A Hybrid Cooperative Spectrum Sensing Technique

for Cognitive Radio Networks Using Linear

Classifiers

Mohamed Gaafar, Yasmine Hassan and Tallal Elshabrawy Communications Department, German University in Cairo

Cairo, Egypt Email: muhamed.gaafar@gmail.com

Abstract-In this paper, a hybrid cooperative spectrum sensing technique ( HCSST) is proposed merging between energy detection (ED) and cyclostationary feature detection (CFD) such that both low computational complexity as well as the superior detection performance are achieved. In HCSST, individual Cognitive Radio (CR) nodes decide independently on using ED or CFD as their spectrum sensing technique based on the received signal-to-noise ratio at each cognitive end. Cooperative decision about spectrum availability is made using a trained linear classifier (LC) at the fusion center (FC) . Results have shown that HCSST provides superior performance over ED and a slightly degraded performance compared to CFD. Further, the computational complexity is reduced noticeably at high SNR regimes.

Index Terms-Cognitive Radio, Cooperative Spectrum Sensing, E nergy Detection, Cyclostationary feature detection, Linear Classifier

I. INTRODUCTION Cognitive Radio (CR) is a promising technology to solve

the spectrum scarcity and the inefficiency in spectrum usage problems. The key characteristic of CR systems is sensing the electromagnetic environment to adapt their operational parameters to the dynamic radio environment. CR networks improve the spectrum utilization by allowing unlicensed secondary users (SUs) to opportunistically use frequency bands not utilized by licensed primary users (PUs). SUs in CR networks are restrained by causing no interference to PUs. Hence, they need to employ effective and efficient spectrum sensing techniques that ensure the Quality of Service (QoS) for PUs and exploit all dynamic spectrum opportunities [1].

Spectrum sensing is one of the main challenges that researchers face in the dynamic opportunistic spectrum access. It is responsible for providing efficient and fair spectrum access among licensed and unlicensed users and mitigating interference with PUs. Spectrum sensing techniques can be divided into two main categories: parametric and non-parametric. In parametric spectrum sensing, a prior information about the transmitted signal should be known to SUs such as operating frequency, bandwidth, modulation type, etc. On the other hand, in non-parametric methods, a prior knowledge about the

transmitted signal does not have to be available at the CR node. The performance of the parametric algorithms is usually better than of the non-parametric techniques. However, if non-accurate information is used in parametric algorithms, the detection performance degrades significantly. In this paper, a sensing scheme merging between a non-parametric technique which is Energy Detection (ED) and a parametric one which is Cyclostationary Feature Detection (CFD) is proposed. The overall objective of any spectrum sensing scheme is to minimize the false alarm probability Pj (no PU is transmitting but the CR decides that the spectrum is not idle) while maximizing the detection probability Pd (there is a PU and the CRs decide that the spectrum is not available).

ED is the most common spectrum sensing technique due to its simplicity and not requiring any prior knowledge about the transmitted signal to be detected. Further, it has low complexity [2]. However, the performance of ED is degraded greatly in low signal-to-noise (SNR) ratio. On the other hand, CFD has a robustness detection in low SNR conditions. However, its implementation and computational complexity is very high compared to ED [3].

Real world constraints may affect the detection performance of the spectrum sensing algorithms such as noise uncertainty, multipath fading and shadowing effects [4][5]. The key solution to all these problems is cooperative spectrum sensing. It takes advantage of the spatial diversity, i.e. different channel conditions, in which CR nodes cooperate together to make the global decision. The global decision can be made in a fusion center (FC) according to hard decision rules, such as logical OR, AND, N-out-of-M rules, or soft decision rules, such as likelihood ratio test, soft linear combining, polynomial classifiers [1] [6].

