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Limited reporting-based cooperative spectrum sensing for multiband cognitive radio networks
Accepted Manuscript Title: Limited Reporting-based Cooperative Spectrum Sensing for Multiband Cognitive Radio Networks Author: id="aut0005" > Jaewoo So id="aut0010" > Taesoo Kwon PII: DOI: Reference:
S1434-8411(15)30033-9 http://dx.doi.org/doi:10.1016/j.aeue.2015.12.017 AEUE 51536
To appear in: Received date: Revised date: Accepted date:
6-8-2015 5-11-2015 22-12-2015
Please cite this article as: Jaewoo So, Taesoo Kwon, Limited Reportingbased Cooperative Spectrum Sensing for Multiband Cognitive Radio Networks, (2016), http://dx.doi.org/10.1016/j.aeue.2015.12.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Limited Reporting-based Cooperative Spectrum Sensing for Multiband Cognitive Radio Networks Jaewoo So∗
Taesoo Kwon
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Department of Electronic Engineering Sogang University, Seoul 04107, Republic of Korea
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Department of Computer Science and Engineering Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
Abstract
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The performance of cooperative spectrum sensing depends on the sensing time, the reporting time of transmitting sensing results, and the fusion scheme. While longer sensing and reporting time will improve the sensing performance, this shortens the allowable data transmission time, which in turn degrades the throughput of secondary users. In a cognitive radio network with multi-primary bands, the reporting time increases with the number of reporting nodes and primary bands to be reported. This paper proposes a limited reporting scheme for multiband cooperative spectrum sensing with a soft combination rule in order to reduce the reporting time while satisfying the detection probability constraint. In the proposed reporting scheme, the upper bound of the number of reporting nodes and the reported primary bands are dynamically controlled according to the number of cooperative secondary users. We formulate a trade-off between the throughput of secondary users and the overheads of cooperative spectrum sensing. Simulation results show that the sensing time and reporting time should be jointly optimized in order to maximize the throughput of secondary users. Moreover, in comparison with the conventional sensing-throughput optimization schemes, the proposed reporting scheme significantly increases the throughput of secondary users by reducing the reporting time.
1. Introduction
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Keywords: Cognitive radio, sensing-throughput optimization, multiband cooperative spectrum sensing, sensing-reporting overhead.
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In cognitive radio (CR) networks with multi-primary bands, spectrum sensing is a key technology to realize spectrum sharing over a confined spectrum (e.g. DTVbands). Generally, the signal detection techniques can be classified into energy detection, matched filtering detection, and cyclostationary feature detection [1]. However, in response to the transitional detectors being inefficient when noisy uncertainty is severe, an entropyI This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2058084) and it was also supported by the NRF grant funded by the Korea government (MSIP) (2012R1A2A2A01012059). ∗ Corresponding author: J. So. Email addresses: [email protected] (Jaewoo So), [email protected] (Taesoo Kwon)
Preprint submitted to AEU - Int. J. of Electronics and Communications
based detector that is robust to the noise uncertainty has been proposed [2, 3]. In practice, many factors, such as multipath fading, shadowing, and the hidden primary user (PU) problem, may significantly affect detection performance. To solve this challenging problem, cooperative spectrum sensing (CSS) has been extensively studied in efforts to increase the sensing performance [4–6]. The CSS has three successive phases, sensing, reporting, and decision. In the sensing phase, each sensing node locally senses the signal of PUs. Then, in the next reporting phase, sensing nodes report their observed sensing results to a fusion center (FC). In the decision phase, the FC determines the presence of a PU by combining multiple independent sensing results reported by sensing nodes, where it can use hard combination methods (e.g., OR-rule, AND-rule, and k-outof-K rule) or a soft combination method [7–9]. It beDecember 30, 2015
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anisms and spatial-spectral diversity over multiple primary channels. However, the above studies of [19–22] failed to propose a reporting scheme that reduces the reporting overhead in order to increase the throughput of SUs. Some researchers have endeavored to reduce the sensing time or reporting overhead. In conventional hard combination-based CSS, each SU reports only onebit decision to the FC. Its reporting overhead is thereby minimized but it suffers degradation of the sensing performance because of information loss caused by local hard decisions. To achieve a balanced trade-off between the sensing performance and the reporting overhead, some researchers have proposed a two-bit or three-bit combination rule [8,23,24]. The authors of [25,26] proposed a two-stage spectrum sensing scheme in order to reduce the sensing time and maximize the sensing performance, where coarse sensing based on energy detection is performed in the first stage and, if required, fine sensing is performed in the second stage. While [25,26] did not consider CSS, the authors of [2, 27] proposed a two-stage spectrum sensing scheme in the CSS. The author of [2] improved the sensing performance via a two-stage two-bit CSS and the authors of [27] reduced energy consumption via two-stage energy-efficient onebit CSS. This paper discusses multiband CSS in CR networks with a soft combination method. The contribution of this paper is twofold. First, this paper proposes a new reporting scheme that reduces the reporting overhead in multiband CR networks. The proposed scheme dynamically controls the upper bound of the number of reporting nodes and reported bands in multiband CSS according to the number of cooperative SUs. The proposed limited reporting scheme significantly increases the throughput of SUs by reducing the reporting overhead of multiband cooperative sensing while satisfying the detection probability constraint. Second, this paper formulates a trade-off problem between the throughput of SUs and the overheads of CSS including both the sensing time and the reporting time. Whereas most previous studies of [11, 12, 14] formulated a sensingthroughput trade-off problem without taking the reporting time into consideration. Although a few works investigated the effect of the reporting overhead on the sensing performance, they assumed that the FC uses a hard combination method and moreover they failed to propose an idea that reduces the reporting overhead [17, 20]. The remainder of this paper is organized as follows: Section 2 describes the system model, where the processes of four phases, sensing, reporting, decision, and
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comes obvious that the performance of the CSS is dependent on the sensing time, reporting time, and the fusion scheme [10]. As the sensing and reporting time increase, the sensing performance increases; however, with a fixed frame size, the allowable data transmission time of secondary users (SUs) is shortened and therefore the throughput of SUs decreases. One of the important issues in the design of CSS is determining the sensing time, reporting time, and parameters for the fusion scheme. Many researchers have endeavored to find the optimal parameters that maximize the throughput of SUs. Some researchers have focused on finding the optimal sensing time by formulating a sensing-throughput trade-off problem when a hard combination method is adopted at the FC [11–14]. Other researchers have focused on finding the optimal fusion parameters (e.g., the reporting threshold for the OR-rule and a voting threshold for the k-out-of-K rule) that maximize the sensing performance or the throughput of SUs [9, 15, 16]. The authors of [17] formulated a sensing-reporting optimization problem to find the optimal division of time between the sensing time and the reporting time when the k-out-of-K rule is adopted at an FC, where they assumed the sum of the sensing time and the reporting time is fixed. The author of [2] proposed two-stage entropy-based CSS in order to counteract the effect of noise uncertainty, where the proposed entropy-based CSS scheme required less computational complexity but still outperformed the previous hard combination-based CSS schemes. However, the above studies of [2, 9, 11–17] did not take into consideration the effect of the reporting time on the throughput of SUs, and moreover they considered single band CSS. Moreover, they adopted a hard combination method, an OR-rule or a k-out-of-K rule, at an FC. A soft combination method shows better sensing performance than hard combination methods at the cost of increased bandwidth of reporting channels [8, 18]. In contrast with the above work for single band CSS, some studies have considered CSS with multiple primary bands [19–22]. The authors of [19] proposed a sensor allocation and quantization scheme for multiband CSS. The authors of [20] formulated a sensingthroughput trade-off problem to find a pair of the sensing time and the number of SUs that report their sensing results when an OR-rule is adopted at an FC in multiband CR networks. The authors of [21] formulated a sensing-throughput optimization problem to find the optimal time setting to sense multiple primary bands and they proposed a slotted-time sensing mode and a continuous-time sensing mode. The authors of [22] investigated the relationship between cooperation mech-
2
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[Reporting Phase] Selected k SUs report sensing results about n PU bands
PU
band 1 band 2
band N
.. .
Tf Tr Reporting
SU 1
1 SU 2
PU
Ts Sensing 2
... N 1
2
τs
.. .
1 2 ... l frequency
SU's data transmission l, k, n : optimization variables
1 2 ... n
Sense PU signal for l samples at each band
Report sensing results about n bands via a reporting channel
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Figure 1: Proposed system model.
... i ... k
τr
CR base station
SU K
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[Sensing Phase] All SUs sense N PU bands
Figure 2: Frame structure of the CR network.
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transmission of SUs, are described and a limited reporting scheme is proposed in the reporting phase. Section 3 analyzes the false alarm probability of the multiband CSS with the proposed reporting scheme. Section 4 formulates a sensing-reporting-bands optimization problem and presents an iterative algorithm to solve the optimization problem. Section 5 presents the numerical results and finally, Section 6 concludes the paper.
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• In the sensing duration, each SU sequentially senses N bands during T s , where each SU observes the PU signal during l sample time at each band. Hence, the total sensing time can be represented by T s = l · N · τ s , where τ s is one sample time duration. The sensing time increases in proportion to the number of primary bands to be sensed regardless of the number of SUs because all SUs observe the PU signal at the same time.
2. System Model
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2.1. System Description As shown in Fig. 1, we consider a centralized CR network with N primary frequency bands (termed bands hereafter) and K SUs, where a CR base station functions as an FC and each SU functions as a cooperative sensing node. In the proposed system model, some of K SUs are selected to report their sensing results to the FC, where the sensing result reported by a selected SU includes the observed sensing information about n bands not all N bands. That is, k SUs out of K SUs are selected to report sensing results for n bands out of N bands. Let the symbol i denote the index of SUs or reporting nodes. Let the symbol j denote the index of primary frequency bands, i.e., j ∈ N = {1, 2, · · · , N}. In each band, a PU exists but may not be active all the time. An energy detector is implemented at each SU. The FC determines the presence of a PU at each band by combining multiple independent sensing results from SUs, where the FC uses an MRC-based soft combination method [16]. As shown in Fig. 2, each frame of a CR network is divided into sensing duration, reporting duration, and data transmission duration. Let the frame time, sensing time, reporting time, and data transmission time be respectively denoted by T f , T s , T r , and T d , where T f = T s + T r + T d . The overall operation of each duration is as follows:
• In the reporting duration, SUs report their sensing results to the FC. Let the number of SUs who are selected to report their sensing results be n. The total reporting time is then given by T r = k · n · τr , where τr is the duration of a time slot.
