A Novel Framework for Spectrum Sensing in Cognitive Radio Networks
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PAPER
A Novel Framework for Spectrum Sensing in Cognitive Radio Networks Navid TAFAGHODI KHAJAVI†a) , Siavash SADEGHI IVRIGH†b) , Nonmembers, and Seyed Mohammad-Sajad SADOUGH†c) , Member
SUMMARY Cognitive radio (CR) is a key solution for the problem of inefficient usage of spectral resources. Spectrum sensing in each CR aims at detecting whether a preassigned spectrum band is occupied by a primary user or not. Conventional techniques do not allow the CR to communicate with its own base station during the spectrum sensing process. So, only a part of the frame can be used for cognitive data transmission. In this paper, we introduce a new spectrum sensing framework that combines a blind source separation technique with conventional spectrum sensing techniques. In this way, the cognitive transmitter can continue to transmit during spectrum sensing, if it was in operation in the previous frame. Moreover, the accuracy is improved since the decision made by the spectrum unit in each frame depends on the decision made in the previous frame. We use Markov chain tools to model the behavior of our spectrum sensing proposal and to derive the parameters that characterize its performance. Numerical results are provided to confirm the superiority of the proposed technique compared to conventional spectrum sensing techniques. key words: cognitive radio, spectrum sensing, blind source separation, covariance spectrum sensing, Markov chain modeling
1.
Introduction
Cognitive radio (CR) technology [1] allows secondary users to access spectrum bands allocated to primary users (PU) in an opportunistic manner. To avoid the interference on primary transmission, the CR has to sense the spectrum constantly in order to stop transmission when it senses that the primary user is in operation [2]. However, due to channel fading conditions and due to the so-called hidden terminal problem [3], spectrum sensing is usually imperfect and imposes interference on the primary network. Employing multiple cognitive users in order to exploit the available spatial diversity, is referred to as cooperative spectrum sensing and improves the detection reliability. In cooperative spectrum sensing methods, each CR user senses the spectrum during a sensing period and sends its sensed signal or its decision in a particular spectrum band allocated to the PU to the cognitive base station (BS). In conventional cooperative spectrum sensing methods based on energy detection (ED) [4], [5] and covariance detection [6], [7], spectrum sensing is usually performed at the Manuscript received January 11, 2011. Manuscript revised May 4, 2011. † The authors are with the Cognitive Telecommunication Research Group, Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University G.C., 1983963113, Tehran, Iran. a) E-mail: [email protected] b) E-mail: [email protected] c) E-mail: s [email protected] DOI: 10.1587/transcom.E94.B.2600
beginning of each frame with the requirement that the cognitive transmitter does not communicate with its BS during this operation. Obviously, this requirement degrades the spectral efficiency, especially when the cognitive transmitter was in operation and the decision of spectrum sensing is to maintain the cognitive transmission. In energy detection [4], [5], the energy of the received signal is measured and used as a metric to determine whether the primary user is present or not. Also, a new spectrum sensing method based on energy detection is proposed in [8] which improves the total achievable throughputs of the network. In covariance detection [6], [7], spectrum sensing is performed based on the eignvalues of the covariance matrix of the received signal calculated at the cognitive BS. One recent method in this regard relies on the difference that exists between the eigenvalues of the received signal covariance matrix when the primary signal is not in operation. For instance, the differences between statistical distributions of the eignvalues of the signal covariance matrix and Gaussian noise covariance matrix are shown in [7]. In [7], covariance detection is implemented in such a way that there is no need to dispose an estimate of the noise power [9]. Moreover, a new cooperative spectrum sensing method based on the IEEE 802.22 proposal for active cognitive network has recently been proposed in [10], where the cognitive users sense the spectrum while one of them transmits its data. In addition, a study on the interference imposed by the cognitive network on the primary transmission is presented in [11]. Blind signal processing (BSP) is one of the areas in signal processing with solid theoretical foundations and many potential applications [12]. State of the art spectrum sensing methods such as energy detection and covariance detection cannot sense the mixed primary and secondary signals. So, in order to overcome the limitation of these methods, spectrum sensing based on blind source separation (BSS) was recently proposed and investigated in [13]–[15], for instance. Note that BSS spectrum sensing does not require any prior information about the primary signal and performs well for correlated signals. In [13], BSS is proposed to separate the mixed primary and secondary signals, in a multiantenna scenario. In [14], BSS is used inside a cooperative spectrum sensing scheme to improve the detection reliability. Recently in [15], a new BSS metric is proposed to determine whether the primary signals is present or not. In this paper, we propose a new spectrum sensing framework that combines the BSS approach with conven-
c 2011 The Institute of Electronics, Information and Communication Engineers Copyright
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tional spectrum sensing. More precisely, we propose to alternate between correlation spectrum sensing and BSS spectrum sensing in a constructive manner. In this joint method, unlike conventional spectrum sensing methods, there is no need for the cognitive signal to be synchronized with the primary signal. In other words, the CR can transmit its data even during the spectrum sensing process. We will see that this feature not only increases the total achievable throughputs but also improves the accuracy and reliability of the spectrum sensing process. Moreover, we model the proposed spectrum sensing method by a four-state Markov chain that we use to analyze the behavior and to derive the performance measures associated with our proposed technique. The rest of this paper is organized as follows. Our spectrum sensing system model is introduced in Sect. 2. In Sect. 3, we introduce the covariance based detection and the BSS spectrum sensing as the two main components of our framework. Section 4 describes our improved spectrum sensing framework. In this Section, we also derive analytically the performance measures characterizing our proposed framework. Section 5 provides simulation results and some discussions about the performance of the proposed technique. Finally, Sect. 6 draws our conclusions. 2.
Spectrum Sensing System Model
Sensing the presence of a primary transmitter inside a given frequency band is usually viewed as binary hypotheses problem with H0 denoting the absence of the primary signal, and H1 denoting the presence of the primary signal, as ⎧ ⎪ ⎪ ⎨H0 : primary user is not in operation, (1) ⎪ ⎪ ⎩H1 : primary user is in operation. 1 to denote the decision made 0 and H Similarly, we define H by spectrum sensing about the absence and the presence of the primary signal, respectively. We have ⎧ 0 : CR decides that the primary user is ⎪ ⎪ H ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ not in operation, ⎪ ⎨ (2) ⎪ ⎪ ⎪ 1 : CR decides that the primary user is ⎪ ⎪ H ⎪ ⎪ ⎪ ⎪ ⎩ in operation. The above hypotheses are usually used to define the following conditional probabilities 0 | H1 , (3) Pm = P H and
1 | H0 . Pf = P H
(4)
The conditional probability in (3) (referred to as missdetection probability) is a performance metric for cases where the CR fails to detect the presence of the primary signal whereas equation (4) (referred to as false-alarm probability) is another performance metric for cases where the CR
Fig. 1 Architecture of the considered cognitive radio network. In this architecture, both the primary and the cognitive networks can transmit their respective signals over the same bandwidth.
fails to detect the absence of the primary signal [16]. Figure 1 depicts the considered cognitive system composed of J cognitive terminals that perform cooperative spectrum sensing. In our model, when the spectrum is allocated for secondary transmission, one of the CR terminals (denoted by cognitive transmitter as shown in Fig. 1) has the permission to communicate with the cognitive BS. Obviously, if primary and cognitive users are in operation simultaneously, the signal received at the j-th ( j = 1, ..., J) CR user can be written as x j = h1, j sPN + h2, j sCN + z j ,
(5)
where the vectors x j = [x j,1 , . . . , x j,L ]T , sPN = CN T T CN = [sCN [s1PN , . . . , sPN L ] and s 1 , . . . , sL ] respectively denote the symbols received during spectrum sensing, the primary transmitted symbols and the secondary transmitted symbols during the sensing period; the noise vector z j = [z j,1 , . . . , z j,L ]T is assumed to be zero-mean circularly symmetric complex Gaussian (ZMCSCG) with distribution z j ∼ CN(0, σ2z j IL ), L is the number of sensing symbols, and hi, j is the channel coefficient that follows a Rayleigh distribution i.e., hi, j ∼ CN(0, σ2h ). Channel coefficients are assumed to be constant during a frame and change to new independent values from one frame to another, i.e., we assume a quasi-static channel model. Equation (5) can be rewritten in a more compact form as ⎧ ⎪ 1 , H0 }, ⎪ under {H ⎨z j (6) xj = ⎪ ⎪ ⎩R j + z j otherwise, 1 , H0 } indicates that the CR transmitter does not where {H transmit since it has decided that the primary is in operation, and the primary user is actually not in operation. This is referred to as a false-alarm event (see (4)) occurred during the spectrum sensing period. In fact, R j in (6) is one of the following signals
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⎧ ⎪ ⎪ h1, j sPN ⎪ ⎪ ⎪ ⎨ Rj = ⎪ h2, j sCN ⎪ ⎪ ⎪ ⎪ ⎩h1, j sPN + h2, j sCN
1 , H1 }, under{H 0 , H0 }, under{H 0 , H1 }, under{H
(7)
0 , H1 } indicates a miss-detection event (see (3)) where {H occurred during the spectrum sensing period. Moreover, in the above model, the cognitive radio network gives permission to one of its users (CR transmitter) to send data through the sensed frequency band when the spectrum sensing deci0 . Similarly, the CR transmitter stops its transmission is H sion as soon as the spectrum sensing decides in favor of the 1 . hypothesis H 3.