Cooperation of cognitive users is performed utilizing a soft decision rule, in which a linear combination of received energies is used to make a decision in [7]. The advantage of linear combining is that users with better channel conditions are given higher weights in making the decision. Hence, more reliable decision is obtained. However, the problem of finding the optimal combing weights becomes more challenging when multiple sensing techniques are utilized in the proposed scheme. In [6],

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the performance of pattern recognition models such as linear and polynomial classifiers has been studied as a soft decision combining rule for energy detection. Results indicated that both classifiers have comparable performance in terms of the detection probability. Hence, in this paper, a linear classifier (LC) will be utilized for global decision making where the weights are obtained through a supervised pattern recognition model. LCs are chosen here due to their reduced complexity and similar performance to polynomial classifiers.

The rest of the paper is organized as follows: In Section II, we present the problem formulation and system model. Section III illustrates the ED and CFD techniques. The proposed technique is fully investigated in Section IV. Linear classifier based cooperative Soft decision rule is explained in Section V. Simulation results are given in Section VI. Section VII concludes the paper.

II. PROBLEM FORMULATION AND SYSTEM MODEL In this paper, we consider spectrum sensing in a CR

network consisting of !vI CR nodes with a central node (i.e. FC ) that decides on the channel availability. PU network and CR network are assumed to be present within the same geographical area. CR nodes must not cause harmful interference to PUs.

In the proposed system, SUs are constantly sensing the spectrum band for primary signal detection. \Vithin a SU receiver, discriminative features are extracted from the observed signal based on one of the spectrum sensing techniques discussed in Section III. The features are transmitted to the FC through a relatively low data rate control channel. A global decision is made by CR base station using LC that is discussed in Section V. The binary hypothesis test for spectrum sensing is formulated as follows:

(1)

where i = 1,2, ..... !vI, Ydn] is the received signal by the ithreceiver at the nthtime instant, x (n) is the PU's signal to be detected. Further, Ho represents the null hypothesis meaning that there is no primary signal and only A\VGN noise, ni(n) with variance 17; , exists, while HI describes the existence of a PU's signal in addition to AWG N noise, ni (n) . The primary signal is passed through a wireless channel with channel gain equivalent to hi which is modeled as a slow fiat rayleigh fading channel, i.e. the coherence time of the channel Tc is set to be much larger than the primary signal's symbol duration Ts.

Different CR nodes are assumed to have independent and identically distributed (i.i.d. ) channel coefficients. The ith CR is assumed to receive a signal with S N Ri that differs according to its position from the PU. The SN Ri (in dB) follows a normal distribution with a variance 172 and mean equivalent to SN Ravg to account for the large scale path loss.

III. PRIOR SPECTRUM SENSING TECHNIQUES Over the past few years different techniques were pro

posed for spectrum sensing based on energy detection (ED) and cyclostationary feature detection (CFD) .

A. Energy Detection (ED) ED is one of the most commonly used methods in

spectrum sensing as it is simple to implement and does not require any prior information about the transmitted signal to be detected. Furthermore, it has reduced execution time, low computational and implementation complexity. The detection statistics Ti is defined as follows:

(2)

where i = 1,2, ... , !vI. N is the number of samples during one observation period and Ydn] is the received signal by the ithreceiver. The decision rule at each CR node is given by:

(3)

where Ai is the decision threshold. The selection of the threshold in ED depends on the noise power; hence, it is highly affected by noise uncertainty. Furthermore, in low signal to noise ratio (SNR) regimes, reliable detection of the transmitted signal is cumbersome.