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• In the data transmission duration, if the FC decides the absence of a PU at band j, one SU selected by the FC transmits data at band j, where the FC is assumed to use a round-robin (RR) scheduling algorithm.
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Additionally, we assume that the errors due to the reporting of sensing results are negligible. 2.2. Local Spectrum Sensing at SUs When the ith SU senses during l samples at each band, the observed energy value of the ith SU at band j can then be expressed as { ∑l wi, j (t)2 , H 0, j ∑t=1 Yi, j = (1) l 2 , H 1, j , t=1 (si, j (t) + wi, j (t)) where H 0, j and H 1, j represent that the PU in band j is idle and busy, respectively; t is the sample index; si, j (t) is the received PU signal and wi, j (t) is the white 3
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of the detection probability, PDj ≥ λ. Moreover, the parameters do not have to be broadcast in every frame. Whenever the number of cooperative SUs changes or every hundreds or thousands of frames, the parameters can be periodically broadcast to SUs in order to inform who reports sensing results and how many bands are reported. The optimization problem to find the optimal values of k and n is described in Section 4.
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noise at the tth sample of the ith SU at band j, respectively. The noise at each sample is assumed to be Gaussian distributed with zero mean and unit variance, i.e., wi, j (t) ∼ N(0, σ2 ), where σ2 = 1. Let γi, j represent the received instantaneous signalto-noise ratio (SNR) of the signal received by the ith SU at band j within the observation period, defined as ∑ γi, j = 1l lt=1 si, j (t)2 /σ2 [8]. We assume γi, j varies from (observation) period to period. We suppose γi, j ’s of SUs are independent and identically distributed (i.i.d.). This assumption is valid for a small-sized CR network or for the case that the appearances of PUs are uniformly distributed [21, 23]. Furthermore, we assume an i.i.d. channel for each band. The probability density function (pdf) and cumulative distribution function (cdf) of the received SNR of each SU at each band are respectively denoted by fγ (γ) and Fγ (γ).
Yj
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2.4. Decision of the PU’s Presence at the FC Let Yi, j represent the sensing energy on band j in the ith received reporting message. If the number of received reporting messages including the sensing information on band j is m at the FC, an MRC-based weighted summation of the FC at band j can then be expressed as m ∑
=
ωi, j Yi, j ,
1 ≤ j ≤ N,
(2)
i=1
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2.3. Proposed Limited Reporting Scheme
where ωi, j is a weight factor. Let γi, j be the PU’s SNR at band j in the ith received reporting message and let the set of γi, j be denoted by γm, j = {γ1, j , γ2, j , · · · , γm, j }, where m is the number of SUs who report a sensing result on band j. The optimal value of ωi, j can then be √ ∑m ( )2 approximated as ω∗i, j ≈ γi, j / [8]. i=1 γi, j D Given a detection probability of P j and the SNR list of γm, j , the conditional false alarm probability at band j can then be expressed as [8, 21] v t m ∑ −1 D F P j (γm, j ; l) = Q Q (P j ) ω2i, j (1 + 2γi, j ) i=1 √ m ∑ l ωi, j γi, j , (3) + 2 i=1
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In the conventional multiband CSS scheme, each SU reports sensing results for all PU bands. The required total reporting time therefore becomes T r = K · N · τr , where K is the number of cooperative SUs, N is the number of primary bands, and τr is the duration of one reporting time slot. In order to reduce the reporting overhead of multiband CSS, we propose a new reporting scheme. The proposed scheme determines the upper bound of the number of reporting nodes and the reported bands in multiband CSS while satisfying the detection probability constraint. The FC randomly selects k SUs as reporting nodes out of K SUs. Each selected SU reports sensing results for n bands out of N bands on the basis of the received SNR value at each band. Hence, in the proposed reporting scheme, the reporting time becomes T r = k · n · τr , where k ≤ K and n ≤ N. The reported bands are determined in descending order of the observed SNRs at each band. For example, an SU has an observed SNR list of N = 5 bands as follows {−5 dB, −9 dB, −12 dB, −7 dB, −11 dB}. If the number of bands to be reported is n = 3, the SU reports the sensing results for band 1, band 2, and band 4 after a sorting process based on the observed SNR values. The design of the proposed reporting scheme involves choosing the values of k and n. As smaller values of k and n decrease the reporting time, this may deteriorate the sensing performance. To provide sufficient protection to the PU, the detection probability, PDj , should be no smaller than a prescribed threshold, λ. Hence, the values of k and n are adaptively determined according to the number of cooperative SUs under the constraint
where l∫ is the number of sensing time samples and ∞ 2 Q(x) = x √12π e−t /2 dt.
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2.5. Data Transmission of SUs For a CR network, we assume a Rayleigh fading channel with additive white Gaussian noise of zero mean and unit variance. Let ζ j be the instantaneous SNR of an SU during the SU’s data transmission at band j. When the PU’s frequency band j is idle and the FC identifies the absence of a PU, one selected SU transmits data, where the FC is assumed to select an SU according to an RR scheduling algorithm. According to Shannon’s capacity theorem, the average SU’s spectral efficiency at band j is given by ∫ ∞ ( ) c0, j = log2 1 + ζ j fζ (ζ j )dζ j , H 0, j , (4) 0
4
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where fζ (ζ j ) is the pdf of ζ j . When the FC falsely detects the presence of a PU although there is a PU, an SU can transmit data. Hence, when the frequency band j is used by a PU, the average SU’s spectral efficiency at band j is given by ( ) ∫ ∞∫ ∞ ζj c1, j = log2 1 + 1 + γj 0 0 × fζ (ζ j ) fγ (γ j )dζ j dγ j , H 1, j , (5)
the SU can report the sensing information observed at the jth band to the FC, where γu is the SNR observed at the uth band. Consequently, the probability that the ith SU reports the SNR, γi, j , observed at the jth band can be expressed as follows: N ∑ g j (γi, j ; n) = Pr I(γi,u > γi, j ) < n fγ (γi, j ) =
where γ j is the SNR from the PU to the SU at band j. Consequently, the average achievable capacity of an SU at each band can then be formulated as ( ) l · N · τ s k · n · τr C(l, k, n) = 1 − − Tf Tf N { ∑ F 1 × c0, j (1 − P j )P(H0, j ) N j=1 } D + c1, j (1 − P j )P(H1, j ) , (6)
α(N − 1, v, γi, j ) fγ (γi, j ).
v=0
(8)
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Given the number of m, the average false alarm probability at band j can then be expressed as ∫ ∫ ∫ F ··· PFj (γm, j ; l) P j (m; l, n) = | {z } γ1, j γ2, j γm, j
×
m ∏
an
D
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u=1,u, j
n−1 ∑
Conditional false alarm probability given γm, j in (3)
g j (γi, j ; n) dγ1, j dγ2, j · · · dγm, j , (9)
i=1
F
where m is the number of received reporting messages including sensing information on band j at the FC. The probability that the SU reports the sensing information observed at band j is given by q j (n) = ∫∞ g (γ; n)dγ. Let p j (m; k, n) denote the conditional j 0 probability that m messages out of k received reporting messages at the FC include the sensing information on band j. The probability can then be expressed as follows: ( ) ( )k−m k p j (m; k, n) = q j (n)m 1 − q j (n) . (10) m
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where P j and P j are the average detection probability and false alarm probability at band j, respectively. Given the value of the detection probability, the averF age false alarm probability, P j , is dependent on the reporting scheme and parameters, (l, k, n), for the fusion scheme. We first derive the average false alarm probability of the multiband CSS with the proposed reporting scheme in Section 3. We then formulate the optimization problem to find the optimal parameters of (l, k, n) in Section 4.
Consequently, given parameters, (l, k, n), the average false alarm probability of band j can then be expressed as k ∑ F F Pj = (11) p j (m; k, n) P j (m; l, n).
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3. Average False Alarm Probability of CSS with a Proposed Limited Reporting Scheme Let γu represent the observed SNR at band u. Additionally, let α(N, v, η) be the probability that the number of bands with γu > η is v among the total N bands, where u ∈ N. The probability can then be expressed as follows: N ∑ I(γu > η) = v α(N, v, η) , Pr
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m=1
4. Optimization Problem 4.1. Problem Formulation In multiband CSS, with given fixed values of K, N, and T f , an optimization problem that maximizes the average capacity of an SU can be formulated as follows:
u=1
=
( )( )v N 1 − Fγ (η) Fγ (η)N−v , v
(7)
max
C(l, k, n)
s.t.
Pj ≥ λ
l,k,n
where I(x) is the index function, which is defined as follows: if x is true, I(x) = 1; otherwise, I(x) = 0. In the proposed reporting scheme, the number of bands to be reported by an SU is limited to n in descending order of SNRs observed at each band. Hence, if an ∑N SU satisfies the condition of u=1,u, j I(γu > γ j ) < n,
D
(12) for ∀ j
0
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and ∆2 f1 (l) = 0. Moreover, we have
max l,k,n
∆ f2 (l) = = =
N ( )} F 1 ∑{ (1 − lN∆ s − kn∆r ) × 1 − P j (l, k, n) N j=1 | {z }
′
f2 (l ) − f2 (l) [ F ] F ′ − P (l ) − P (l) k ∫ ∫ ∑ − p(m) · · · γm m=1 { } ′ × PF (γm ; l ) − PF (γm ; l) | {z }
<0 because Q(l) of (3) is a decreasing function w.r.t l
, Cˆ j (l, k, n)
D
P j ≥ λ for ∀ j 0
g j (γi, j ) d γm
0
where γm represents the m-tuple (γ1 , · · · , γm ) and dm γm is the m-dimensional differential. Additionally, ∆2 f2 (l) < 0 because PF (γm ; l) is a function of Q(l) in (3). Consequently,
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∆2 ( f1 (l) f2 (l)) =
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4.2. Suboptimal Problem and Algorithm
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The problem of (13) is nonconvex and is a mixed integer problem, which is usually NP-hard to be solved. We propose an iterative algorithm that solves (13) by decoupling it into three single variable problems that have a discretely concave function. Because of the assumption of an i.i.d. channel for each band, the optimization problem of (13) can be solved by finding the optimal parameters of (l, k, n) that maximize Cˆ j (l, k, n) at band j. Let the functions f1 (l, k, n) and f2 (l, k, n) respectively represent f1 (l, k, n) = 1 − lN∆ s − kn∆r and f2 (l, k, n) = F 1 − P j (l, k, n); therefore Cˆ j (l, k, n) = f1 (l, k, n) f2 (l, k, n).