A Survey on Conventional Covariance and BSS Spectrum Sensing Techniques
Here, we provide an overview on covariance based and the BSS spectrum sensing technique proposed in [15]. Note that these two techniques are the two main components that we will use inside our improved framework propose in the next section. The received signal at each CR user is transmitted to the cognitive BS and gathered in matrix X as ⎡ ⎤ ⎡ T⎤ ⎢⎢⎢ x1,1 x1,2 . . . x1,L ⎥⎥⎥ ⎢⎢⎢x1 ⎥⎥⎥ ⎢⎢⎢⎢ x2,1 x2,2 . . . x2,L ⎥⎥⎥⎥ ⎢⎢⎢⎢xT ⎥⎥⎥⎥ ⎥ ⎢ 2⎥ X = ⎢⎢⎢⎢⎢ . (8) .. .. ⎥⎥⎥⎥ = ⎢⎢⎢⎢ . ⎥⎥⎥⎥, ⎢⎢⎢ .. . . ⎥⎥⎥ ⎢⎢⎢⎢ .. ⎥⎥⎥⎥ ⎣ ⎦ ⎣ T⎦ x J,1 x J,2 . . . x J,L xJ where x j,i for i = 1, . . . , L and j = 1, . . . , J is the i-th sensing symbol of the j-th CR user. Also, x j for j = 1, . . . , J is referred to the sensed vector at the j-th user. Conventional spectrum sensing techniques based on energy detection compare the signal energy of each CR user (E j ) in the sensing period to a predefined threshold [17], [18] selected based on the statistics of the noise and channel. The decision rule at the j-th cognitive user writes ⎧ ⎪ ⎪ if E j ≥ ζ j , ⎨H1 ED θˆ j = ⎪ (9) ⎪ ⎩H0 if E j < ζ j , where ζ j is the energy threshold applied at the j-th cognitive user to differentiate between the two hypotheses H0 and H1 . Moreover, we have 1 2 1 |x j | = |h j si + zi, j |2 , Ej = L i=1 L i=1 L
L
In covariance based spectrum sensing techniques, e.g., maximum-minimum eigenvalue (MME) detection [6] and random matrix theory (RMT) detection [7], the empirical estimate of the covariance matrix is evaluated at the cognitive BS based on the knowledge of X as Σ=
(12)
In [6], a new method based on the eigenvalues of the covariance matrix Σ is proposed. Moreover, a recent covariance based spectrum sensing method [7] is that based on the difference between the maximum (λmax ) and the minimum (λmin ) eigenvalues of the covariance matrix Σ. In this approach, the decision about the presence/absence of the primary signal is made as ⎧ ⎪ 1 ⎪ if λλmax ≥ ξ, ⎨H cov min (13) θ =⎪ λ ⎪ max ⎩H0 if λmin < ξ, where ξ is the threshold applied in covariance based spectrum sensing [6]. The main difference between the ED based method introduced in [17], [18] and the covariance based method proposed in [6], [7] is that in the first one each CR user makes its local decision just based on the measured energy in the sensing period and then sends this local decision to the cognitive BS in order to make the cooperative spectrum sensing decision, while in covariance detection, all the CR users’ sensed symbols are sent to the cognitive BS and the covariance matrix of the received symbols (Σ) is constructed. Then, based on the statistical distribution of the eigenvalues of Σ the final cooperative spectrum sensing decision is made. Thus, covariance detection differs from the conventional ED whereas in covariance detection, the decision is made based on the constructed covariance matrix (Σ). The adopted BSS spectrum sensing is based on the well known independent component analysis (ICA) method. The goal is to separate the original source signal vectors (gathered in matrix Y) by choosing the appropriate matrix W, in a blind manner. More precisely, we have Y = W X, where
y Y = 1,1 y2,1
(10)
where h j for j ∈ {1, . . . , J} is the sensing channel coefficient and J is the number of cognitive users (see Fig. 1). Then each CR user sends its decision (θˆ ED j ) to the cognitive BS. The cooperative spectrum sensing using ED can make its final decision about the presence of the primary signal using an OR logic rule (11) considering decisions of all CR users, as follows: ⎧ ⎪ ⎪ if there are at least one j ∈ {1, . . . , J}, H1 ⎪ ⎪ ⎪ ⎨ ED (11) θˆ = ⎪ s.t. θˆ ED j = H1 , ⎪ ⎪ ⎪ ⎪ ⎩H0 otherwise.
1 XXH . J
and
w W = 1,1 w2,1
(14)
y1,2 y2,2
w1,2 w2,2
T y . . . y1,L = 1T , . . . y2,L y2 T w . . . w1,J = 1T . . . . w2,J w2
(15)
(16)
The distinction between primary and secondary signals is usually based on the non-gaussianity of these components. The fast ICA algorithm [19], [20] is used to find the separated signals in Y, using an approximation of the negentropy [21]. Then, in order to make a decision, different metrics such as correlation and negentropy are used to
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measure the non-gaussianity of the separated signals. Here, we use the Kurtosis metric proposed in [15] as a measure of the signal non-gaussianity to make a decision about the presence or the absence of the primary signal. The Kurtosis metric is defined as Kurtosis(yi )
E{(yi − μi )4 } , σ4
(17)
where yi for (i = 1, 2) is the i-th independent component of the BSS algorithm with mean μi and variance σ2i . Note that we subtract the mean of the mixed signals at the input of the ICA algorithm. Also, the fast ICA algorithm outputs normalized separated signals. So, the signals at the output of the fast ICA algorithm, i.e., y1 and y2 , are zero mean with unit variances. Therefore, the Kurtosis metric in (17) is rewritten as: Kurtosis(yi ) = E{yi 4 }.
(18)
To calculate the Kurtosis metric, first, we calculate the vector yi for i = 1, 2: yi =
J
wi, j x j .
(19)
j=1
Kurtosis(yi ) = E{(si + z )4 }.
Let us denote by θ1BS S and θ2BS S the decision of the BSS spectrum sensing for the case where the cognitive transmitter is currently in operation or not, respectively. The BSS spectrum sensing process based on the Kurtosis metric for the two proposed scenarios can be summarized as follows 1. The cognitive transmitter is in operation: ⎧ ⎪ 1 ⎪ if min{Kurtosis(yi )} ≤ T 1 , ⎨H BS S (25) θ1 = ⎪ ⎪ 0 ⎩H if min{Kurtosis(yi )} > T 1 , 2. The cognitive transmitter is not in operation: ⎧ ⎪ 1 ⎪ if max{Kurtosis(yi )} ≤ T 2 , ⎨H BS S θ2 = ⎪ ⎪ 0 ⎩H if max{Kurtosis(yi )} > T 2 ,
BSS Spectrum Sensing Algorithm ◦ For k = 1 : K • Separate the mixed source signals at the k-th frame using (14). • Apply the Kurtosis metric (17) on all separated signals. • If the cognitive transmitter is in operation during the k-th frame at the sensing time:
Use (25) to determine θ1BS S (k). • Else If the cognitive transmitter is not functioning during the k-th frame at the sensing time:
Use (26) to determine θ2BS S (k). • End If ◦ End For
k=1
where sk = sPN for k = 1 and sk = sCN for k = 2. Therefore, we have: yi =
2
ai si + z
(21)
i=1
where z = Jj=1 wi, j z j and ai for i = 1, 2 are constant coefficients. Note that z is a linear combination of the gaussian variables and so has a gaussian distribution. If the fast ICA method performs well, the following equation will be satisfied and then for yi , one of the constant coefficients (ai for i = 1, 2) is “0” and the other one is “1.” WH I where matrix H is equal to ⎤ ⎡ ⎢⎢⎢h1,1 h2,1 ⎥⎥⎥ ⎢⎢⎢⎢h1,2 h2,2 ⎥⎥⎥⎥ ⎥ H = ⎢⎢⎢⎢⎢ . .. ⎥⎥⎥⎥ , ⎢⎢⎢ .. . ⎥⎥⎥ ⎦ ⎣ h1,J h2,J
(22)
(23)
with components defined in (7), and matrix I is the J × J identity matrix. Therefore, when (22) is satisfied, (18) can be calculated as
(26)
where T 1 and T 2 are thresholds applied in Kurtosis based BSS spectrum sensing, chosen so as to satisfy a desired false-alarm probability. The overall procedure followed in BSS spectrum sensing can be summarized as follows (k denotes the k-th primary frame and K is the total number of the primary frames):
For the case in which both of the primary signal and the cognitive signal are present, the vector yi can be rewritten as: ⎛ 2 ⎞ J ⎜⎜⎜ ⎟⎟⎟ wi, j ⎜⎜⎜⎝ hk, j sk + z j ⎟⎟⎟⎠ , yi = (20) j=1
(24)
4.
An Improved Framework for Spectrum Sensing
In this section, we propose to use jointly the covariance based detection and the Kurtosis based BSS spectrum sensing methods. First, we explain our proposed spectrum sensing algorithm. Then, in order to characterize its associated performance, we model our algorithm by using tools from the Markov chain theory [22]. 4.1 Improved Spectrum Sensing Framework Algorithm Let us first explain the methodology followed in our proposed technique. This is more clearly depicted in Fig. 2. As
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Fig. 2 Overview of the proposed spectrum sensing framework, “m1 ” denotes covariance detection and “m2 ” denotes BSS detection.
shown, we start the spectrum sensing process by using covariance detection, assuming that the CR transmitter is off. When the decision of spectrum sensing allows the CR transmitter to transmit (i.e., it decides that the primary is off), we switch the sensing method to BSS which has the capability of separating the cognitive and primary signals. In this way, we can keep the cognitive transmission on during the spectrum sensing until the algorithm detects the presence of a primary signal. In this case, we turn off the CR transmitter and switch the sensing method to covariance detection, and so on. In fact, by using our method, the adopted sensing technique in a given cognitive sensing window (CSW) depends on the decision made by the algorithm in the previous CSW. For the sake of simplicity hereafter, we refer the covariance based detection as method one (m1 ) and the Kurtosis based BSS detection as method two (m2 ). More precisely, based on the result of the spectrum sensing in the (n − 1)th CSW, the type of the spectrum sensing method adopted within the n-th CSW is selected as follows. • Covariance spectrum sensing (method m1 ) is adopted in the n-th CSW, if the CR decision in the (n − 1)-th 1 (in this case, the cognitive transmitter can CSW is H not be active during the the n-th CSW), • Kurtosis based BSS spectrum sensing (method m2 ) is adopted in the n-th CSW, if the CR decision in the (n − 0 (in this case, the cognitive transmitter 1)-th CSW is H can be active during the n-th CSW). The overall operation summarizing the proposed new spectrum sensing framework is provided in the following algorithm. In this algorithm, the index n is the index of the CSW (a cognitive sensing window which is a portion of the primary frame) and the parameter, N, is the total numbers of CSWs. Here, we consider T as the number of primary symbols per frame, and for convenience we define as =
Fig. 3 Transition diagram that models the proposed spectrum sensing framework by a finite-state machine with four states. Pi j indicates the transition probability from the i-th state at time (n − 1) to the j-th state at time n.