B. Cyclostationary Feature Detection (CFD)

As most communication signals introduce built-in periodicity in their mean and autocorrelation, they can be modeled as cyclostationary random processes. This underlying periodicity is produced as a result of coupling stationary message signals with sinusoidal carriers, cyclic prefixes, sampling, etc. The spectral correlation density (SCD) of a cyclostationary signal is the Fourier transform of its cyclic autocorrelation function (CAF ) as follows [8]:

6.t

S(j) = lim lim T

1" /2 YT (t , j + ) Y;' (t , J - ) dt T--'tCXJ t--'tCXJ ut 6.t 2 2 -2

where

t+ T YT(t , l) = 1 "2 y(m)e-j27rmldm

t-

(4)

(5)

is the complex envelope of the spectral component of y(t) , a is the second order cycle frequency, J = j, is the frequency resolution and t is the averaging time over which the SCD is estimated. It is obvious from (4) that the SCD represents the temporal cross correlation between shifted versions of the signal y(t) in the frequency domain by . The hypothesis model of the CFD is as follows:

(6)

where Si;, represents the SCD of the A\VGN at a certain cyclic frequency a = ao when no signal is present, h is the channel gain due to shadowing and multipath fading and S;:,o [k] is the SCD of the primary signal. The decision rule at each CR node is given by:

HI

T'Y t < It (7) Ho

where Ii is the decision threshold. The CFD has a robustness detection in low SNR regime. However, its computational complexity is very high compared to the ED method.

IV. PROPOSED SYSTEM As illustrated in Section III, CFD has a better detection

performance than ED for the same average received SNR. ED has many advantages such as short execution time, simplicity and not requiring any prior knowledge of the PU's signal. Thus, it is considered as the optimum spectrum sensing technique at good SNR regimes. On the other hand, CFD has a better performance even under bad SNR conditions. However, its high complexity, processing time and necessity of prior knowledge of the PU's signal give birth to the idea of merging the two techniques together in order to get a good performance comparable with CFD detection performance with much less complexity and processing time. This method is called hybrid cooperative spectrum sensing technique (HCSST).

A. Principle of HCSST In HCSST, ED can be utilized by CR nodes till a certain

SNR threshold SN Rtf!) satisfying a certain requirement on Pd. In other words, ED can be used if the average received primary signal's SNR is above this SNR threshold; otherwise, CFD will be deployed. Hence, when the average received SNR is above the SNR threshold, the required detection performance can be achieved with less complexity and execution time due to adopting ED. On the other hand, when the average received SNR is below the SNR threshold, CFD is adopted and the detection performance is way better than the case if ED is deployed. The block diagram of the proposed method is depicted in Figure 1.

After each CR node selects the sensing technique based on the average received SNR, it transmits its calculated features, energy or peaks of the SCD, to the FC which makes the global decision using LC. The detailed explanation of LC is shown in Section V. Overall, HCSST makes use of the short processing time of ED at good SNR regimes and the better performance of CFD at low SNR regimes. Hence, the overall complexity and sensing time is greatly reduced compared to the CFD time and the

3

Rx Signal

1 SNRavg >= SNRth

ED eFD

Figure 1. Block diagram of the proposed method adaptation

detection performance is much better than the detection performance of ED.

B. Selection of the SNR Threshold

The detection performance of ED degrades severely at low SNR regimes. Hence, the SNR threshold (SNRth) at which the CR network must convert to CFD, must be determined based on ED detection performance. In this work, SNRth is defined as the average received SNR at which Pd is smaller than 90% at Pf of 10% in order to fulfill the requirements of the IEEE 802.22 standard [9]. SNRth can be derived as follows: When AWGN only presents in the spectrum with variance o'f, ED detection statistics Ti will be the sum of the square of N zero mean Gaussian random variables. Hence the detection statistics will have a central Chi-square distribution with N degrees of freedom. \Vhereas, when the primary signal is present the detection statistics will have a non-central Chi-square distribution with N degrees of freedom as follows [7]:

(8)

where

(9)

is the local SNR at each CR node. Es is the signal energy of PU and hi is the channel gain. The average SNR at the

E Ihl2 output of the local energy detector is equal to ----:-:--+-. :v OJ i

For a large number of samples N, Ti can be consIdered asymptotically normally distributed with mean:

4

and variance

The SN Rth can be derived as follows:

ex) 2

(10)

(11)