∆2 f1 (l) f2 (l) + 2 ∆ f1 (l) ∆ f2 (l) | {z } |{z} |{z} =0
+
0 < f1 (l) < 1
<
<0
>0
f1 (l) ∆2 f2 (l) |{z} | {z } <0
0.
(16)
Hence, because ∆2 ( f1 (l) f2 (l)) < 0, f1 (l) f2 (l) is a concave function with respect to l. Lemma 2 (with respect to k). For given l = l˜ and n = n˜ , the function Cˆ j (l, k, n) is a concave function with respect to k. Proof. For simplicity of notation, we omit the subscript j and other variables (l, n); i.e., we use f1 (k) and f2 (k) instead of f1 (l,˜ k, n˜ ) and f2 (l,˜ k, n˜ ), respectively. ′ For k = k + h > k, we have
Lemma 1 (with respect to l). For given k = k˜ and n = n˜ , the function Cˆ j (l, k, n) is a concave function with respect to l.
Ac
∆ f1 (k) =
′
f1 (k ) − f1 (k) = −n∆r h < 0
(17)
and ∆2 f1 (k) = 0. Moreover, we have ∆ f2 (k) > 0 from (18) and ∆2 f2 (k) < 0 because PF (x) is a function of Q(x) in (3). Consequently, because ∆2 ( f1 (k) f2 (k)) = 2 ∆ f1 (k) f2 (k) + 2∆ f1 (k)∆ f2 (k) + f1 (k)∆2 f2 (k) < 0, f1 (k) f2 (k) is a concave function with respect to k.
Proof. We define the discrete derivative of a function f (x) as follows: for the first forward difference, ∆ f (x) = f (x + h) − f (x), and for the second forward difference, ∆2 f (x) = f (x + 2h) + f (x) − 2 f (x + h). For simplicity of notation, we omit the subscript j and other variables (k, n); i.e., we use f1 (l) and f2 (l) instead ˜ n˜ ) and f2 (l, k, ˜ n˜ ), respectively. of f1 (l, k, ′ For l = l + h > l, we have f1 (l ) − f1 (l) = −N∆ s h < 0
(15)
us
>
where ∆ s = τ s /T f and ∆r = τr /T f .
′
m
i=1
0
∆ f1 (l) =
m ∏
cr
×
(13) s.t.
ip t
where l, k, and n are optimization discrete variables; and F C(l, k, n) is obtained from (6) by using P j (l, k, n) of (11). For each band, the miss detection probability of 1 − PDj should be sufficiently small to protect the PUs and the parameters of (c0, j , P(H0, j )) are uncontrollable. Hence, the optimization problem of (12) can be approximated as follows:
(14) 6
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F
′
′
k ∑
k ∑
F
p(m; k)P (m) −
m=1
| m=1 {z }
∑k
m=1
=
k ∑
{
−
p(m; k)
m=1 | {z } ′
k ∑
+
∑k′
m=k+1
k ∑
p(m; k )
≈1−
∑k
′
}
F
P (m) | {z }
−
} F F P (k) − P (k + 1) | {z }
m=k+1 F
F
F
∑ε
+
∑k
∑ε
m=ε+1
ε { ∑
F
P (m, n) | {z }
F
{
k ∑
p(m; n)
>
p(m; n) −
=
ε { ∑ m=1
>
′
m=ε+1
ε ∑
−
′
p(m; n )
m=1
F
}
′
P (m, n ) | {z } ′
F
≥ P (ε, n ) for m ≤ ε
F
P (m, n) | {z }
k ∑
−
F
≤ P (ε + 1, n) for m ≥ ε + 1
F
′
m=ε+1
′
P (m, n ) | {z }
p(m; n ) ′
F
}
F
≤ P (ε + 1, n ) < P (ε + 1, n) for m ≥ ε + 1
k k ∑ } F { ∑ } F ′ ′ p(m; n ) P (ε, n ) + p(m; n) − p(m; n ) P (ε + 1, n) ′
′
p(m; n) − p(m; n ) | {z } > 0 for m ≤ ε
F
p(m; n )P (m, n )
m=1
Ac
m=1
ε ∑
′
(18)
∑k
′
F
m=ε+1
ε {∑
+
≥ P (ε, n) > P (ε, n ) for m ≤ ε
ce p +
F
≤ P (k + 1) for m ≥ k + 1
m=1 |{z}
m=1
p(m; n)
m=1
k ∑
−
m=1 |{z}
m=1
=
′
P (n) − P (n ) k ∑ F p(m; n)P (m, n)
M
=
′
f2 (n ) − f2 (n)
d
=
0
te
∆ f2 (n) =
P (m) | {z }
an
> 0 because P (x) is a decreasing function due to Q(x) of (3)
>
F
′
p(m; k )
p(m; k )
{
′
p(m; k )
k ∑ m=k+1
F
≥ P (k) for m ≤ k
′
m=k+1
′
}
′
m=1 | {z
≈ 1 for a large number of k
>
F
′
p(m; k )P (m)
ip t
=
F
P (k) − P (k )
cr
=
′
f2 (k ) − f2 (k)
us
∆ f2 (k) =
}{
m=ε+1 | ∑{z } ≈ 1 − εm=1 p(m; n) F
′
m=ε+1
|
≈1−
{z
∑ε
m=1
} ′
p(m; n )
}
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P (ε, n ) − P (ε + 1, n) | {z } F
> 0 because P (x) is a decreasing function due to Q(x) of (3)
0.
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˜ Lemma 3 (with respect to n). For given l = l˜ and k = k, ˆ the function C j (l, k, n) is a concave function with respect to n.
˜ n) and f2 (l,˜ k, ˜ n), respectively. instead of f1 (l,˜ k, ′ For n = n + h > n, we have ∆ f1 (n) =
Proof. For simplicity of notation, we omit the subscript j and other variables (l, k); i.e., we use f1 (n) and f2 (n)
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(20)
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From (8), q j (n) is an increasing function because g j (γi, j ; n) is an increasing function with respect to n. ′ Hence, for n > n, there exists a value, ε, that satis′ fies the following: if m ≤ ε, p(m; n) > p(m; ( k ) n ); other′ wise p(m; n) < p(m; n ), where p(m; n) = m q j (n)m (1 − ∑ q j (n))k−m from (10) and km=0 p(m; n) = 1. Hence, we have ∆ f2 (n) > 0 from (19) and ∆2 f2 (n) < 0 because PF (x) is a function of Q(x) in (3).
5. Numerical Results
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The average capacity of an SU is evaluated under a cooperative CR network operating in N = 10 primary bands. We assume that the channel of each primary band from the primary transmitters to the SUs is independently and identically Rayleigh distributed with fγ (γ) = 1/¯γ exp(−γ/¯γ), where γ is the PU’s SNR at the SU and γ¯ = −10 dB is the average PU’s SNR at the SU [19]. Moreover, the channel of each primary band during the SU’s data transmission is also assumed to be Rayleigh distributed with an average SNR of 9 dB. Assuming the ON-OFF model for PU appearances, we set P(H0 ) = 0.8 and P(H1 ) = 0.2. The values of the other simulation parameters are as follows: The sampling time ratio is ∆ s = 0.2 × 10−3 , the reporting time ratio is ∆r = 10−3 , and the threshold of detection probability is λ = 0.9. To calculate the multi-fold integration in (9), we reduce the multiple integral to an iterated integral (i.e., a series of integrals of one variable) and use a trapezoidal rule for approximating each definite integral. Fig. 3 to Fig. 7 show the average capacity of an SU for each of l, k, and n, where we check the convexity of the average capacity of an SU with respect to each of l, k, and n in Lemmas 1, 2, and 3. Figures 3 and 4 show the average capacity of an SU as the number of sensing time samples increases, where the number of reporting nodes is fixed to k = K and the number of reporting bands is fixed to n = N. Figure 3 shows that as the value of l increases, the sensing overhead linearly increases and the average false alarm probability decreases. As expected from Lemma 1, Fig. 3 shows that the average capacity of an SU is concave with respect to l when the values of (k, n) are fixed. Figure 4 shows the average capacity of an SU when the number of reporting nodes is respectively 20, 30, and 40. As the number of reporting nodes increases, because the sensing and reporting overheads linearly increase, the optimal value of l that maximizes the average capacity decreases in order to reduce the sensing overhead. Moreover, when there are many reporting nodes, the average capacity decreases as the number of reporting nodes increases because of the excessive reporting overhead. Figure 5 shows the average capacity of an SU, reporting overhead, and false alarm probability as the number of reporting nodes increases, where the number of sensing time samples is fixed to l = 40 and the number of reporting bands is fixed to n = N. As expected from Lemma 2, Fig. 5 shows that the average capacity is concave with respect to k when the values of (l, n) are fixed. Additionally, for the fixed values of (l, n), the average
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Consequently, because ∆2 ( f1 (n) f2 (n)) = ∆2 f1 (n) f2 (n) + 2∆ f1 (n)∆ f2 (n) + f1 (n)∆2 f2 (n) < 0, f1 (n) f2 (n) is a concave function with respect to n.
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From Lemma 1, 2, and 3, we can solve each suboptimization problem by using the bisection search method or the Golden section method [28]. The proposed iterative algorithm is summarized in Algorithm 1.
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Initialize: i←0 /* iteration count */ l(i) ← 1, k(i) ← K, n(i) ← 1 repeat /* For given k and n, find l∗ */
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Algorithm 1 Find the optimal parameters (l∗ , k∗ , n∗ ) that maximize Cˆ j (l, k, n).