L/T . Using we can see that N = −1 K (see Fig. 2 for more details). 4.2 Improved Spectrum Sensing Framework Modeling Spectrum sensing performance evaluation is usually analyzed by means of receiver operating characteristic (ROC) curves that plot the miss-detection probability (defined in (3)) versus the false-alarm probability (defined in (4)). As explained in Sect. 4.1, in our approach, the spectrum sensing decision in the n-th CSW depends on the decision made in the (n − 1)-th CSW. Hence, we propose to use tools from the Markov chain theory [22] to model the spectrum sensing algorithm and obtain the miss-detection and false-alarm probabilities. Note that these two probabilities let us to plot the ROC curve that characterize the performance achieved with our spectrum sensing technique. The decision made 1 . Moreover, the pri0 or H by the spectrum unit is either H mary network transmitter is either on or off characterized by hypotheses H0 and H1 . Thus, in each CSW, four different scenarios can be defined based on the decision made by the spectrum sensing unit and the actual state of the primary transmitter. We propose here to view these four scenarios as the states of a finite-state machine that can be modeled by a Markov chain, as depicted in Fig. 3. Below, we describe each state in more details. 1 , H0 } • State 1: This state corresponds to the event {H and indicates the occurrence of a false-alarm (see the first equation in (6)), 0 , H0 } • State 2: this state corresponds to the event {H and occurs when the cognitive network decides that the primary is off, where the primary is actually off (see the second equation in (7)),
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Proposed Spectrum Sensing Algorithm ◦ Start the sensing algorithm while the cognitive transmitter is not in operation (n = 1) ◦ For n = 1 : N • If the cognitive transmitter is not in operation in the n-th CSW
Apply m1
Calculate the covariance matrix Σ using (12)
Calculate λmax and λmin from the covariance matrix Σ of (12)
Use (13) to determine θcov (n) by using m1 1
If θcov (n) = H Cognitive transmitter is off at the (n + 1)-th CSW 0
Else If θcov (n) = H Cognitive transmitter is on at the (n + 1)-th CSW
End If • Else If the cognitive transmitter is in operation in the n-th CSW
Apply (m2 ) on the n-th CSW
Separate the mixed signals based on (17)
Apply the Kurtosis metric (17) for all separated signals
Use (26) to determine θ2BS S (n) by using m2 1
If θ BS S (n) = H 2
Cognitive transmitter is off at the (n + 1)-th CSW 0
Else If θ BS S (n) = H 2
Cognitive transmitter is on at the (n + 1)-th CSW
End If • End If ◦ End For
0 , H1 } • State 3: this state corresponds to the event {H and indicates the occurrence of a miss-detection (see the third equation in (7)), 1 , H1 } • State 4: this state corresponds to the event {H and occurs when the cognitive network decides that the primary is on, where the primary is actually on (see the first equation in (7)). Note that in general, any transition between the states defined above is possible and has to be considered in our model, as shown in Fig. 3. The set of all transition probabil-
ities involved in our model is provided in the following 4 × 4 matrix ⎤ ⎡ ⎢⎢⎢P11 P12 P13 P14 ⎥⎥⎥ ⎥ ⎢⎢⎢ ⎢⎢⎢P21 P22 P23 P24 ⎥⎥⎥⎥⎥ ⎥, P = ⎢⎢⎢ (27) ⎢⎢⎢P31 P32 P33 P34 ⎥⎥⎥⎥⎥ ⎥⎦ ⎢⎣ P41 P42 P43 P44 where Pi j for (i, j ∈ {1, . . . , 4}) refers to the the transition probability from state i at the (n − 1)-th CSW to state j at the n-th CSW. Let us denote by Si (n) for i ∈ {1, . . . , 4} the state at the n-th CSW. The transition probability Pi j writes (28) Pi j = P S j (n)|Si (n − 1) . i (n) for i ∈ {0, 1} as the primary We also define Hi (n) and H activity hypotheses and spectrum sensing decision at the nth CSW. Let us denote by qi j for i, j ∈ {0, 1}, the probability for the primary transmitter to switch from an on/off state at the (n − 1)-th CSW to an on/off state at the n-th CSW. We have (29) qi j = P H j (n)|Hi (n − 1) , where i = 1 and j = 1 indicate the presence of the primary signal during the (n − 1)-th and the n-th CSW, respectively. Similarly, i = 0 and j = 0 indicate the absence of the primary signal during the (n−1)-th and n-th CSW, respectively. In the sequel, we aim at deriving the transition probabilities defined in (27). Using (28), we start by deriving P11 as 1 (n), H0 (n)|H 1 (n − 1), H0 (n − 1) . P11 = P H (30) Equation (30) can be rewritten as 1 (n)|H0 (n), H 1 (n − 1), H0 (n − 1) P11 = P H 1 (n − 1), H0 (n − 1) . × P H0 (n)|H
(31)
Here, we assume that in a given frame, the cognitive network has no prior knowledge about the presence/absence of the primary signal in the previous CSW. We have 1 (n − 1), H0 (n − 1) P H0 (n)|H = P {H0 (n)|H0 (n − 1)} = q00 ,
(32)
where in (32), we have used the independence between j (n − 1). Note that this independence is due Hi (n) and H to the fact that the actual presence or absence of the primary user is inherent to the channel use of the primary transmitter and hence does not depend to the decision made by the unit at any time instant. spectrum sensing (H) Remember that in our method, the decision of the speci (n)) depends on the decitrum sensing in the n-th CSW (H sion in the (n − 1)-th CSW. More precisely, the hypothesis i (n) does not depend on the actual state of the primary user H (Hi (n − 1)). Hence, (31) can be rewritten in a more simple
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form as P11
1 (n)|H0 (n), H 1 (n − 1) . = q00 × P H
(33)
As explained previously, in our approach, the type of the spectrum sensing method (m1 or m2 ) used in the nth CSW is selected based on the spectrum sensing decii , for i ∈ {0, 1}. sion made in the previous CSW, i.e., H In other words, knowing what method has to be used in a given CSW, is equivalent to knowing the spectrum sensing m j (n) decision made in the previous CSW. We introduce H i (i ∈ {0, 1}, j ∈ {1, 2}) to denote the spectrum sensing decision associated to method m j during the n-th CSW. In this way, we can write (33) in a simpler form as m 1 (n)|H0 (n) . (34) P11 = q00 × P H 1 m1 (n)|H0 (n)} in (34), is According to (4), the quantity P{H 1 actually the false-alarm probability associated to the covariance sensing method (method m1 ), that we denote by Pm1 f (n). We thus have P11 = q00 × Pmf 1 (n) = q00 × Pmf 1 ,
(35)
where Pmf 1 in (35) is defined as: m 1 |H0 . Pmf 1 = P H 1
(36)
P= ⎡ ⎢⎢⎢q00 Pmf 1 ⎢⎢⎢⎢ ⎢⎢⎢ m2 ⎢⎢⎢q00 P f ⎢⎢⎢ ⎢⎢⎢ m2 ⎢⎢⎢q10 P f ⎢⎢⎢ ⎣ q10 Pmf 1
q00 1 − Pmf 1 q00 1 − Pmf 2 q10 1 − Pmf 2 q10 1 − Pmf 1
1 q01 Pm m 2 q01 Pm m 2 q11 Pm m 1 q11 Pm m
(41) Next, the transition matrix P is used for the derivation of the miss-detection and the false-alarm probabilities associated to the improved spectrum sensing framework. 4.3 Derivation of the Performance Measures Associated to the Improved Spectrum Sensing Framework According to the Markov chain theory [22], there is at least one stationary distribution for a finite Markov chain. Here, we analyze the stationary distribution for the transition matrix P in (41). This stationary distribution enables us to derive the miss-detection and the false-alarm probabilities that characterize the overall performance of the improved spectrum sensing framework. We denote by π(n) = [π1 (n), ..., π4 (n)]T the vector of states probabilities at the n-th CSW, where πi (n) for i ∈ {1, . . . , 4} is the probability of being in the i-th state, i.e., πi (n) = P {Si (n)} .
Let us now derive P22 which is by definition given by 0 (n), H0 (n)|H 0 (n − 1), H0 (n − 1) . (37) P22 = P H Following similar line of arguments we provide for equivalence between (31) and (33), we can rewrite (37) as 0 (n)|H0 (n), H 0 (n − 1) . P22 = q00 × P H (38) Again, due to the equivalence that we have in our scheme 0 (n)|H 0 (n − 1)} and {H m2 (n)}, we obbetween the events {H 0 tain m 2 (n)|H0 (n) . (39) P22 = q00 × P H 0 m2 (n)|H0 (n)} is equal to 1 − Pm2 , Since according to (4), P{H 0 f with Pmf 2 being the false-alarm probability associated to method m2 , we obtain P22 = q00 × 1 − Pmf 2 . (40) Following a procedure similar to that adopted for deriving P11 and P22 , it is straightforward to calculate other transition probabilities involved in the transition diagram of Fig. 3. By doing so, the transition matrix (27) can be filled as
⎤ 1 q01 1 − Pm ⎥⎥⎥ m ⎥ ⎥⎥ ⎥ m 2 ⎥ q01 1 − Pm ⎥⎥⎥⎥ ⎥⎥⎥ . ⎥ m 2 ⎥ q11 1 − Pm ⎥⎥⎥⎥ ⎥⎥⎥ ⎦ m 1 ⎥ q11 1 − Pm
(42)
At the beginning of the proposed spectrum sensing framework (i.e., n = 0), we assume that the cognitive transmitter 1 (0)) and we have no a priori knowlis not in operation (H edge about the presence or absence of the primary signal (H0 (0) or H1 (0)). Thus, the algorithm starts at either state 1 or state 4 with equal probabilities of 0.5, depending on the presence or the absence of the primary signal. Moreover, this procedure can never start from state 2 or state 3. Consequently, the initial state probability vector denoted by π(0) is π(0) = [ 0.5, 0, 0, 0.5 ]T .
