques to be more intelligent and efficient.

Acknowledgements The authors convey heartfelt thanks to all the anonymous reviewers for their valuable suggestions that have greatly improved the readability and understanding of the present work.

Disclosure statement No potential conflict of interest was reported by the authors.

Notes on contributors Barnali Dey is currently working as an Assistant Professor at Sikkim Manipal Institute of Technology, Sikkim. She is a Ph.D. scholar (part time) at the National Institute of Technology, Silchar Assam, India. She obtained her B.Tech and M.Tech from Sikkim Manipal Institute of Technology under Sikkim Manipal University, Sikkim, India in the year, 2007 and 2011 respectively. Her fields of research interests are cognitive radio, soft computation and digital communication system. A. Hossain obtained B.Tech. and M.Tech. degrees in Radio Physics & Electronics from the Institute of Radio Physics & Electronics, University of Calcutta, Kolkata, India in 2002 and 2004, respectively. He received a Ph.D. degree in Electronics & Electrical Communication Engg., from Indian Institute of Technology (IIT), Kharagpur, India in 2011. He has served Dept. of Electronics & Communication Engg., Aliah University, Kolkata and Haldia Institute of Technology as Asst. Professor. He is currently working as an Assistant Professor in the Dept. of Electronics & Communication Engg., National Institute of Technology (NIT), Silchar, Assam, India. His research interests include wireless sensor network, communication theory and systems. He is a member of IEEE and IE (India). A. Bhattacharjee obtained a Bachelor’s degree (B. Tech.) in Computer Science and Engineering from Guwahati University in India. He also holds a Master’s Degree (M. Tech.) from Computer Science and Engineering Department of Jadavpur University (India). He has obtained a Ph.D. degree from the National Institute of Technology Silchar in India in 2012. He has worked as a Software Engineer and he is currently with the National Institute of Technology Silchar (India). His research interest includes quality of service in computer networks, network traffic modeling.



Rajeeb Dey obtained his B.Tech (Electrical Engg) from NERIST in 2001 and M.Tech (Control Systems) from IIT Kharagpur in 2007. He received Ph.D. from Jadavpur University in 2012 in Control System Engineering. Dr. Dey is currently working as an Assistant Professor in Electrical Engineering Department, National Institute of Technology, Silchar, India. His research interest includes control and computation. He is a senior member of IEEE and IEEE Executive member for control system society, Kolkata Section since its inception. R. Bera is a professor and Ex-Dean (R&D), HOD (ECE) at Sikkim Manipal Institute of Technology, Sikkim Manipal University and Ex-reader of Calcutta University, India. He was awarded B.Tech, M.Tech and Ph.D. degrees from the Institute of Radio-Physics and Electronics, Calcutta University. His field of interests are in the area of digital radar, RCS imaging, wireless 4G and 5G mobile communication, cognitive radio, radiometric remote sensing, smart antenna based embedded system He has published large number of Journal papers in reputed Journals and two books.

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