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1. Given k(i) and n(i) , find l∗ that maximizes (i) (i) Cˆ j (l, k(i) , n(i) ) from l = 1 to ⌊ 1−kN∆ns ∆r ⌋ by using the Golden section method. 2. l(i+1) ← l∗
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/* For given l and n, find k∗ */
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3. Given l(i+1) and n(i) , find k∗ that maximizes Cˆ j (l(i+1) , k, n(i) ) from k = 1 to ( ) (i+1) s min K, ⌊ 1−ln(i) ∆N∆ ⌋ by using the Golden section r method. 4. k(i+1) ← k∗ /* For given l and k, find n∗ */ 5. Given l(i+1) and k(i+1) , find n∗ that maximizes Cˆ j (l(i+1) , k(i+1) , n) from n = 1 to ) ( (i+1) s ⌋ by using the Golden section min N, ⌊ 1−lk(i+1) ∆N∆ r method. 6. n(i+1) ← n∗ 7. i ← i + 1 until | Cˆ j (l(i) , k(i) , n(i) ) − Cˆ j (l(i−1) , k(i−1) , n(i−1) ) | ≤ ϵ return (l∗ , k∗ , n∗ )
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capacity is dependent on the value of k regardless of the number of SUs. Figures 6 and 7 show the average capacity of an SU as the number of reporting bands increases, where the number of sensing time samples is fixed to l = 40 and the number of reporting nodes is fixed to k = K. Figure 6 shows that as the value of n increases, the reporting overhead linearly increases and the average false alarm probability decreases. As expected from Lemma 3, Fig. 6 shows that the average capacity of an SU is concave with respect to n when the values of (l, k) are fixed. Figure 7 shows the average capacity of an SU when the number of reporting nodes is respectively 20, 30, and 40. As the number of reporting nodes increases, because the sensing and reporting overheads linearly increase, the optimal value of n that maximizes the average ca-
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Figure 7: The average capacity vs. the value of n when l = 40 and k = K = 20, 30, 40.
Figure 4: The average capacity vs. the value of l when k = K = 20, 30, 40 and n = N = 10. 1.4
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Figure 9: The optimal values of (l, k, n) in the proposed multiband CSS scheme.
eration. Figure 9 shows the optimal values of (l, k, n) in the proposed sensing-reporting-bands optimized scheme. As the number of SUs increases, the optimal number of sensing time samples, l∗ , decreases, the optimal number of reporting nodes, k∗ , is almost identical to the number of SUs, and the optimal number of reporting bands, n∗ , decreases. The results show that, in multiband CSS, it is important to control jointly two parameters, the number of sensing time samples and the number of bands to be reported, according to the number of SUs. Moreover, when we control the reporting overhead which is given by (k · n), it is better to control the value of n than the value of k because the proposed scheme increases the selection diversity according to the value of n.
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Figure 8: The average capacity vs. the number of SUs according to the CSS schemes.
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pacity decreases in order to reduce the reporting overhead. As shown in Fig. 7, when the number of reporting nodes increases from 20 to 40, the average capacity is improved by about 12.7% by reducing the number of reporting bands from 5 to 2. This demonstrates that it is important to control the number of reporting bands according to the number of reporting nodes. Figure 8 shows the average capacity of an SU as the number of SUs increases in the following three CSS schemes: (i) a conventional sensing time optimized (lopt) scheme, where the sensing time is adaptively optimized according to the number of SUs [11]; (ii) a sensing-reporting optimized ((l, k)-opt) scheme, where the sensing time and the number of reporting nodes are adaptively optimized according to the number of SUs [12, 17]; and (iii) the proposed sensing-reportingbands optimized ((l, k, n)-opt) scheme with limited reporting, where the sensing time, the number of reporting nodes, and the number of reporting bands are jointly optimized according to the number of SUs. As the number of SUs increases, the average capacity of the conventional l-opt scheme increases owing to the decrease of the false alarm probability but it decreases after a critical number of SUs, e.g., 15 under this simulation environment, because of the excessive reporting overhead. Because the (l, k)-opt scheme controls the number of reporting nodes, although the number of SUs increases beyond 15, it maintains the average capacity of the case of K = 15. However, as the number of SUs increases, the average capacity of the proposed (l, k, n)-opt scheme increases because the proposed scheme adaptively controls the number of bands to be reported by taking the diversity of selecting bands to be reported into consid-
6. Conclusion
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Taking into consideration a cognitive radio network with multiple primary bands, we investigated the average capacity of secondary users which is affected by the sensing time, reporting time, and a fusion scheme. Adopting a soft combination at the FC, we formulated a sensing-reporting-bands optimization problem that maximizes the average capacity of secondary users. Additionally, we proposed a limited reporting scheme for multiband CSS in order to reduce the reporting overhead. We derived the false alarm probability of the multiband CSS with adoption of the proposed reporting scheme. The proposed limited reporting scheme significantly increases the average capacity of secondary users by reducing the sensing and reporting overheads while providing sufficient protection to the PUs. When there 10
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are 40 cooperative secondary users, the proposed multiband CSS scheme with the limited reporting increases the average capacity of secondary users by about 21% in comparison with the conventional sensing-reporting optimized scheme. Since the original sensing-reportingbands optimization problem is a mixed integer nonconvex optimization problem, we proposed an iterative algorithm that solves the problem by dividing it three single variable suboptimization problems, where each suboptimization problem was proved to be concave.
[10] J. So, R. Srikant, Improving channel utilization via cooperative spectrum sensing with opportunistic feedback in cognitive radio networks, IEEE Commun. Lett. 19 (6) (2015) 1065–1068.
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[11] Y. Liang, Y. Zeng, E. Peh, A. Hoang, Sensingthroughput tradeoff for cognitive radio networks, IEEE Trans. Wireless Commun. 7 (4) (2008) 1326–1377. [12] E. Peh, Y. Liang, Y. Guan, Y. Zeng, Optimization of cooperative sensing in cognitive radio networks: A sensing-throughput tradeoff view, IEEE Trans. Veh. Technol. 58 (9) (2009) 5294–5299.
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References [1] T. Y¨ucek, H. Arslan, A survey of spectrum sensing algorithms for cognitive radio applications, IEEE Communications Surveys & Tutorials 11 (1) (2009) 116–130.
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[13] H. He, G. Li, S. Li, Adaptive spectrum sensing for time-varying channels in cognitive radios, IEEE Wireless Commun. Lett. 2 (2) (2013) 227–230. [14] W. Lee, D. Cho, Enhanced spectrum sensing scheme in cognitive radio systems with MIMO antennae, IEEE Trans. Veh. Technol. 60 (3) (2011) 1072–1085.
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[2] N. Zhao, A novel two-stage entropy-based robust cooperative spectrum sensing scheme with twobit decision in cognitive radio, Wireless Personal Commun. 69 (4) (2013) 1551–1565.
[15] J. Lai, E. Dutkiewicz, R. Liu, R. Vesilo, Performance optimization of cooperative spectrum sensing in cognitive radio networks, in: Proc. IEEE WCNC, 2013, pp. 631–636.
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[3] Y. L. Zhang, Q. Y. Zhang, T. Melodia, A frequency-domain entropy-based detector for robust spectrum sensing in cognitive radio networks, IEEE Commun. Lett. 14 (6) (2010) 533–535.
[16] E. Peh, Y. Liang, Y. Guan, Y. Zeng, Cooperative spectrum sensing in cognitive radio networks with weighted decision fusion schemes, IEEE Trans. Wireless Commun. 9 (12) (2010) 3838–3847.
[5] Y. Liang, K. Chen, G. Li, P. Mahonen, Cognitive radio networking and communications: an overview, IEEE Trans. Veh. Technol. 60 (7) (2011) 3386–3407.
[17] A. Noel, R. Schober, Convex sensing-reporting optimization for cooperative spectrum sensing, IEEE Trans. Wireless Commun. 11 (5) (2012) 1900–1910.
[6] K. Kalimuthu, R. Kumar, Capacity maximization in spectrum sensing for cognitive radio networks thru outage probability, Int. J. Electron. Commun. 67 (1) (2013) 35–39.
[18] N. Han, H. Li, Cooperative spectrum sensing with location information, IEEE Trans. Veh. Technol. 61 (7) (2012) 3015–3024.
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[4] S. Atapattu, C. Tellambura, H. Jiang, Performance of an energy detector over channels with both multipath fading and shadowing, IEEE Trans. Wireless Commun. 9 (12) (2010) 3662–3670.
[7] E. Peh, Y. Liang, Optimization for cooperative sensing in cognitive radio networks, in: Proc. IEEE WCNC, 2007, pp. 27–32.
[19] P. Kaligineedi, V. Bhargava, Sensor allocation and quantization schemes for multi-band cognitive radio cooperative sensing system, IEEE Trans. Wireless Commun. 10 (1) (2011) 284–293.
[8] J. Ma, G. Zhao, Y. Li, Soft combination and detection for cooperative spectrum sensing in cognitive radio networks, IEEE Trans. Wireless Commun. 7 (11) (2008) 4502–4507.
[20] Y. Choi, W. Pak, Y. Xin, S. Rangarajan, Throughput analysis of cooperative spectrum sensing in Rayleigh-faded cognitive radio systems, IET Commun. 6 (9) (2012) 1104–1110.
[9] W. Zhang, R. Mallik, K. Letaief, Optimization of cooperative spectrum sensing with energy detection in cognitive radio networks, IEEE Trans. Wireless Commun. 8 (12) (2009) 5761–5766.
[21] R. Fan, H. Jiang, Optimal multi-channel cooperative sensing in cognitive radio networks, IEEE Trans. Wireless Commun. 9 (3) (2010) 1128– 1138. 11
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[22] N. Zhao, F. Pu, X. Xu, N. Chen, Optimisation of multi-channel cooperative sensing in cognitive radio networks, IET Commun. 7 (12) (2013) 1177– 1190.
network solutions. From 2005 to 2007, he was a Senior Engineer at Samsung Electronics, Suwon, Korea, where he involved in the design, performance evaluation, and development of mobile WiMAX systems and B3G wireless systems. From 2007 to 2008, he was a Postdoctoral Fellow in the Department of Electrical Engineering, Stanford University, Stanford, CA, USA. From August 2014 to July 2015, he was a visiting professor in the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, IL, USA. Since September 2008, he has been with the Department of Electronic Engineering, Sogang University, Seoul, Korea, where he is currently an Associate Professor. His current research interests include radio resource management, multiple antenna systems, cognitive radio networks, and IoT networks.
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[23] P. Kaligineedi, V. Bhargava, Distributed detection of primary signals in fading channels for cognitive radio networks, in: Proc. IEEE Globecom, 2008, pp. 1–5.
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[24] M. Mustonen, M. Matinmikko, A. M¨ammel¨a, Cooperative spectrum sensing using quantized soft decision combining, in: Proc. Int. Conf. CROWNCOM, 2009, pp. 1–5.
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[25] S. Maleki, A. Pandharipande, G. Leus, Two-stage spectrum sensing for cognitive radios, in: Proc. IEEE Int. Conf. Acoustics Speech and Signal Processing (ICASSP), 2010, pp. 2946–2949.
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[26] P. Nair, A. Vinod, K. Smitha, A. Krishna, Fast two-stage spectrum detector for cognitive radios in uncertain noise channels, IET Commun. 6 (11) (2012) 1341–1348.