(43)
According to the Markov chain theory [22], the state probabilities at the n-th CSW for the transition diagram in Fig. 3 can be written as π(n) = Pn π(0).
(44)
Considering the states probability vector (44) and the transition matrix (27), the stationary distribution for the proposed spectrum sensing method is given by [22] π = lim π(n) = lim Pn π(0), n→∞
n→∞
(45)
where π = [π1 , ..., π4 ]T is the stationary distribution vector and πi for i ∈ {1, . . . , 4} is the stationary probability of being in the i-th state. Since the Markov chain theory guarantees the existence
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of a solution for (45) [22], we solve the following equation (finding the eigenvector π for the transition matrix P of (27)) to calculate the stationary probability vector π [22]. P × π = π.
(46)
Three independent equations can be extracted from (46) while there are four variables (πi for i ∈ {1, . . . , 4}). So, we add the following equation to calculate the unknown stationary probability vector. 4
πi = 1.
(47)
i=1
It is straightforward to obtain the vector π from (46) and (47). After solving this problem, the miss-detection and the false-alarm probabilities for the improved spectrum sensing framework are obtained as 0 , H1 P H π3 I Pm = = , (48) P{H1 } P{H1 } and PIf =
1 , H0 P H P{H0 }
=
π1 , P{H0 }
Fig. 4 The ROC curves for improved and conventional spectrum sensing methods with sensing SNR=10 dB. (“Imp” denotes the improved spectrum sensing method).
(49)
respectively, where P{Hi } for i ∈ {0, 1} is the a priori probability on the presence or the absence of the primary signal. Here, we assume that the CR network has no knowledge about the presence or the absence of the primary signal and thus these a priori probabilities are set equal to 0.5. 5.
Numerical Results and Discussion
In this section, we provide numerical results to evaluate the performance provided by the proposed combined spectrum sensing method in comparison with each one of the conventional techniques [7] (covariance detection) and [13], [14] (BSS detection). Throughout the simulations, the transmitted power for both primary and cognitive transmitters is normalized to one. The length of the sensing window is set to L = 100 samples. The rest of the parameters are extracted form the IEEE 802.22 standard [23]. Figure 4 plots the ROC curves, i.e., the miss-detection probability Pm versus the false-alarm probability P f to compare the sensing performance achieved with our proposed joint method and conventional methods m1 and m2 under a sensing signal-to-noise ratio (SNR) of 10 dB. This figure is plotted in order to see the effect of parameter on spectrum sensing performance. We observe that whereas the value of has no effect on conventional methods, the proposed method’s sensing performance is improved for smaller values of parameter . This can be explained by the fact that when decreases, the correlation between primary frames becomes larger (characterized by the decrease of q01 and q10 ) and since our method inherently takes this correlation into account, the sensing performance is improved. In other
Fig. 5 The miss-detection probability Pm versus the parameter for improved and covariance sensing techniques, sensing SNRs are equal to 0, 5 and 10 dB, (“Imp” denotes the improved spectrum sensing method).
words, the primary signal in the n-th CSW is correlated to the (n − 1)-th CSW; so, there are some information about the primary signal in the decision that is made in the (n − 1)th CSW. In conventional spectrum sensing methods such as covariance spectrum sensing, spectrum sensing decision is made only based on the information that can be extracted from the n-th CSW, while in our proposed spectrum sensing method, the decision is based on both the information in the n-th and the (n−1)-th CSWs, which obviously contains more information. For more precisions, we have shown in Fig. 5 the miss-detection probability Pm versus the primary network parameter when the false-alarm probability is set to
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pared to the conventional covariance sensing method even for bad sensing conditions (characterized by a sensing SNR of 0 dB). Figure 7 plots the miss-detection probability Pm versus the sensing SNR when the false-alarm probability is set to 0.01. We observe that our proposed method remains more accurate than its competitive methods for a wide range of sensing SNR. 6.
Fig. 6 The ROC curves for improved and covariance spectrum sensing, sensing SNR=0 dB (“Imp” denotes the improved spectrum sensing method, “CT” denotes cognitive transmitter).
Conclusion
Spectrum sensing is one of the most important parts in the implementation of each CR system. Conventional spectrum sensing techniques such as covariance detection do not allow the CR transmitter to transmit during the sensing process. Obviously, this leads to a waste of spectral resources. Although spectrum sensing based ob BSS can overcome this limitation, it has relatively a lower performance compared to energy detection and covariance detection. Here, we proposed a new spectrum sensing framework that combines blind source separation algorithms jointly with conventional covariance detection. We also derived by means of Markov chain modeling, the performance measures associated to our proposed technique in terms of miss-detection and false-alarm probabilities. Numerical results indicated that our proposed method outperforms conventional covariance detection technique. In addition, by using our sensing technique, the CR transmitter can continue to transmit even during spectrum sensing. References
Fig. 7 The miss-detection probability Pm versus the sensing SNR for the comparison between the improved spectrum sensing method and its constructive methods (“Imp” denotes the improved spectrum sensing method, “CT” denotes cognitive transmitter).
0.01. The figure illustrates the comparison between the improved spectrum sensing and the covariance spectrum sensing for sensing SNRs of 0, 5 and 10 dB. We observe that the improved method provides smaller miss-detection probability (i.e., becomes more accurate) when the ratio of the cognitive network sensing window to the primary frame length (i.e., the parameter ) decreases. Similar ROC curves are depicted in Fig. 6 comparing our proposed joint method with the covariance spectrum sensing under a sensing SNR equal to 0 dB. We observe that our proposed sensing method is still of advantage com-
[1] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE J. Sel. Areas Commun., vol.23, no.2, pp.201–220, Feb. 2005. [2] A. Ghasemi and E.S. Sousa, “Opportunistic spectrum access in fading channels through collobrative sensing,” J. Commun., vol.2, no.2, pp.71–82, March 2007. [3] W. Zhang and K.B. Letaief, “Cooperative spectrum sensing with transmit and relay diversity in cognitive radio networks,” IEEE Trans. Wirel. Commun., vol.7, pp.4761–4766, Dec. 2008. [4] C. Sun, W. Zhang, and K.B. Letaief, “Cooperative spectrum sensing for cognitive radio under bandwidth constraints,” Proc. IEEE WCNC, pp.1–5, Hong Kong, March 2007. [5] A. Taherpour, Y. Norouzi, M. Nasiri-Kenari, A. Jamshidi, and Z. Zeinalpour-Yazdi, “Asymptotically optimum detection of primary user in cognitive radio networks,” IET Trans. Commun., vol.1, pp.225–232, 2007. [6] Y. Zeng and Y.C. Liang, “Maximum-minimum eigenvalue detection for cognitive radio,” Proc. IEEE 18th Int. Symp. Personal, Indoor Mobile Radio Commun. (PIMRC 2007), pp.1–5, Athens, Greece, Sept. 2007. [7] L.S. Cardoso, M. Debbah, P. Bianchi, and J. Najim, “Cooperative spectrum sensing using random matrix theory,” ISWPC, pp.334– 338, May 2008. [8] N. Tafaghodi Khajavi and S.M.S. Sadough, “Improved spectrum sensing and achieved throughputs in cognitive radio networks,” Proc. Wireless Advanced, London, June 2010. [9] X. Xie, Cognitive Radio Technology and Application, Publishing House of Electronic Industry, Beijing China, 2008. [10] S.H. Hong, K. Hamidi, and K.B. Letaief, “Spectrum sensing with
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active cognitive system,” Wireless Commun., vol.9, no.6, pp.1849– 1854, June 2010. N. Tafaghodi Khajavi and S.M.S. Sadough, “On the interference imposed on primary transmission in cognitive radio networks,” Proc. Wireless Advanced, London, June 2010. J. Mitola, Cognitive Radio Architecture: the Engineering Foundations of Radio XML, pp.26–31, John Wiley and Sons, 2006. G. Xu, Y. Lu, J. He, and N. Hu, “Primary users detect for multipleantenna cognitive radio based on blind source separation,” International Symposium on Intelligent Information Technology Application Workshops, pp.777–780, Dec. 2008. Y. Zheng, X. Xie, and L. Yang, “Cooperative spectrum sensing based on blind source separation for cognitive radio,” 1st International Conference on Future Information Networks (ICFIN), pp.398–402, 2009. N. Tafaghodi Khajavi, S. Sadeghi, and S.M.S. Sadough, “An improved blind spectrum sensing technique for cognitive radio systems,” 5th International Symposium on Telecommunications (IST2010), Dec. 2010. F.F. Digham, M.S. Alouini, and M.K. Simon, “On the energy detection of unknown signals over fading channels,” IEEE Trans. Commun., vol.55, pp.21–24, Jan. 2007. K.B. Letaief and W. Zhang, “Cooperative communications for cognitive radio networks,” Proc. IEEE, vol.97, no.5, pp.878–893, May 2009. A. Ghasemi and E.S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” Proc. IEEE DySPAN, Nov. 2005. A. Hyvarinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Trans. Neural Netw., vol.10, no.3, pp.626–634, 1999. A. Hyvarinen and E. Oja, “A fast fixed-point algorithm for independent component analysis,” Neural Comput., vol.9, no.7, pp.1483– 1492, 1997. A. Hyvarinen, “New approximations of differential entropy for independent component analysis and projection pursuit,” Advances in Neural Information Processing Systems, vol.10, pp.273–279, 1998. A.D. Allen, Probability, Statistics and Queueing Theory, Academic Press New York. Standard for Wireless Regional Area Networks (WRAN) - Specific requirements - Part 22: Cognitive Wireless RAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: Policies and procedures for operation in the TV Bands.