(12)

where the Q-function is defined as vkr Ix exp( - )du. -1

By taking Q , squaring of both sides and defining a number 2 as follows:

2 = A; -2N (J"; [Q-l (Pd(i)) r -2AiO"; N + N2(J"; (13) vVe can derive the following equation:

(J";T); + (2N(J"; -2Ai(J"; -4(J";[Q-l (Pd(i) ) ]2) T)i +2 = 0 (14)

By solving (14), one can get the value of T)i and calculate S N R;; as follows:

SNR(i) = T)i

th N (15)

In this case, each CR node selects S N Rth to achieve Pd of 90% at Pf of 10% at each node.

C. Complexity of HCSST The main aim of the HCSST method is to reduce the

computational complexity with respect to CFD. Here, we need to note that we are considering Software defined Radios (SDRs), hence there is no hardware complexity is considered. The main complexity comes due to the number of operations needed to be performed. Table I shows the computational complexity of ED and CFD for single user where L is the smoothing window size [10]. It is clearly shown that the computational complexity of CFD is very large, approximately log2 N times, comparable with ED. The complexity of HCSST can be formulated as follows:

O(HCSST) = O(ED) *Pr(ED) +O(CFD) *Pr(CFD) (16)

where O(x) is the complexity of the method (x) and Pr(x) is the probability that a CR node selects the method (x). As mentioned in Section II, SNRi follows a normal distribution with mean SN Ravg and variance (J"2, hence its probability density function (PDF) is as follows:

1 1 y-SNRavg ( ( ) 2)

fSNRi (Y) = (J"y'27T

exp -"2 (J" (17)

Pr(ED) = Pr(SNRi > SNRth)

_ 1 != ( 1 ( Y-SNRavg ) 2) d' - -- exp -- Y (J"y'27T SNRth 2 (J"

(18)

(19)

By solving the integral in (19) , we can formulate Pr(ED) as follows:

Pr(ED) = Q (SNRth SNRavg )

therefore:

(20)

Pr(CFD) = l-Q (SNRth SNRavg ) (21)

Hence, the complexity of HCSST can be calculated using (16).

Table I ROUGH COMPUTATIONAL COMPLEXITY OF THE ED AND CFD

METHOD

Technique Real Multiply Real Add CFD 2N log2 N + 5L 3N log2 N + 3L

ED 4N 3N

V. LINEAR CLASSIFIER BASED COOPERATIVE SOFT DECISION RULE

Spectrum sensing in CR networks has been introduced as a pattern recognition problem [6]. Generally speaking, the main aim of pattern recognition is assigning a signal to one of a number of known categories based on features derived to emphasize commonalities between those signals. Typically, pattern recognition is used to address problems including speech and face recognition. Input signals that need to be classified are usually referred to as patterns. In most cases, patterns are not useful for classification, and they need to be pre-processed in order to acquire more useful input to the classifier. This processed information is called features and the process of acquiring them is called feature extraction. Pattern recognition is used at the cognitive network FC to detect the available spectrum holes so that detection probability is maximized for a desired false alarm rate [6]. Cognitive users monitor the spectrum through the appropriate sensing scheme according to the received SNR. The sensed information by each user provides discriminative features to the FC. At the FC, the received features are applied to the designated classifier model where a global decision is made about the presence of primary transmission.

As shown in Figure 2, the steps of the global decision making can be summarized as follows: The first step, sensing, involves collecting the signal received by antennas at different CR receivers. The following stage is the feature extraction, in which each CR computes more useful data ti, i.e. energy or peaks of cyclic spectrum, after deciding on the appropriate sensing scheme to be used. Thereafter,

the extracted features are applied to the designed classifier at the FC to obtain a global decision variable. Features extracted by any of the above sensing schemes will follow a certain pattern when the spectrum is occupied by a primary user. The pattern extracted would be different when only noise is present in the spectrum. The difference between these two patterns will be exploited as discriminative input data to the classifier for decision making. In this paper, the classifier model to be implemented for spectrum sensing in CR network is LC. The problem of spectrum sensing can be formulated as a multiinput single-output (MISO) polynomial classifier. Features extracted by different receivers, t [tl ... t M], form an !vIdimensional input vector to the classifier. The classifier is required to provide a single output score Yd, representing the decision of whether or not a primary signal is present. The output score fi is obtained at the output block after linearly combining the expansion terms t as follows:

(22)

where Wi is the model of class i. Hence, each feature ti received from a certain CR is multiplied by a weight according to the received SNR. Therefore, users with higher reliability are given higher weight in making the global decision on spectrum availability. In supervised pattern recognition, a set of training data is assumed to be available and the classifier model weights are obtained by exploiting this a prior known information. Once the model parameters are estimated, the model can be used to classify new novel data. Assuming a set of training data M, which is a Q x !vI matrix where Q is the number of feature vectors used in the training process and lvI is the dimensionality of the input feature vectors (provided by lvI CR users). Our goal is to solve for the best model parameters {wd that minimizes the Euclidean distance between Ii in (22) and the desired ideal output {zd for class i. The ideal output Zi is a column vector of length Q consisting of elements equal to ones for the indices corresponding to primary signal present and zeros otherwise. LC is trained to find an optimum set of weights, w that minimizes the Euclidean distance between the ideal target vector Zi and the training matrix M using meansquared error as objective criterion, by solving the problem in (23).

opt wi = arg minllMw-zil12 (23)

w

The problem of (23) can be solved using the method of normal equation:

(24)

which is used to compute class models {Wi }, i = 1,2. After training, the estimated class models {Wi} are used for classification of novel data sets. At the end, the output score Ii is compared to a threshold A to decide on Hi, for i = {O, I}, corresponding to the binary hypothesis in (1).

r---,-------, : ..:...I : CR, CR",

6

is better than the performance of the ED method and it is very close to the CFD method. For example, at SNRavg = -18 dB, Pd is around 0.2, 0.76 and 0.84 for ED, HCSST and CFD respectively. For Pd of 90%, the required SNRavg is -16 dB, -14 dB and -7.5 dB for CFD, HCSST and ED respectively resulting in a gain of 6.5 dB for HCSST over ED. Moreover, CFD is better than HCSST by around 2 dB only on average.

Figure 4 shows the complexity comparison between ED, CFD and HCSST. The results clearly show that the complexity of HCSST is significantly reduced compared to the CFD. At low SNR values, SNRavg < -10 dB, the complexity of HCSST and CFD are almost equal and for SN Ravg 2': -10 dB, the complexity of HCSST starts to decrease rapidly and the detection performance is very close to CFD. For example, at SNRavg = -2 dB, the complexity is 1.7 x 104, 6 x 104,12 x 104operations for ED, HCSST and CFD respectively.

"O : :0 ro .0 E c. c o U Q) 1ii o

-20 -15 -10 -5 Average received SNR (dB)

o

Figure 3. The detection performance of ED, CFD and HCSST

11 (f) 2 10 Q) 8" 9 ...J 8 " @ 7 o S;! 6 c;; 5 >. 'lOi 4 Q) Q. E 3 o u

2

Average Received SNR (dB)

5

Figure 4. The computational complexity of ED, CFD and HCSST

VII. CONCLUSIONS In this paper, a novel hybrid cooperative spectrum sens

ing technique (HCSST) is proposed. HCSST combines ED and CFD according to a certain SNR threshold (SNRth). Cooperative decision about existence of PU's signal is made using a trained linear classifier (LC ) at the fusion center (FC ) . The mathematical expression of SN Rth is derived based on the detection performance of ED. The overall complexity of HCSST is calculated mathematically. Simulation results show that the overall computational complexity, sensing time of HCSST are significantly reduced compared to CFD and the detection performance is much better than the performance of ED and comparable with CFD.

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