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[27] N. Zhao, F. R. Yu, H. Sun, A. Nallanathan, Energy-efficient cooperative spectrum sensing schemes for cognitive radio networks, EURASIP J. Wireless Commun. and Networking 69 (4) (2013) 1551–1565.
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[28] S. Boyd, L. Vandenberghe (Eds.), Convex Optimization, Cambridge University Press, Cambridge, MA, 2004.
Jaewoo So received the B.S. degree in electronic engineering from Yonsei University, Seoul, Korea, in 1997, and received the M.S. and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 1999 and 2002, respectively. From 2001 to 2005, he was with IP One, Seoul, Korea, where he led several research projects and developed IEEE 802.11a/b/g products and heterogeneous
Taesoo Kwon received the B.S., M.S., and Ph.D. degrees from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2001, 2003, and 2007, respectively, all in electrical engineering and computer science. From 2007 to 2011, he was a Senior Researcher with Samsung Advanced Institute of Technology, Yongin, Korea, where he was involved in research on the LTEAdvanced systems, beyond the 4G wireless communication systems, and nanoscale communication technologies. In 2008 and 2011, he was a Visiting Scholar with the Department of Electrical Engineering, Stanford University, Stanford, CA, USA. From 2011 to 2012, he was a Postdoctoral Fellow with the Department of Electrical and Computer Engineering, the University of British Columbia, Vancouver, BC, Canada. From 2013 to 2015, he was a Senior Researcher with the Electronics and Telecommunications Research Institute (ETRI), Daejeon, where he was engaged in research on the 5G wireless communication systems. Since 2015, he has been an Assistant Professor with the Department of Computer Science and Engineering, Seoul National University of Science and Technology (SeoulTech), Seoul. His research interests include wireless networks, stochastic geometry, optimization, and data analytics.
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S1434-8411(15)30033-9 http://dx.doi.org/doi:10.1016/j.aeue.2015.12.017 AEUE 51536
To appear in: Received date: Revised date: Accepted date:
6-8-2015 5-11-2015 22-12-2015
Please cite this article as: Jaewoo So, Taesoo Kwon, Limited Reportingbased Cooperative Spectrum Sensing for Multiband Cognitive Radio Networks, (2016), http://dx.doi.org/10.1016/j.aeue.2015.12.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Limited Reporting-based Cooperative Spectrum Sensing for Multiband Cognitive Radio Networks Jaewoo So∗
Taesoo Kwon
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Department of Electronic Engineering Sogang University, Seoul 04107, Republic of Korea
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Department of Computer Science and Engineering Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
Abstract
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The performance of cooperative spectrum sensing depends on the sensing time, the reporting time of transmitting sensing results, and the fusion scheme. While longer sensing and reporting time will improve the sensing performance, this shortens the allowable data transmission time, which in turn degrades the throughput of secondary users. In a cognitive radio network with multi-primary bands, the reporting time increases with the number of reporting nodes and primary bands to be reported. This paper proposes a limited reporting scheme for multiband cooperative spectrum sensing with a soft combination rule in order to reduce the reporting time while satisfying the detection probability constraint. In the proposed reporting scheme, the upper bound of the number of reporting nodes and the reported primary bands are dynamically controlled according to the number of cooperative secondary users. We formulate a trade-off between the throughput of secondary users and the overheads of cooperative spectrum sensing. Simulation results show that the sensing time and reporting time should be jointly optimized in order to maximize the throughput of secondary users. Moreover, in comparison with the conventional sensing-throughput optimization schemes, the proposed reporting scheme significantly increases the throughput of secondary users by reducing the reporting time.
1. Introduction
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Keywords: Cognitive radio, sensing-throughput optimization, multiband cooperative spectrum sensing, sensing-reporting overhead.
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In cognitive radio (CR) networks with multi-primary bands, spectrum sensing is a key technology to realize spectrum sharing over a confined spectrum (e.g. DTVbands). Generally, the signal detection techniques can be classified into energy detection, matched filtering detection, and cyclostationary feature detection [1]. However, in response to the transitional detectors being inefficient when noisy uncertainty is severe, an entropyI This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2058084) and it was also supported by the NRF grant funded by the Korea government (MSIP) (2012R1A2A2A01012059). ∗ Corresponding author: J. So. Email addresses: [email protected] (Jaewoo So), [email protected] (Taesoo Kwon)
Preprint submitted to AEU - Int. J. of Electronics and Communications
based detector that is robust to the noise uncertainty has been proposed [2, 3]. In practice, many factors, such as multipath fading, shadowing, and the hidden primary user (PU) problem, may significantly affect detection performance. To solve this challenging problem, cooperative spectrum sensing (CSS) has been extensively studied in efforts to increase the sensing performance [4–6]. The CSS has three successive phases, sensing, reporting, and decision. In the sensing phase, each sensing node locally senses the signal of PUs. Then, in the next reporting phase, sensing nodes report their observed sensing results to a fusion center (FC). In the decision phase, the FC determines the presence of a PU by combining multiple independent sensing results reported by sensing nodes, where it can use hard combination methods (e.g., OR-rule, AND-rule, and k-outof-K rule) or a soft combination method [7–9]. It beDecember 30, 2015
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anisms and spatial-spectral diversity over multiple primary channels. However, the above studies of [19–22] failed to propose a reporting scheme that reduces the reporting overhead in order to increase the throughput of SUs. Some researchers have endeavored to reduce the sensing time or reporting overhead. In conventional hard combination-based CSS, each SU reports only onebit decision to the FC. Its reporting overhead is thereby minimized but it suffers degradation of the sensing performance because of information loss caused by local hard decisions. To achieve a balanced trade-off between the sensing performance and the reporting overhead, some researchers have proposed a two-bit or three-bit combination rule [8,23,24]. The authors of [25,26] proposed a two-stage spectrum sensing scheme in order to reduce the sensing time and maximize the sensing performance, where coarse sensing based on energy detection is performed in the first stage and, if required, fine sensing is performed in the second stage. While [25,26] did not consider CSS, the authors of [2, 27] proposed a two-stage spectrum sensing scheme in the CSS. The author of [2] improved the sensing performance via a two-stage two-bit CSS and the authors of [27] reduced energy consumption via two-stage energy-efficient onebit CSS. This paper discusses multiband CSS in CR networks with a soft combination method. The contribution of this paper is twofold. First, this paper proposes a new reporting scheme that reduces the reporting overhead in multiband CR networks. The proposed scheme dynamically controls the upper bound of the number of reporting nodes and reported bands in multiband CSS according to the number of cooperative SUs. The proposed limited reporting scheme significantly increases the throughput of SUs by reducing the reporting overhead of multiband cooperative sensing while satisfying the detection probability constraint. Second, this paper formulates a trade-off problem between the throughput of SUs and the overheads of CSS including both the sensing time and the reporting time. Whereas most previous studies of [11, 12, 14] formulated a sensingthroughput trade-off problem without taking the reporting time into consideration. Although a few works investigated the effect of the reporting overhead on the sensing performance, they assumed that the FC uses a hard combination method and moreover they failed to propose an idea that reduces the reporting overhead [17, 20]. The remainder of this paper is organized as follows: Section 2 describes the system model, where the processes of four phases, sensing, reporting, decision, and
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comes obvious that the performance of the CSS is dependent on the sensing time, reporting time, and the fusion scheme [10]. As the sensing and reporting time increase, the sensing performance increases; however, with a fixed frame size, the allowable data transmission time of secondary users (SUs) is shortened and therefore the throughput of SUs decreases. One of the important issues in the design of CSS is determining the sensing time, reporting time, and parameters for the fusion scheme. Many researchers have endeavored to find the optimal parameters that maximize the throughput of SUs. Some researchers have focused on finding the optimal sensing time by formulating a sensing-throughput trade-off problem when a hard combination method is adopted at the FC [11–14]. Other researchers have focused on finding the optimal fusion parameters (e.g., the reporting threshold for the OR-rule and a voting threshold for the k-out-of-K rule) that maximize the sensing performance or the throughput of SUs [9, 15, 16]. The authors of [17] formulated a sensing-reporting optimization problem to find the optimal division of time between the sensing time and the reporting time when the k-out-of-K rule is adopted at an FC, where they assumed the sum of the sensing time and the reporting time is fixed. The author of [2] proposed two-stage entropy-based CSS in order to counteract the effect of noise uncertainty, where the proposed entropy-based CSS scheme required less computational complexity but still outperformed the previous hard combination-based CSS schemes. However, the above studies of [2, 9, 11–17] did not take into consideration the effect of the reporting time on the throughput of SUs, and moreover they considered single band CSS. Moreover, they adopted a hard combination method, an OR-rule or a k-out-of-K rule, at an FC. A soft combination method shows better sensing performance than hard combination methods at the cost of increased bandwidth of reporting channels [8, 18]. In contrast with the above work for single band CSS, some studies have considered CSS with multiple primary bands [19–22]. The authors of [19] proposed a sensor allocation and quantization scheme for multiband CSS. The authors of [20] formulated a sensingthroughput trade-off problem to find a pair of the sensing time and the number of SUs that report their sensing results when an OR-rule is adopted at an FC in multiband CR networks. The authors of [21] formulated a sensing-throughput optimization problem to find the optimal time setting to sense multiple primary bands and they proposed a slotted-time sensing mode and a continuous-time sensing mode. The authors of [22] investigated the relationship between cooperation mech-
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[Reporting Phase] Selected k SUs report sensing results about n PU bands
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band N
.. .
Tf Tr Reporting
SU 1
1 SU 2
PU
Ts Sensing 2
... N 1
2
τs
.. .
1 2 ... l frequency
SU's data transmission l, k, n : optimization variables
1 2 ... n
Sense PU signal for l samples at each band
Report sensing results about n bands via a reporting channel
cr
Figure 1: Proposed system model.
... i ... k
τr
CR base station
SU K
Td
ip t
[Sensing Phase] All SUs sense N PU bands
Figure 2: Frame structure of the CR network.
us
transmission of SUs, are described and a limited reporting scheme is proposed in the reporting phase. Section 3 analyzes the false alarm probability of the multiband CSS with the proposed reporting scheme. Section 4 formulates a sensing-reporting-bands optimization problem and presents an iterative algorithm to solve the optimization problem. Section 5 presents the numerical results and finally, Section 6 concludes the paper.
M
an
• In the sensing duration, each SU sequentially senses N bands during T s , where each SU observes the PU signal during l sample time at each band. Hence, the total sensing time can be represented by T s = l · N · τ s , where τ s is one sample time duration. The sensing time increases in proportion to the number of primary bands to be sensed regardless of the number of SUs because all SUs observe the PU signal at the same time.