Navid Tafaghodi Khajavi received his B.Sc. degree in Electrical Engineering (communication) from Faculty of Engineering at the Ferdowsi University, Mashhad, Iran. He is currently pursuing the M.S. degree in Electrical Engineering (telecommunication) at Shahid Beheshti University, Tehran, Iran. His current research interests include cognitive radio, resource allocation algorithms, convex optimization problems and wireless communications.
Siavash Sadeghi Ivrigh received his B.Sc. degree in Electrical Engineering from the department of Electrical Engineering at Noshirvani Institute of Technology, Babol, Iran. He is currently pursuing M.Sc. degree in Electrical Engineering at Shahid Beheshti University, Tehran, Iran. His current research interests include cognitive radio, blind source separation, source localization and wireless communications.
Seyed Mohammad-Sajad Sadough was born in Paris in 1979. He received the B.Sc. degree in Electrical Engineering (electronics) from Shahid Beheshti University, Tehran, I.R. Iran in 2002 and the M.Sc. and the Ph.D. degrees in Electrical Engineering (telecommunication) from Paris-Sud 11 University, Orsay, France, in 2004 and 2008, respectively. From 2004 to 2007, he was jointly with the National Engineering School in Advanced Techniques (ENSTA), Paris, France, and the Laboratory of Signals and Systemes (LSS), at Sup´elec, Gif-sur-Yvette, France. He was a lecturer with the Depertment of Electronics and Computer Engineering (UEI), ENSTA, where his research activities were focused on improved reception schemes for ultra-wideband communication systems. From December 2007 to September 2008, he was a postdoctoral researcher with the LSS, Sup´elec-CNRS, where he was involved in the European research project TVMSL with Alcatel-Lucent France. Since October 2008, he has been with the Faculty of Electrical & Computer Engineering, Shahid Beheshti University, where he is currently an Assistant Professor with the Department of Telecommunication. Dr. Sadough’s areas of research include signal processing, communication theory, and digital communication.
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PAPER
A Novel Framework for Spectrum Sensing in Cognitive Radio Networks Navid TAFAGHODI KHAJAVI†a) , Siavash SADEGHI IVRIGH†b) , Nonmembers, and Seyed Mohammad-Sajad SADOUGH†c) , Member
SUMMARY Cognitive radio (CR) is a key solution for the problem of inefficient usage of spectral resources. Spectrum sensing in each CR aims at detecting whether a preassigned spectrum band is occupied by a primary user or not. Conventional techniques do not allow the CR to communicate with its own base station during the spectrum sensing process. So, only a part of the frame can be used for cognitive data transmission. In this paper, we introduce a new spectrum sensing framework that combines a blind source separation technique with conventional spectrum sensing techniques. In this way, the cognitive transmitter can continue to transmit during spectrum sensing, if it was in operation in the previous frame. Moreover, the accuracy is improved since the decision made by the spectrum unit in each frame depends on the decision made in the previous frame. We use Markov chain tools to model the behavior of our spectrum sensing proposal and to derive the parameters that characterize its performance. Numerical results are provided to confirm the superiority of the proposed technique compared to conventional spectrum sensing techniques. key words: cognitive radio, spectrum sensing, blind source separation, covariance spectrum sensing, Markov chain modeling
1.
Introduction
Cognitive radio (CR) technology [1] allows secondary users to access spectrum bands allocated to primary users (PU) in an opportunistic manner. To avoid the interference on primary transmission, the CR has to sense the spectrum constantly in order to stop transmission when it senses that the primary user is in operation [2]. However, due to channel fading conditions and due to the so-called hidden terminal problem [3], spectrum sensing is usually imperfect and imposes interference on the primary network. Employing multiple cognitive users in order to exploit the available spatial diversity, is referred to as cooperative spectrum sensing and improves the detection reliability. In cooperative spectrum sensing methods, each CR user senses the spectrum during a sensing period and sends its sensed signal or its decision in a particular spectrum band allocated to the PU to the cognitive base station (BS). In conventional cooperative spectrum sensing methods based on energy detection (ED) [4], [5] and covariance detection [6], [7], spectrum sensing is usually performed at the Manuscript received January 11, 2011. Manuscript revised May 4, 2011. † The authors are with the Cognitive Telecommunication Research Group, Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Shahid Beheshti University G.C., 1983963113, Tehran, Iran. a) E-mail: [email protected] b) E-mail: [email protected] c) E-mail: s [email protected] DOI: 10.1587/transcom.E94.B.2600
beginning of each frame with the requirement that the cognitive transmitter does not communicate with its BS during this operation. Obviously, this requirement degrades the spectral efficiency, especially when the cognitive transmitter was in operation and the decision of spectrum sensing is to maintain the cognitive transmission. In energy detection [4], [5], the energy of the received signal is measured and used as a metric to determine whether the primary user is present or not. Also, a new spectrum sensing method based on energy detection is proposed in [8] which improves the total achievable throughputs of the network. In covariance detection [6], [7], spectrum sensing is performed based on the eignvalues of the covariance matrix of the received signal calculated at the cognitive BS. One recent method in this regard relies on the difference that exists between the eigenvalues of the received signal covariance matrix when the primary signal is not in operation. For instance, the differences between statistical distributions of the eignvalues of the signal covariance matrix and Gaussian noise covariance matrix are shown in [7]. In [7], covariance detection is implemented in such a way that there is no need to dispose an estimate of the noise power [9]. Moreover, a new cooperative spectrum sensing method based on the IEEE 802.22 proposal for active cognitive network has recently been proposed in [10], where the cognitive users sense the spectrum while one of them transmits its data. In addition, a study on the interference imposed by the cognitive network on the primary transmission is presented in [11]. Blind signal processing (BSP) is one of the areas in signal processing with solid theoretical foundations and many potential applications [12]. State of the art spectrum sensing methods such as energy detection and covariance detection cannot sense the mixed primary and secondary signals. So, in order to overcome the limitation of these methods, spectrum sensing based on blind source separation (BSS) was recently proposed and investigated in [13]–[15], for instance. Note that BSS spectrum sensing does not require any prior information about the primary signal and performs well for correlated signals. In [13], BSS is proposed to separate the mixed primary and secondary signals, in a multiantenna scenario. In [14], BSS is used inside a cooperative spectrum sensing scheme to improve the detection reliability. Recently in [15], a new BSS metric is proposed to determine whether the primary signals is present or not. In this paper, we propose a new spectrum sensing framework that combines the BSS approach with conven-
c 2011 The Institute of Electronics, Information and Communication Engineers Copyright
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tional spectrum sensing. More precisely, we propose to alternate between correlation spectrum sensing and BSS spectrum sensing in a constructive manner. In this joint method, unlike conventional spectrum sensing methods, there is no need for the cognitive signal to be synchronized with the primary signal. In other words, the CR can transmit its data even during the spectrum sensing process. We will see that this feature not only increases the total achievable throughputs but also improves the accuracy and reliability of the spectrum sensing process. Moreover, we model the proposed spectrum sensing method by a four-state Markov chain that we use to analyze the behavior and to derive the performance measures associated with our proposed technique. The rest of this paper is organized as follows. Our spectrum sensing system model is introduced in Sect. 2. In Sect. 3, we introduce the covariance based detection and the BSS spectrum sensing as the two main components of our framework. Section 4 describes our improved spectrum sensing framework. In this Section, we also derive analytically the performance measures characterizing our proposed framework. Section 5 provides simulation results and some discussions about the performance of the proposed technique. Finally, Sect. 6 draws our conclusions. 2.
Spectrum Sensing System Model
Sensing the presence of a primary transmitter inside a given frequency band is usually viewed as binary hypotheses problem with H0 denoting the absence of the primary signal, and H1 denoting the presence of the primary signal, as ⎧ ⎪ ⎪ ⎨H0 : primary user is not in operation, (1) ⎪ ⎪ ⎩H1 : primary user is in operation. 1 to denote the decision made 0 and H Similarly, we define H by spectrum sensing about the absence and the presence of the primary signal, respectively. We have ⎧ 0 : CR decides that the primary user is ⎪ ⎪ H ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ not in operation, ⎪ ⎨ (2) ⎪ ⎪ ⎪ 1 : CR decides that the primary user is ⎪ ⎪ H ⎪ ⎪ ⎪ ⎪ ⎩ in operation. The above hypotheses are usually used to define the following conditional probabilities 0 | H1 , (3) Pm = P H and
1 | H0 . Pf = P H
(4)
The conditional probability in (3) (referred to as missdetection probability) is a performance metric for cases where the CR fails to detect the presence of the primary signal whereas equation (4) (referred to as false-alarm probability) is another performance metric for cases where the CR
Fig. 1 Architecture of the considered cognitive radio network. In this architecture, both the primary and the cognitive networks can transmit their respective signals over the same bandwidth.
fails to detect the absence of the primary signal [16]. Figure 1 depicts the considered cognitive system composed of J cognitive terminals that perform cooperative spectrum sensing. In our model, when the spectrum is allocated for secondary transmission, one of the CR terminals (denoted by cognitive transmitter as shown in Fig. 1) has the permission to communicate with the cognitive BS. Obviously, if primary and cognitive users are in operation simultaneously, the signal received at the j-th ( j = 1, ..., J) CR user can be written as x j = h1, j sPN + h2, j sCN + z j ,
(5)
where the vectors x j = [x j,1 , . . . , x j,L ]T , sPN = CN T T CN = [sCN [s1PN , . . . , sPN L ] and s 1 , . . . , sL ] respectively denote the symbols received during spectrum sensing, the primary transmitted symbols and the secondary transmitted symbols during the sensing period; the noise vector z j = [z j,1 , . . . , z j,L ]T is assumed to be zero-mean circularly symmetric complex Gaussian (ZMCSCG) with distribution z j ∼ CN(0, σ2z j IL ), L is the number of sensing symbols, and hi, j is the channel coefficient that follows a Rayleigh distribution i.e., hi, j ∼ CN(0, σ2h ). Channel coefficients are assumed to be constant during a frame and change to new independent values from one frame to another, i.e., we assume a quasi-static channel model. Equation (5) can be rewritten in a more compact form as ⎧ ⎪ 1 , H0 }, ⎪ under {H ⎨z j (6) xj = ⎪ ⎪ ⎩R j + z j otherwise, 1 , H0 } indicates that the CR transmitter does not where {H transmit since it has decided that the primary is in operation, and the primary user is actually not in operation. This is referred to as a false-alarm event (see (4)) occurred during the spectrum sensing period. In fact, R j in (6) is one of the following signals
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⎧ ⎪ ⎪ h1, j sPN ⎪ ⎪ ⎪ ⎨ Rj = ⎪ h2, j sCN ⎪ ⎪ ⎪ ⎪ ⎩h1, j sPN + h2, j sCN
1 , H1 }, under{H 0 , H0 }, under{H 0 , H1 }, under{H
(7)
0 , H1 } indicates a miss-detection event (see (3)) where {H occurred during the spectrum sensing period. Moreover, in the above model, the cognitive radio network gives permission to one of its users (CR transmitter) to send data through the sensed frequency band when the spectrum sensing deci0 . Similarly, the CR transmitter stops its transmission is H sion as soon as the spectrum sensing decides in favor of the 1 . hypothesis H 3.
A Survey on Conventional Covariance and BSS Spectrum Sensing Techniques
Here, we provide an overview on covariance based and the BSS spectrum sensing technique proposed in [15]. Note that these two techniques are the two main components that we will use inside our improved framework propose in the next section. The received signal at each CR user is transmitted to the cognitive BS and gathered in matrix X as ⎡ ⎤ ⎡ T⎤ ⎢⎢⎢ x1,1 x1,2 . . . x1,L ⎥⎥⎥ ⎢⎢⎢x1 ⎥⎥⎥ ⎢⎢⎢⎢ x2,1 x2,2 . . . x2,L ⎥⎥⎥⎥ ⎢⎢⎢⎢xT ⎥⎥⎥⎥ ⎥ ⎢ 2⎥ X = ⎢⎢⎢⎢⎢ . (8) .. .. ⎥⎥⎥⎥ = ⎢⎢⎢⎢ . ⎥⎥⎥⎥, ⎢⎢⎢ .. . . ⎥⎥⎥ ⎢⎢⎢⎢ .. ⎥⎥⎥⎥ ⎣ ⎦ ⎣ T⎦ x J,1 x J,2 . . . x J,L xJ where x j,i for i = 1, . . . , L and j = 1, . . . , J is the i-th sensing symbol of the j-th CR user. Also, x j for j = 1, . . . , J is referred to the sensed vector at the j-th user. Conventional spectrum sensing techniques based on energy detection compare the signal energy of each CR user (E j ) in the sensing period to a predefined threshold [17], [18] selected based on the statistics of the noise and channel. The decision rule at the j-th cognitive user writes ⎧ ⎪ ⎪ if E j ≥ ζ j , ⎨H1 ED θˆ j = ⎪ (9) ⎪ ⎩H0 if E j < ζ j , where ζ j is the energy threshold applied at the j-th cognitive user to differentiate between the two hypotheses H0 and H1 . Moreover, we have 1 2 1 |x j | = |h j si + zi, j |2 , Ej = L i=1 L i=1 L
L
In covariance based spectrum sensing techniques, e.g., maximum-minimum eigenvalue (MME) detection [6] and random matrix theory (RMT) detection [7], the empirical estimate of the covariance matrix is evaluated at the cognitive BS based on the knowledge of X as Σ=
(12)
In [6], a new method based on the eigenvalues of the covariance matrix Σ is proposed. Moreover, a recent covariance based spectrum sensing method [7] is that based on the difference between the maximum (λmax ) and the minimum (λmin ) eigenvalues of the covariance matrix Σ. In this approach, the decision about the presence/absence of the primary signal is made as ⎧ ⎪ 1 ⎪ if λλmax ≥ ξ, ⎨H cov min (13) θ =⎪ λ ⎪ max ⎩H0 if λmin < ξ, where ξ is the threshold applied in covariance based spectrum sensing [6]. The main difference between the ED based method introduced in [17], [18] and the covariance based method proposed in [6], [7] is that in the first one each CR user makes its local decision just based on the measured energy in the sensing period and then sends this local decision to the cognitive BS in order to make the cooperative spectrum sensing decision, while in covariance detection, all the CR users’ sensed symbols are sent to the cognitive BS and the covariance matrix of the received symbols (Σ) is constructed. Then, based on the statistical distribution of the eigenvalues of Σ the final cooperative spectrum sensing decision is made. Thus, covariance detection differs from the conventional ED whereas in covariance detection, the decision is made based on the constructed covariance matrix (Σ). The adopted BSS spectrum sensing is based on the well known independent component analysis (ICA) method. The goal is to separate the original source signal vectors (gathered in matrix Y) by choosing the appropriate matrix W, in a blind manner. More precisely, we have Y = W X, where
y Y = 1,1 y2,1
(10)
where h j for j ∈ {1, . . . , J} is the sensing channel coefficient and J is the number of cognitive users (see Fig. 1). Then each CR user sends its decision (θˆ ED j ) to the cognitive BS. The cooperative spectrum sensing using ED can make its final decision about the presence of the primary signal using an OR logic rule (11) considering decisions of all CR users, as follows: ⎧ ⎪ ⎪ if there are at least one j ∈ {1, . . . , J}, H1 ⎪ ⎪ ⎪ ⎨ ED (11) θˆ = ⎪ s.t. θˆ ED j = H1 , ⎪ ⎪ ⎪ ⎪ ⎩H0 otherwise.
1 XXH . J
and
w W = 1,1 w2,1
(14)
y1,2 y2,2
w1,2 w2,2
T y . . . y1,L = 1T , . . . y2,L y2 T w . . . w1,J = 1T . . . . w2,J w2
(15)
(16)
The distinction between primary and secondary signals is usually based on the non-gaussianity of these components. The fast ICA algorithm [19], [20] is used to find the separated signals in Y, using an approximation of the negentropy [21]. Then, in order to make a decision, different metrics such as correlation and negentropy are used to
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measure the non-gaussianity of the separated signals. Here, we use the Kurtosis metric proposed in [15] as a measure of the signal non-gaussianity to make a decision about the presence or the absence of the primary signal. The Kurtosis metric is defined as Kurtosis(yi )
E{(yi − μi )4 } , σ4
(17)
where yi for (i = 1, 2) is the i-th independent component of the BSS algorithm with mean μi and variance σ2i . Note that we subtract the mean of the mixed signals at the input of the ICA algorithm. Also, the fast ICA algorithm outputs normalized separated signals. So, the signals at the output of the fast ICA algorithm, i.e., y1 and y2 , are zero mean with unit variances. Therefore, the Kurtosis metric in (17) is rewritten as: Kurtosis(yi ) = E{yi 4 }.
(18)
To calculate the Kurtosis metric, first, we calculate the vector yi for i = 1, 2: yi =
J
wi, j x j .
(19)
j=1
Kurtosis(yi ) = E{(si + z )4 }.
Let us denote by θ1BS S and θ2BS S the decision of the BSS spectrum sensing for the case where the cognitive transmitter is currently in operation or not, respectively. The BSS spectrum sensing process based on the Kurtosis metric for the two proposed scenarios can be summarized as follows 1. The cognitive transmitter is in operation: ⎧ ⎪ 1 ⎪ if min{Kurtosis(yi )} ≤ T 1 , ⎨H BS S (25) θ1 = ⎪ ⎪ 0 ⎩H if min{Kurtosis(yi )} > T 1 , 2. The cognitive transmitter is not in operation: ⎧ ⎪ 1 ⎪ if max{Kurtosis(yi )} ≤ T 2 , ⎨H BS S θ2 = ⎪ ⎪ 0 ⎩H if max{Kurtosis(yi )} > T 2 ,
BSS Spectrum Sensing Algorithm ◦ For k = 1 : K • Separate the mixed source signals at the k-th frame using (14). • Apply the Kurtosis metric (17) on all separated signals. • If the cognitive transmitter is in operation during the k-th frame at the sensing time:
Use (25) to determine θ1BS S (k). • Else If the cognitive transmitter is not functioning during the k-th frame at the sensing time:
Use (26) to determine θ2BS S (k). • End If ◦ End For
k=1
where sk = sPN for k = 1 and sk = sCN for k = 2. Therefore, we have: yi =
2
ai si + z
(21)
i=1
where z = Jj=1 wi, j z j and ai for i = 1, 2 are constant coefficients. Note that z is a linear combination of the gaussian variables and so has a gaussian distribution. If the fast ICA method performs well, the following equation will be satisfied and then for yi , one of the constant coefficients (ai for i = 1, 2) is “0” and the other one is “1.” WH I where matrix H is equal to ⎤ ⎡ ⎢⎢⎢h1,1 h2,1 ⎥⎥⎥ ⎢⎢⎢⎢h1,2 h2,2 ⎥⎥⎥⎥ ⎥ H = ⎢⎢⎢⎢⎢ . .. ⎥⎥⎥⎥ , ⎢⎢⎢ .. . ⎥⎥⎥ ⎦ ⎣ h1,J h2,J
(22)
(23)
with components defined in (7), and matrix I is the J × J identity matrix. Therefore, when (22) is satisfied, (18) can be calculated as
(26)
where T 1 and T 2 are thresholds applied in Kurtosis based BSS spectrum sensing, chosen so as to satisfy a desired false-alarm probability. The overall procedure followed in BSS spectrum sensing can be summarized as follows (k denotes the k-th primary frame and K is the total number of the primary frames):
For the case in which both of the primary signal and the cognitive signal are present, the vector yi can be rewritten as: ⎛ 2 ⎞ J ⎜⎜⎜ ⎟⎟⎟ wi, j ⎜⎜⎜⎝ hk, j sk + z j ⎟⎟⎟⎠ , yi = (20) j=1
(24)
4.