2. System Model
te
d
2.1. System Description As shown in Fig. 1, we consider a centralized CR network with N primary frequency bands (termed bands hereafter) and K SUs, where a CR base station functions as an FC and each SU functions as a cooperative sensing node. In the proposed system model, some of K SUs are selected to report their sensing results to the FC, where the sensing result reported by a selected SU includes the observed sensing information about n bands not all N bands. That is, k SUs out of K SUs are selected to report sensing results for n bands out of N bands. Let the symbol i denote the index of SUs or reporting nodes. Let the symbol j denote the index of primary frequency bands, i.e., j ∈ N = {1, 2, · · · , N}. In each band, a PU exists but may not be active all the time. An energy detector is implemented at each SU. The FC determines the presence of a PU at each band by combining multiple independent sensing results from SUs, where the FC uses an MRC-based soft combination method [16]. As shown in Fig. 2, each frame of a CR network is divided into sensing duration, reporting duration, and data transmission duration. Let the frame time, sensing time, reporting time, and data transmission time be respectively denoted by T f , T s , T r , and T d , where T f = T s + T r + T d . The overall operation of each duration is as follows:
• In the reporting duration, SUs report their sensing results to the FC. Let the number of SUs who are selected to report their sensing results be n. The total reporting time is then given by T r = k · n · τr , where τr is the duration of a time slot.
ce p
• In the data transmission duration, if the FC decides the absence of a PU at band j, one SU selected by the FC transmits data at band j, where the FC is assumed to use a round-robin (RR) scheduling algorithm.
Ac
Additionally, we assume that the errors due to the reporting of sensing results are negligible. 2.2. Local Spectrum Sensing at SUs When the ith SU senses during l samples at each band, the observed energy value of the ith SU at band j can then be expressed as { ∑l wi, j (t)2 , H 0, j ∑t=1 Yi, j = (1) l 2 , H 1, j , t=1 (si, j (t) + wi, j (t)) where H 0, j and H 1, j represent that the PU in band j is idle and busy, respectively; t is the sample index; si, j (t) is the received PU signal and wi, j (t) is the white 3
Page 3 of 12
of the detection probability, PDj ≥ λ. Moreover, the parameters do not have to be broadcast in every frame. Whenever the number of cooperative SUs changes or every hundreds or thousands of frames, the parameters can be periodically broadcast to SUs in order to inform who reports sensing results and how many bands are reported. The optimization problem to find the optimal values of k and n is described in Section 4.
ip t
noise at the tth sample of the ith SU at band j, respectively. The noise at each sample is assumed to be Gaussian distributed with zero mean and unit variance, i.e., wi, j (t) ∼ N(0, σ2 ), where σ2 = 1. Let γi, j represent the received instantaneous signalto-noise ratio (SNR) of the signal received by the ith SU at band j within the observation period, defined as ∑ γi, j = 1l lt=1 si, j (t)2 /σ2 [8]. We assume γi, j varies from (observation) period to period. We suppose γi, j ’s of SUs are independent and identically distributed (i.i.d.). This assumption is valid for a small-sized CR network or for the case that the appearances of PUs are uniformly distributed [21, 23]. Furthermore, we assume an i.i.d. channel for each band. The probability density function (pdf) and cumulative distribution function (cdf) of the received SNR of each SU at each band are respectively denoted by fγ (γ) and Fγ (γ).
Yj
us
cr
2.4. Decision of the PU’s Presence at the FC Let Yi, j represent the sensing energy on band j in the ith received reporting message. If the number of received reporting messages including the sensing information on band j is m at the FC, an MRC-based weighted summation of the FC at band j can then be expressed as m ∑
=
ωi, j Yi, j ,
1 ≤ j ≤ N,
(2)
i=1
an
2.3. Proposed Limited Reporting Scheme
where ωi, j is a weight factor. Let γi, j be the PU’s SNR at band j in the ith received reporting message and let the set of γi, j be denoted by γm, j = {γ1, j , γ2, j , · · · , γm, j }, where m is the number of SUs who report a sensing result on band j. The optimal value of ωi, j can then be √ ∑m ( )2 approximated as ω∗i, j ≈ γi, j / [8]. i=1 γi, j D Given a detection probability of P j and the SNR list of γm, j , the conditional false alarm probability at band j can then be expressed as [8, 21] v t m ∑ −1 D F P j (γm, j ; l) = Q Q (P j ) ω2i, j (1 + 2γi, j ) i=1 √ m ∑ l ωi, j γi, j , (3) + 2 i=1
ce p
te
d
M
In the conventional multiband CSS scheme, each SU reports sensing results for all PU bands. The required total reporting time therefore becomes T r = K · N · τr , where K is the number of cooperative SUs, N is the number of primary bands, and τr is the duration of one reporting time slot. In order to reduce the reporting overhead of multiband CSS, we propose a new reporting scheme. The proposed scheme determines the upper bound of the number of reporting nodes and the reported bands in multiband CSS while satisfying the detection probability constraint. The FC randomly selects k SUs as reporting nodes out of K SUs. Each selected SU reports sensing results for n bands out of N bands on the basis of the received SNR value at each band. Hence, in the proposed reporting scheme, the reporting time becomes T r = k · n · τr , where k ≤ K and n ≤ N. The reported bands are determined in descending order of the observed SNRs at each band. For example, an SU has an observed SNR list of N = 5 bands as follows {−5 dB, −9 dB, −12 dB, −7 dB, −11 dB}. If the number of bands to be reported is n = 3, the SU reports the sensing results for band 1, band 2, and band 4 after a sorting process based on the observed SNR values. The design of the proposed reporting scheme involves choosing the values of k and n. As smaller values of k and n decrease the reporting time, this may deteriorate the sensing performance. To provide sufficient protection to the PU, the detection probability, PDj , should be no smaller than a prescribed threshold, λ. Hence, the values of k and n are adaptively determined according to the number of cooperative SUs under the constraint
where l∫ is the number of sensing time samples and ∞ 2 Q(x) = x √12π e−t /2 dt.
Ac
2.5. Data Transmission of SUs For a CR network, we assume a Rayleigh fading channel with additive white Gaussian noise of zero mean and unit variance. Let ζ j be the instantaneous SNR of an SU during the SU’s data transmission at band j. When the PU’s frequency band j is idle and the FC identifies the absence of a PU, one selected SU transmits data, where the FC is assumed to select an SU according to an RR scheduling algorithm. According to Shannon’s capacity theorem, the average SU’s spectral efficiency at band j is given by ∫ ∞ ( ) c0, j = log2 1 + ζ j fζ (ζ j )dζ j , H 0, j , (4) 0
4
Page 4 of 12
where fζ (ζ j ) is the pdf of ζ j . When the FC falsely detects the presence of a PU although there is a PU, an SU can transmit data. Hence, when the frequency band j is used by a PU, the average SU’s spectral efficiency at band j is given by ( ) ∫ ∞∫ ∞ ζj c1, j = log2 1 + 1 + γj 0 0 × fζ (ζ j ) fγ (γ j )dζ j dγ j , H 1, j , (5)
the SU can report the sensing information observed at the jth band to the FC, where γu is the SNR observed at the uth band. Consequently, the probability that the ith SU reports the SNR, γi, j , observed at the jth band can be expressed as follows: N ∑ g j (γi, j ; n) = Pr I(γi,u > γi, j ) < n fγ (γi, j ) =
where γ j is the SNR from the PU to the SU at band j. Consequently, the average achievable capacity of an SU at each band can then be formulated as ( ) l · N · τ s k · n · τr C(l, k, n) = 1 − − Tf Tf N { ∑ F 1 × c0, j (1 − P j )P(H0, j ) N j=1 } D + c1, j (1 − P j )P(H1, j ) , (6)
α(N − 1, v, γi, j ) fγ (γi, j ).
v=0
(8)
us
cr
Given the number of m, the average false alarm probability at band j can then be expressed as ∫ ∫ ∫ F ··· PFj (γm, j ; l) P j (m; l, n) = | {z } γ1, j γ2, j γm, j
×
m ∏
an
D
ip t
u=1,u, j
n−1 ∑
Conditional false alarm probability given γm, j in (3)
g j (γi, j ; n) dγ1, j dγ2, j · · · dγm, j , (9)
i=1
F
where m is the number of received reporting messages including sensing information on band j at the FC. The probability that the SU reports the sensing information observed at band j is given by q j (n) = ∫∞ g (γ; n)dγ. Let p j (m; k, n) denote the conditional j 0 probability that m messages out of k received reporting messages at the FC include the sensing information on band j. The probability can then be expressed as follows: ( ) ( )k−m k p j (m; k, n) = q j (n)m 1 − q j (n) . (10) m
te
d
M
where P j and P j are the average detection probability and false alarm probability at band j, respectively. Given the value of the detection probability, the averF age false alarm probability, P j , is dependent on the reporting scheme and parameters, (l, k, n), for the fusion scheme. We first derive the average false alarm probability of the multiband CSS with the proposed reporting scheme in Section 3. We then formulate the optimization problem to find the optimal parameters of (l, k, n) in Section 4.
Consequently, given parameters, (l, k, n), the average false alarm probability of band j can then be expressed as k ∑ F F Pj = (11) p j (m; k, n) P j (m; l, n).
ce p
3. Average False Alarm Probability of CSS with a Proposed Limited Reporting Scheme Let γu represent the observed SNR at band u. Additionally, let α(N, v, η) be the probability that the number of bands with γu > η is v among the total N bands, where u ∈ N. The probability can then be expressed as follows: N ∑ I(γu > η) = v α(N, v, η) , Pr
Ac
m=1
4. Optimization Problem 4.1. Problem Formulation In multiband CSS, with given fixed values of K, N, and T f , an optimization problem that maximizes the average capacity of an SU can be formulated as follows:
u=1
=
( )( )v N 1 − Fγ (η) Fγ (η)N−v , v
(7)
max
C(l, k, n)
s.t.
Pj ≥ λ
l,k,n
where I(x) is the index function, which is defined as follows: if x is true, I(x) = 1; otherwise, I(x) = 0. In the proposed reporting scheme, the number of bands to be reported by an SU is limited to n in descending order of SNRs observed at each band. Hence, if an ∑N SU satisfies the condition of u=1,u, j I(γu > γ j ) < n,
D
(12) for ∀ j
0
Page 5 of 12
and ∆2 f1 (l) = 0. Moreover, we have
max l,k,n
∆ f2 (l) = = =
N ( )} F 1 ∑{ (1 − lN∆ s − kn∆r ) × 1 − P j (l, k, n) N j=1 | {z }
′
f2 (l ) − f2 (l) [ F ] F ′ − P (l ) − P (l) k ∫ ∫ ∑ − p(m) · · · γm m=1 { } ′ × PF (γm ; l ) − PF (γm ; l) | {z }
<0 because Q(l) of (3) is a decreasing function w.r.t l
, Cˆ j (l, k, n)
D
P j ≥ λ for ∀ j 0
g j (γi, j ) d γm
0
where γm represents the m-tuple (γ1 , · · · , γm ) and dm γm is the m-dimensional differential. Additionally, ∆2 f2 (l) < 0 because PF (γm ; l) is a function of Q(l) in (3). Consequently,
an
∆2 ( f1 (l) f2 (l)) =
M
4.2. Suboptimal Problem and Algorithm
ce p
te
d
The problem of (13) is nonconvex and is a mixed integer problem, which is usually NP-hard to be solved. We propose an iterative algorithm that solves (13) by decoupling it into three single variable problems that have a discretely concave function. Because of the assumption of an i.i.d. channel for each band, the optimization problem of (13) can be solved by finding the optimal parameters of (l, k, n) that maximize Cˆ j (l, k, n) at band j. Let the functions f1 (l, k, n) and f2 (l, k, n) respectively represent f1 (l, k, n) = 1 − lN∆ s − kn∆r and f2 (l, k, n) = F 1 − P j (l, k, n); therefore Cˆ j (l, k, n) = f1 (l, k, n) f2 (l, k, n).
∆2 f1 (l) f2 (l) + 2 ∆ f1 (l) ∆ f2 (l) | {z } |{z} |{z} =0
+
0 < f1 (l) < 1
<
<0
>0
f1 (l) ∆2 f2 (l) |{z} | {z } <0
0.
(16)
Hence, because ∆2 ( f1 (l) f2 (l)) < 0, f1 (l) f2 (l) is a concave function with respect to l. Lemma 2 (with respect to k). For given l = l˜ and n = n˜ , the function Cˆ j (l, k, n) is a concave function with respect to k. Proof. For simplicity of notation, we omit the subscript j and other variables (l, n); i.e., we use f1 (k) and f2 (k) instead of f1 (l,˜ k, n˜ ) and f2 (l,˜ k, n˜ ), respectively. ′ For k = k + h > k, we have
Lemma 1 (with respect to l). For given k = k˜ and n = n˜ , the function Cˆ j (l, k, n) is a concave function with respect to l.
Ac
∆ f1 (k) =
′
f1 (k ) − f1 (k) = −n∆r h < 0
(17)
and ∆2 f1 (k) = 0. Moreover, we have ∆ f2 (k) > 0 from (18) and ∆2 f2 (k) < 0 because PF (x) is a function of Q(x) in (3). Consequently, because ∆2 ( f1 (k) f2 (k)) = 2 ∆ f1 (k) f2 (k) + 2∆ f1 (k)∆ f2 (k) + f1 (k)∆2 f2 (k) < 0, f1 (k) f2 (k) is a concave function with respect to k.
Proof. We define the discrete derivative of a function f (x) as follows: for the first forward difference, ∆ f (x) = f (x + h) − f (x), and for the second forward difference, ∆2 f (x) = f (x + 2h) + f (x) − 2 f (x + h). For simplicity of notation, we omit the subscript j and other variables (k, n); i.e., we use f1 (l) and f2 (l) instead ˜ n˜ ) and f2 (l, k, ˜ n˜ ), respectively. of f1 (l, k, ′ For l = l + h > l, we have f1 (l ) − f1 (l) = −N∆ s h < 0
(15)
us
>
where ∆ s = τ s /T f and ∆r = τr /T f .
′
m
i=1
0
∆ f1 (l) =
m ∏
cr
×
(13) s.t.
ip t
where l, k, and n are optimization discrete variables; and F C(l, k, n) is obtained from (6) by using P j (l, k, n) of (11). For each band, the miss detection probability of 1 − PDj should be sufficiently small to protect the PUs and the parameters of (c0, j , P(H0, j )) are uncontrollable. Hence, the optimization problem of (12) can be approximated as follows:
(14) 6
Page 6 of 12
F
′
′
k ∑
k ∑
F
p(m; k)P (m) −
m=1
| m=1 {z }
∑k
m=1
=
k ∑
{
−
p(m; k)
m=1 | {z } ′
k ∑
+
∑k′
m=k+1
k ∑
p(m; k )
≈1−
∑k
′
}
F
P (m) | {z }
−
} F F P (k) − P (k + 1) | {z }
m=k+1 F
F
F
∑ε
+
∑k
∑ε
m=ε+1
ε { ∑
F
P (m, n) | {z }
F
{
k ∑
p(m; n)
>
p(m; n) −
=
ε { ∑ m=1
>
′
m=ε+1
ε ∑
−
′
p(m; n )
m=1
F
}
′
P (m, n ) | {z } ′
F
≥ P (ε, n ) for m ≤ ε
F
P (m, n) | {z }
k ∑
−
F
≤ P (ε + 1, n) for m ≥ ε + 1
F
′
m=ε+1
′
P (m, n ) | {z }
p(m; n ) ′
F
}
F
≤ P (ε + 1, n ) < P (ε + 1, n) for m ≥ ε + 1
k k ∑ } F { ∑ } F ′ ′ p(m; n ) P (ε, n ) + p(m; n) − p(m; n ) P (ε + 1, n) ′
′
p(m; n) − p(m; n ) | {z } > 0 for m ≤ ε
F
p(m; n )P (m, n )
m=1
Ac
m=1
ε ∑
′
(18)
∑k
′
F
m=ε+1
ε {∑
+
≥ P (ε, n) > P (ε, n ) for m ≤ ε
ce p +
F
≤ P (k + 1) for m ≥ k + 1
m=1 |{z}
m=1
p(m; n)
m=1
k ∑
−
m=1 |{z}
m=1
=
′
P (n) − P (n ) k ∑ F p(m; n)P (m, n)
M
=
′
f2 (n ) − f2 (n)
d
=
0
te
∆ f2 (n) =
P (m) | {z }
an
> 0 because P (x) is a decreasing function due to Q(x) of (3)
>
F
′
p(m; k )
p(m; k )
{
′
p(m; k )
k ∑ m=k+1
F
≥ P (k) for m ≤ k
′
m=k+1
′
}
′
m=1 | {z
≈ 1 for a large number of k
>
F
′
p(m; k )P (m)
ip t
=
F
P (k) − P (k )
cr
=
′
f2 (k ) − f2 (k)
us
∆ f2 (k) =
}{
m=ε+1 | ∑{z } ≈ 1 − εm=1 p(m; n) F
′
m=ε+1
|
≈1−
{z
∑ε
m=1
} ′
p(m; n )
}
F
P (ε, n ) − P (ε + 1, n) | {z } F
> 0 because P (x) is a decreasing function due to Q(x) of (3)
0.
(19)
˜ Lemma 3 (with respect to n). For given l = l˜ and k = k, ˆ the function C j (l, k, n) is a concave function with respect to n.
˜ n) and f2 (l,˜ k, ˜ n), respectively. instead of f1 (l,˜ k, ′ For n = n + h > n, we have ∆ f1 (n) =
Proof. For simplicity of notation, we omit the subscript j and other variables (l, k); i.e., we use f1 (n) and f2 (n)
′
f1 (n ) − f1 (n) = −k∆r h < 0
(20)
and ∆2 f1 (n) = 0. 7
Page 7 of 12
From (8), q j (n) is an increasing function because g j (γi, j ; n) is an increasing function with respect to n. ′ Hence, for n > n, there exists a value, ε, that satis′ fies the following: if m ≤ ε, p(m; n) > p(m; ( k ) n ); other′ wise p(m; n) < p(m; n ), where p(m; n) = m q j (n)m (1 − ∑ q j (n))k−m from (10) and km=0 p(m; n) = 1. Hence, we have ∆ f2 (n) > 0 from (19) and ∆2 f2 (n) < 0 because PF (x) is a function of Q(x) in (3).
5. Numerical Results
ip t
The average capacity of an SU is evaluated under a cooperative CR network operating in N = 10 primary bands. We assume that the channel of each primary band from the primary transmitters to the SUs is independently and identically Rayleigh distributed with fγ (γ) = 1/¯γ exp(−γ/¯γ), where γ is the PU’s SNR at the SU and γ¯ = −10 dB is the average PU’s SNR at the SU [19]. Moreover, the channel of each primary band during the SU’s data transmission is also assumed to be Rayleigh distributed with an average SNR of 9 dB. Assuming the ON-OFF model for PU appearances, we set P(H0 ) = 0.8 and P(H1 ) = 0.2. The values of the other simulation parameters are as follows: The sampling time ratio is ∆ s = 0.2 × 10−3 , the reporting time ratio is ∆r = 10−3 , and the threshold of detection probability is λ = 0.9. To calculate the multi-fold integration in (9), we reduce the multiple integral to an iterated integral (i.e., a series of integrals of one variable) and use a trapezoidal rule for approximating each definite integral. Fig. 3 to Fig. 7 show the average capacity of an SU for each of l, k, and n, where we check the convexity of the average capacity of an SU with respect to each of l, k, and n in Lemmas 1, 2, and 3. Figures 3 and 4 show the average capacity of an SU as the number of sensing time samples increases, where the number of reporting nodes is fixed to k = K and the number of reporting bands is fixed to n = N. Figure 3 shows that as the value of l increases, the sensing overhead linearly increases and the average false alarm probability decreases. As expected from Lemma 1, Fig. 3 shows that the average capacity of an SU is concave with respect to l when the values of (k, n) are fixed. Figure 4 shows the average capacity of an SU when the number of reporting nodes is respectively 20, 30, and 40. As the number of reporting nodes increases, because the sensing and reporting overheads linearly increase, the optimal value of l that maximizes the average capacity decreases in order to reduce the sensing overhead. Moreover, when there are many reporting nodes, the average capacity decreases as the number of reporting nodes increases because of the excessive reporting overhead. Figure 5 shows the average capacity of an SU, reporting overhead, and false alarm probability as the number of reporting nodes increases, where the number of sensing time samples is fixed to l = 40 and the number of reporting bands is fixed to n = N. As expected from Lemma 2, Fig. 5 shows that the average capacity is concave with respect to k when the values of (l, n) are fixed. Additionally, for the fixed values of (l, n), the average
us
cr
Consequently, because ∆2 ( f1 (n) f2 (n)) = ∆2 f1 (n) f2 (n) + 2∆ f1 (n)∆ f2 (n) + f1 (n)∆2 f2 (n) < 0, f1 (n) f2 (n) is a concave function with respect to n.