An Improved Framework for Spectrum Sensing
In this section, we propose to use jointly the covariance based detection and the Kurtosis based BSS spectrum sensing methods. First, we explain our proposed spectrum sensing algorithm. Then, in order to characterize its associated performance, we model our algorithm by using tools from the Markov chain theory [22]. 4.1 Improved Spectrum Sensing Framework Algorithm Let us first explain the methodology followed in our proposed technique. This is more clearly depicted in Fig. 2. As
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Fig. 2 Overview of the proposed spectrum sensing framework, “m1 ” denotes covariance detection and “m2 ” denotes BSS detection.
shown, we start the spectrum sensing process by using covariance detection, assuming that the CR transmitter is off. When the decision of spectrum sensing allows the CR transmitter to transmit (i.e., it decides that the primary is off), we switch the sensing method to BSS which has the capability of separating the cognitive and primary signals. In this way, we can keep the cognitive transmission on during the spectrum sensing until the algorithm detects the presence of a primary signal. In this case, we turn off the CR transmitter and switch the sensing method to covariance detection, and so on. In fact, by using our method, the adopted sensing technique in a given cognitive sensing window (CSW) depends on the decision made by the algorithm in the previous CSW. For the sake of simplicity hereafter, we refer the covariance based detection as method one (m1 ) and the Kurtosis based BSS detection as method two (m2 ). More precisely, based on the result of the spectrum sensing in the (n − 1)th CSW, the type of the spectrum sensing method adopted within the n-th CSW is selected as follows. • Covariance spectrum sensing (method m1 ) is adopted in the n-th CSW, if the CR decision in the (n − 1)-th 1 (in this case, the cognitive transmitter can CSW is H not be active during the the n-th CSW), • Kurtosis based BSS spectrum sensing (method m2 ) is adopted in the n-th CSW, if the CR decision in the (n − 0 (in this case, the cognitive transmitter 1)-th CSW is H can be active during the n-th CSW). The overall operation summarizing the proposed new spectrum sensing framework is provided in the following algorithm. In this algorithm, the index n is the index of the CSW (a cognitive sensing window which is a portion of the primary frame) and the parameter, N, is the total numbers of CSWs. Here, we consider T as the number of primary symbols per frame, and for convenience we define as =
Fig. 3 Transition diagram that models the proposed spectrum sensing framework by a finite-state machine with four states. Pi j indicates the transition probability from the i-th state at time (n − 1) to the j-th state at time n.
L/T . Using we can see that N = −1 K (see Fig. 2 for more details). 4.2 Improved Spectrum Sensing Framework Modeling Spectrum sensing performance evaluation is usually analyzed by means of receiver operating characteristic (ROC) curves that plot the miss-detection probability (defined in (3)) versus the false-alarm probability (defined in (4)). As explained in Sect. 4.1, in our approach, the spectrum sensing decision in the n-th CSW depends on the decision made in the (n − 1)-th CSW. Hence, we propose to use tools from the Markov chain theory [22] to model the spectrum sensing algorithm and obtain the miss-detection and false-alarm probabilities. Note that these two probabilities let us to plot the ROC curve that characterize the performance achieved with our spectrum sensing technique. The decision made 1 . Moreover, the pri0 or H by the spectrum unit is either H mary network transmitter is either on or off characterized by hypotheses H0 and H1 . Thus, in each CSW, four different scenarios can be defined based on the decision made by the spectrum sensing unit and the actual state of the primary transmitter. We propose here to view these four scenarios as the states of a finite-state machine that can be modeled by a Markov chain, as depicted in Fig. 3. Below, we describe each state in more details. 1 , H0 } • State 1: This state corresponds to the event {H and indicates the occurrence of a false-alarm (see the first equation in (6)), 0 , H0 } • State 2: this state corresponds to the event {H and occurs when the cognitive network decides that the primary is off, where the primary is actually off (see the second equation in (7)),
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Proposed Spectrum Sensing Algorithm ◦ Start the sensing algorithm while the cognitive transmitter is not in operation (n = 1) ◦ For n = 1 : N • If the cognitive transmitter is not in operation in the n-th CSW
Apply m1
Calculate the covariance matrix Σ using (12)
Calculate λmax and λmin from the covariance matrix Σ of (12)
Use (13) to determine θcov (n) by using m1 1
If θcov (n) = H Cognitive transmitter is off at the (n + 1)-th CSW 0
Else If θcov (n) = H Cognitive transmitter is on at the (n + 1)-th CSW
End If • Else If the cognitive transmitter is in operation in the n-th CSW
Apply (m2 ) on the n-th CSW
Separate the mixed signals based on (17)
Apply the Kurtosis metric (17) for all separated signals
Use (26) to determine θ2BS S (n) by using m2 1
If θ BS S (n) = H 2
Cognitive transmitter is off at the (n + 1)-th CSW 0
Else If θ BS S (n) = H 2
Cognitive transmitter is on at the (n + 1)-th CSW
End If • End If ◦ End For
0 , H1 } • State 3: this state corresponds to the event {H and indicates the occurrence of a miss-detection (see the third equation in (7)), 1 , H1 } • State 4: this state corresponds to the event {H and occurs when the cognitive network decides that the primary is on, where the primary is actually on (see the first equation in (7)). Note that in general, any transition between the states defined above is possible and has to be considered in our model, as shown in Fig. 3. The set of all transition probabil-
ities involved in our model is provided in the following 4 × 4 matrix ⎤ ⎡ ⎢⎢⎢P11 P12 P13 P14 ⎥⎥⎥ ⎥ ⎢⎢⎢ ⎢⎢⎢P21 P22 P23 P24 ⎥⎥⎥⎥⎥ ⎥, P = ⎢⎢⎢ (27) ⎢⎢⎢P31 P32 P33 P34 ⎥⎥⎥⎥⎥ ⎥⎦ ⎢⎣ P41 P42 P43 P44 where Pi j for (i, j ∈ {1, . . . , 4}) refers to the the transition probability from state i at the (n − 1)-th CSW to state j at the n-th CSW. Let us denote by Si (n) for i ∈ {1, . . . , 4} the state at the n-th CSW. The transition probability Pi j writes (28) Pi j = P S j (n)|Si (n − 1) . i (n) for i ∈ {0, 1} as the primary We also define Hi (n) and H activity hypotheses and spectrum sensing decision at the nth CSW. Let us denote by qi j for i, j ∈ {0, 1}, the probability for the primary transmitter to switch from an on/off state at the (n − 1)-th CSW to an on/off state at the n-th CSW. We have (29) qi j = P H j (n)|Hi (n − 1) , where i = 1 and j = 1 indicate the presence of the primary signal during the (n − 1)-th and the n-th CSW, respectively. Similarly, i = 0 and j = 0 indicate the absence of the primary signal during the (n−1)-th and n-th CSW, respectively. In the sequel, we aim at deriving the transition probabilities defined in (27). Using (28), we start by deriving P11 as 1 (n), H0 (n)|H 1 (n − 1), H0 (n − 1) . P11 = P H (30) Equation (30) can be rewritten as 1 (n)|H0 (n), H 1 (n − 1), H0 (n − 1) P11 = P H 1 (n − 1), H0 (n − 1) . × P H0 (n)|H
(31)
Here, we assume that in a given frame, the cognitive network has no prior knowledge about the presence/absence of the primary signal in the previous CSW. We have 1 (n − 1), H0 (n − 1) P H0 (n)|H = P {H0 (n)|H0 (n − 1)} = q00 ,
(32)
where in (32), we have used the independence between j (n − 1). Note that this independence is due Hi (n) and H to the fact that the actual presence or absence of the primary user is inherent to the channel use of the primary transmitter and hence does not depend to the decision made by the unit at any time instant. spectrum sensing (H) Remember that in our method, the decision of the speci (n)) depends on the decitrum sensing in the n-th CSW (H sion in the (n − 1)-th CSW. More precisely, the hypothesis i (n) does not depend on the actual state of the primary user H (Hi (n − 1)). Hence, (31) can be rewritten in a more simple
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form as P11
1 (n)|H0 (n), H 1 (n − 1) . = q00 × P H
(33)
As explained previously, in our approach, the type of the spectrum sensing method (m1 or m2 ) used in the nth CSW is selected based on the spectrum sensing decii , for i ∈ {0, 1}. sion made in the previous CSW, i.e., H In other words, knowing what method has to be used in a given CSW, is equivalent to knowing the spectrum sensing m j (n) decision made in the previous CSW. We introduce H i (i ∈ {0, 1}, j ∈ {1, 2}) to denote the spectrum sensing decision associated to method m j during the n-th CSW. In this way, we can write (33) in a simpler form as m 1 (n)|H0 (n) . (34) P11 = q00 × P H 1 m1 (n)|H0 (n)} in (34), is According to (4), the quantity P{H 1 actually the false-alarm probability associated to the covariance sensing method (method m1 ), that we denote by Pm1 f (n). We thus have P11 = q00 × Pmf 1 (n) = q00 × Pmf 1 ,
(35)
where Pmf 1 in (35) is defined as: m 1 |H0 . Pmf 1 = P H 1
(36)
P= ⎡ ⎢⎢⎢q00 Pmf 1 ⎢⎢⎢⎢ ⎢⎢⎢ m2 ⎢⎢⎢q00 P f ⎢⎢⎢ ⎢⎢⎢ m2 ⎢⎢⎢q10 P f ⎢⎢⎢ ⎣ q10 Pmf 1
q00 1 − Pmf 1 q00 1 − Pmf 2 q10 1 − Pmf 2 q10 1 − Pmf 1
1 q01 Pm m 2 q01 Pm m 2 q11 Pm m 1 q11 Pm m
(41) Next, the transition matrix P is used for the derivation of the miss-detection and the false-alarm probabilities associated to the improved spectrum sensing framework. 4.3 Derivation of the Performance Measures Associated to the Improved Spectrum Sensing Framework According to the Markov chain theory [22], there is at least one stationary distribution for a finite Markov chain. Here, we analyze the stationary distribution for the transition matrix P in (41). This stationary distribution enables us to derive the miss-detection and the false-alarm probabilities that characterize the overall performance of the improved spectrum sensing framework. We denote by π(n) = [π1 (n), ..., π4 (n)]T the vector of states probabilities at the n-th CSW, where πi (n) for i ∈ {1, . . . , 4} is the probability of being in the i-th state, i.e., πi (n) = P {Si (n)} .