an
From Lemma 1, 2, and 3, we can solve each suboptimization problem by using the bisection search method or the Golden section method [28]. The proposed iterative algorithm is summarized in Algorithm 1.
d
Initialize: i←0 /* iteration count */ l(i) ← 1, k(i) ← K, n(i) ← 1 repeat /* For given k and n, find l∗ */
M
Algorithm 1 Find the optimal parameters (l∗ , k∗ , n∗ ) that maximize Cˆ j (l, k, n).
te
1. Given k(i) and n(i) , find l∗ that maximizes (i) (i) Cˆ j (l, k(i) , n(i) ) from l = 1 to ⌊ 1−kN∆ns ∆r ⌋ by using the Golden section method. 2. l(i+1) ← l∗
ce p
/* For given l and n, find k∗ */
Ac
3. Given l(i+1) and n(i) , find k∗ that maximizes Cˆ j (l(i+1) , k, n(i) ) from k = 1 to ( ) (i+1) s min K, ⌊ 1−ln(i) ∆N∆ ⌋ by using the Golden section r method. 4. k(i+1) ← k∗ /* For given l and k, find n∗ */ 5. Given l(i+1) and k(i+1) , find n∗ that maximizes Cˆ j (l(i+1) , k(i+1) , n) from n = 1 to ) ( (i+1) s ⌋ by using the Golden section min N, ⌊ 1−lk(i+1) ∆N∆ r method. 6. n(i+1) ← n∗ 7. i ← i + 1 until | Cˆ j (l(i) , k(i) , n(i) ) − Cˆ j (l(i−1) , k(i−1) , n(i−1) ) | ≤ ϵ return (l∗ , k∗ , n∗ )
8
Page 8 of 12
Average false alarm prob. (
0.6
)
0.4
0.4
0.2
0.2
0.0 20
30
40
50
60
70
80
Number of sensing time samples,
90
0.6
Tr Tf /
)
Pf
Average false alarm prob. ( 0.4
2
3
4
5
6
7
Number of reporting bands,
0.6
0.4
)
0.2
0.0 8
9
10
n
Figure 6: The average capacity, reporting overhead, and false alarm probability according to the value of n when l = 40 and k = K = 30. 1.7
an 1.6
(bps/Hz)
C
1.2
1.5
1.4
0.8
d
0.6
Number of reporting nodes = 20 Number of reporting nodes = 30
Average capacity,
M
1.0
0.4
1.3
1.2
Number of reporting nodes = 20 Number of reporting nodes = 30
1.1
Number of reporting nodes = 40
0.2 0
10
20
30
40
50
60
te
Number of reporting nodes = 40
70
80
90
1.0 1
100
Ac
)
Tr Tf
Reporting overhead (
/
)
Pf
Average false alarm prob. (
0.6
)
0.4
0.4
0.2
0.2
0.0
or P
C
f
0.8
Average capacity (
0.6
1.0
f
0.8
0.0 0
3
6
9
12
15
18
21
Number of reporting nodes,
24
5
6
7
8
9
10
n
capacity is dependent on the value of k regardless of the number of SUs. Figures 6 and 7 show the average capacity of an SU as the number of reporting bands increases, where the number of sensing time samples is fixed to l = 40 and the number of reporting nodes is fixed to k = K. Figure 6 shows that as the value of n increases, the reporting overhead linearly increases and the average false alarm probability decreases. As expected from Lemma 3, Fig. 6 shows that the average capacity of an SU is concave with respect to n when the values of (l, k) are fixed. Figure 7 shows the average capacity of an SU when the number of reporting nodes is respectively 20, 30, and 40. As the number of reporting nodes increases, because the sensing and reporting overheads linearly increase, the optimal value of n that maximizes the average ca-
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Figure 7: The average capacity vs. the value of n when l = 40 and k = K = 20, 30, 40.
Figure 4: The average capacity vs. the value of l when k = K = 20, 30, 40 and n = N = 10. 1.4
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Figure 5: The average capacity, reporting overhead, and false alarm probability according to the value of k when l = 40, n = N = 10, and K = 30.
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l-opt scheme [9] (l, k)-opt scheme [10],[15] Proposed (l, k, n)-opt scheme
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Figure 9: The optimal values of (l, k, n) in the proposed multiband CSS scheme.
eration. Figure 9 shows the optimal values of (l, k, n) in the proposed sensing-reporting-bands optimized scheme. As the number of SUs increases, the optimal number of sensing time samples, l∗ , decreases, the optimal number of reporting nodes, k∗ , is almost identical to the number of SUs, and the optimal number of reporting bands, n∗ , decreases. The results show that, in multiband CSS, it is important to control jointly two parameters, the number of sensing time samples and the number of bands to be reported, according to the number of SUs. Moreover, when we control the reporting overhead which is given by (k · n), it is better to control the value of n than the value of k because the proposed scheme increases the selection diversity according to the value of n.
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Figure 8: The average capacity vs. the number of SUs according to the CSS schemes.
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pacity decreases in order to reduce the reporting overhead. As shown in Fig. 7, when the number of reporting nodes increases from 20 to 40, the average capacity is improved by about 12.7% by reducing the number of reporting bands from 5 to 2. This demonstrates that it is important to control the number of reporting bands according to the number of reporting nodes. Figure 8 shows the average capacity of an SU as the number of SUs increases in the following three CSS schemes: (i) a conventional sensing time optimized (lopt) scheme, where the sensing time is adaptively optimized according to the number of SUs [11]; (ii) a sensing-reporting optimized ((l, k)-opt) scheme, where the sensing time and the number of reporting nodes are adaptively optimized according to the number of SUs [12, 17]; and (iii) the proposed sensing-reportingbands optimized ((l, k, n)-opt) scheme with limited reporting, where the sensing time, the number of reporting nodes, and the number of reporting bands are jointly optimized according to the number of SUs. As the number of SUs increases, the average capacity of the conventional l-opt scheme increases owing to the decrease of the false alarm probability but it decreases after a critical number of SUs, e.g., 15 under this simulation environment, because of the excessive reporting overhead. Because the (l, k)-opt scheme controls the number of reporting nodes, although the number of SUs increases beyond 15, it maintains the average capacity of the case of K = 15. However, as the number of SUs increases, the average capacity of the proposed (l, k, n)-opt scheme increases because the proposed scheme adaptively controls the number of bands to be reported by taking the diversity of selecting bands to be reported into consid-
6. Conclusion
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Taking into consideration a cognitive radio network with multiple primary bands, we investigated the average capacity of secondary users which is affected by the sensing time, reporting time, and a fusion scheme. Adopting a soft combination at the FC, we formulated a sensing-reporting-bands optimization problem that maximizes the average capacity of secondary users. Additionally, we proposed a limited reporting scheme for multiband CSS in order to reduce the reporting overhead. We derived the false alarm probability of the multiband CSS with adoption of the proposed reporting scheme. The proposed limited reporting scheme significantly increases the average capacity of secondary users by reducing the sensing and reporting overheads while providing sufficient protection to the PUs. When there 10
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are 40 cooperative secondary users, the proposed multiband CSS scheme with the limited reporting increases the average capacity of secondary users by about 21% in comparison with the conventional sensing-reporting optimized scheme. Since the original sensing-reportingbands optimization problem is a mixed integer nonconvex optimization problem, we proposed an iterative algorithm that solves the problem by dividing it three single variable suboptimization problems, where each suboptimization problem was proved to be concave.
[10] J. So, R. Srikant, Improving channel utilization via cooperative spectrum sensing with opportunistic feedback in cognitive radio networks, IEEE Commun. Lett. 19 (6) (2015) 1065–1068.
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[11] Y. Liang, Y. Zeng, E. Peh, A. Hoang, Sensingthroughput tradeoff for cognitive radio networks, IEEE Trans. Wireless Commun. 7 (4) (2008) 1326–1377. [12] E. Peh, Y. Liang, Y. Guan, Y. Zeng, Optimization of cooperative sensing in cognitive radio networks: A sensing-throughput tradeoff view, IEEE Trans. Veh. Technol. 58 (9) (2009) 5294–5299.
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network solutions. From 2005 to 2007, he was a Senior Engineer at Samsung Electronics, Suwon, Korea, where he involved in the design, performance evaluation, and development of mobile WiMAX systems and B3G wireless systems. From 2007 to 2008, he was a Postdoctoral Fellow in the Department of Electrical Engineering, Stanford University, Stanford, CA, USA. From August 2014 to July 2015, he was a visiting professor in the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, IL, USA. Since September 2008, he has been with the Department of Electronic Engineering, Sogang University, Seoul, Korea, where he is currently an Associate Professor. His current research interests include radio resource management, multiple antenna systems, cognitive radio networks, and IoT networks.
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Jaewoo So received the B.S. degree in electronic engineering from Yonsei University, Seoul, Korea, in 1997, and received the M.S. and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 1999 and 2002, respectively. From 2001 to 2005, he was with IP One, Seoul, Korea, where he led several research projects and developed IEEE 802.11a/b/g products and heterogeneous
Taesoo Kwon received the B.S., M.S., and Ph.D. degrees from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2001, 2003, and 2007, respectively, all in electrical engineering and computer science. From 2007 to 2011, he was a Senior Researcher with Samsung Advanced Institute of Technology, Yongin, Korea, where he was involved in research on the LTEAdvanced systems, beyond the 4G wireless communication systems, and nanoscale communication technologies. In 2008 and 2011, he was a Visiting Scholar with the Department of Electrical Engineering, Stanford University, Stanford, CA, USA. From 2011 to 2012, he was a Postdoctoral Fellow with the Department of Electrical and Computer Engineering, the University of British Columbia, Vancouver, BC, Canada. From 2013 to 2015, he was a Senior Researcher with the Electronics and Telecommunications Research Institute (ETRI), Daejeon, where he was engaged in research on the 5G wireless communication systems. Since 2015, he has been an Assistant Professor with the Department of Computer Science and Engineering, Seoul National University of Science and Technology (SeoulTech), Seoul. His research interests include wireless networks, stochastic geometry, optimization, and data analytics.
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