Let us now derive P22 which is by definition given by 0 (n), H0 (n)|H 0 (n − 1), H0 (n − 1) . (37) P22 = P H Following similar line of arguments we provide for equivalence between (31) and (33), we can rewrite (37) as 0 (n)|H0 (n), H 0 (n − 1) . P22 = q00 × P H (38) Again, due to the equivalence that we have in our scheme 0 (n)|H 0 (n − 1)} and {H m2 (n)}, we obbetween the events {H 0 tain m 2 (n)|H0 (n) . (39) P22 = q00 × P H 0 m2 (n)|H0 (n)} is equal to 1 − Pm2 , Since according to (4), P{H 0 f with Pmf 2 being the false-alarm probability associated to method m2 , we obtain P22 = q00 × 1 − Pmf 2 . (40) Following a procedure similar to that adopted for deriving P11 and P22 , it is straightforward to calculate other transition probabilities involved in the transition diagram of Fig. 3. By doing so, the transition matrix (27) can be filled as
⎤ 1 q01 1 − Pm ⎥⎥⎥ m ⎥ ⎥⎥ ⎥ m 2 ⎥ q01 1 − Pm ⎥⎥⎥⎥ ⎥⎥⎥ . ⎥ m 2 ⎥ q11 1 − Pm ⎥⎥⎥⎥ ⎥⎥⎥ ⎦ m 1 ⎥ q11 1 − Pm
(42)
At the beginning of the proposed spectrum sensing framework (i.e., n = 0), we assume that the cognitive transmitter 1 (0)) and we have no a priori knowlis not in operation (H edge about the presence or absence of the primary signal (H0 (0) or H1 (0)). Thus, the algorithm starts at either state 1 or state 4 with equal probabilities of 0.5, depending on the presence or the absence of the primary signal. Moreover, this procedure can never start from state 2 or state 3. Consequently, the initial state probability vector denoted by π(0) is π(0) = [ 0.5, 0, 0, 0.5 ]T .
(43)
According to the Markov chain theory [22], the state probabilities at the n-th CSW for the transition diagram in Fig. 3 can be written as π(n) = Pn π(0).
(44)
Considering the states probability vector (44) and the transition matrix (27), the stationary distribution for the proposed spectrum sensing method is given by [22] π = lim π(n) = lim Pn π(0), n→∞
n→∞
(45)
where π = [π1 , ..., π4 ]T is the stationary distribution vector and πi for i ∈ {1, . . . , 4} is the stationary probability of being in the i-th state. Since the Markov chain theory guarantees the existence
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of a solution for (45) [22], we solve the following equation (finding the eigenvector π for the transition matrix P of (27)) to calculate the stationary probability vector π [22]. P × π = π.
(46)
Three independent equations can be extracted from (46) while there are four variables (πi for i ∈ {1, . . . , 4}). So, we add the following equation to calculate the unknown stationary probability vector. 4
πi = 1.
(47)
i=1
It is straightforward to obtain the vector π from (46) and (47). After solving this problem, the miss-detection and the false-alarm probabilities for the improved spectrum sensing framework are obtained as 0 , H1 P H π3 I Pm = = , (48) P{H1 } P{H1 } and PIf =
1 , H0 P H P{H0 }
=
π1 , P{H0 }
Fig. 4 The ROC curves for improved and conventional spectrum sensing methods with sensing SNR=10 dB. (“Imp” denotes the improved spectrum sensing method).
(49)
respectively, where P{Hi } for i ∈ {0, 1} is the a priori probability on the presence or the absence of the primary signal. Here, we assume that the CR network has no knowledge about the presence or the absence of the primary signal and thus these a priori probabilities are set equal to 0.5. 5.
Numerical Results and Discussion
In this section, we provide numerical results to evaluate the performance provided by the proposed combined spectrum sensing method in comparison with each one of the conventional techniques [7] (covariance detection) and [13], [14] (BSS detection). Throughout the simulations, the transmitted power for both primary and cognitive transmitters is normalized to one. The length of the sensing window is set to L = 100 samples. The rest of the parameters are extracted form the IEEE 802.22 standard [23]. Figure 4 plots the ROC curves, i.e., the miss-detection probability Pm versus the false-alarm probability P f to compare the sensing performance achieved with our proposed joint method and conventional methods m1 and m2 under a sensing signal-to-noise ratio (SNR) of 10 dB. This figure is plotted in order to see the effect of parameter on spectrum sensing performance. We observe that whereas the value of has no effect on conventional methods, the proposed method’s sensing performance is improved for smaller values of parameter . This can be explained by the fact that when decreases, the correlation between primary frames becomes larger (characterized by the decrease of q01 and q10 ) and since our method inherently takes this correlation into account, the sensing performance is improved. In other
Fig. 5 The miss-detection probability Pm versus the parameter for improved and covariance sensing techniques, sensing SNRs are equal to 0, 5 and 10 dB, (“Imp” denotes the improved spectrum sensing method).
words, the primary signal in the n-th CSW is correlated to the (n − 1)-th CSW; so, there are some information about the primary signal in the decision that is made in the (n − 1)th CSW. In conventional spectrum sensing methods such as covariance spectrum sensing, spectrum sensing decision is made only based on the information that can be extracted from the n-th CSW, while in our proposed spectrum sensing method, the decision is based on both the information in the n-th and the (n−1)-th CSWs, which obviously contains more information. For more precisions, we have shown in Fig. 5 the miss-detection probability Pm versus the primary network parameter when the false-alarm probability is set to
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pared to the conventional covariance sensing method even for bad sensing conditions (characterized by a sensing SNR of 0 dB). Figure 7 plots the miss-detection probability Pm versus the sensing SNR when the false-alarm probability is set to 0.01. We observe that our proposed method remains more accurate than its competitive methods for a wide range of sensing SNR. 6.
Fig. 6 The ROC curves for improved and covariance spectrum sensing, sensing SNR=0 dB (“Imp” denotes the improved spectrum sensing method, “CT” denotes cognitive transmitter).
Conclusion
Spectrum sensing is one of the most important parts in the implementation of each CR system. Conventional spectrum sensing techniques such as covariance detection do not allow the CR transmitter to transmit during the sensing process. Obviously, this leads to a waste of spectral resources. Although spectrum sensing based ob BSS can overcome this limitation, it has relatively a lower performance compared to energy detection and covariance detection. Here, we proposed a new spectrum sensing framework that combines blind source separation algorithms jointly with conventional covariance detection. We also derived by means of Markov chain modeling, the performance measures associated to our proposed technique in terms of miss-detection and false-alarm probabilities. Numerical results indicated that our proposed method outperforms conventional covariance detection technique. In addition, by using our sensing technique, the CR transmitter can continue to transmit even during spectrum sensing. References
Fig. 7 The miss-detection probability Pm versus the sensing SNR for the comparison between the improved spectrum sensing method and its constructive methods (“Imp” denotes the improved spectrum sensing method, “CT” denotes cognitive transmitter).
0.01. The figure illustrates the comparison between the improved spectrum sensing and the covariance spectrum sensing for sensing SNRs of 0, 5 and 10 dB. We observe that the improved method provides smaller miss-detection probability (i.e., becomes more accurate) when the ratio of the cognitive network sensing window to the primary frame length (i.e., the parameter ) decreases. Similar ROC curves are depicted in Fig. 6 comparing our proposed joint method with the covariance spectrum sensing under a sensing SNR equal to 0 dB. We observe that our proposed sensing method is still of advantage com-
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Navid Tafaghodi Khajavi received his B.Sc. degree in Electrical Engineering (communication) from Faculty of Engineering at the Ferdowsi University, Mashhad, Iran. He is currently pursuing the M.S. degree in Electrical Engineering (telecommunication) at Shahid Beheshti University, Tehran, Iran. His current research interests include cognitive radio, resource allocation algorithms, convex optimization problems and wireless communications.
Siavash Sadeghi Ivrigh received his B.Sc. degree in Electrical Engineering from the department of Electrical Engineering at Noshirvani Institute of Technology, Babol, Iran. He is currently pursuing M.Sc. degree in Electrical Engineering at Shahid Beheshti University, Tehran, Iran. His current research interests include cognitive radio, blind source separation, source localization and wireless communications.
Seyed Mohammad-Sajad Sadough was born in Paris in 1979. He received the B.Sc. degree in Electrical Engineering (electronics) from Shahid Beheshti University, Tehran, I.R. Iran in 2002 and the M.Sc. and the Ph.D. degrees in Electrical Engineering (telecommunication) from Paris-Sud 11 University, Orsay, France, in 2004 and 2008, respectively. From 2004 to 2007, he was jointly with the National Engineering School in Advanced Techniques (ENSTA), Paris, France, and the Laboratory of Signals and Systemes (LSS), at Sup´elec, Gif-sur-Yvette, France. He was a lecturer with the Depertment of Electronics and Computer Engineering (UEI), ENSTA, where his research activities were focused on improved reception schemes for ultra-wideband communication systems. From December 2007 to September 2008, he was a postdoctoral researcher with the LSS, Sup´elec-CNRS, where he was involved in the European research project TVMSL with Alcatel-Lucent France. Since October 2008, he has been with the Faculty of Electrical & Computer Engineering, Shahid Beheshti University, where he is currently an Assistant Professor with the Department of Telecommunication. Dr. Sadough’s areas of research include signal processing, communication theory, and digital communication.
