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Energy-Efficient Partial-Cooperative Spectrum Sensing in Cognitive Radio over Fading Channels Saud Althunibat(1) , Sandeep Narayanan(2,3) , Marco Di Renzo(4) , Fabrizio Granelli(1) (1) (2) (3) (4)
University of Trento, DISI, Via Sommarive 14, I-38123, Trento, Italy
WEST Aquila s.r.l., Via G. Gronchi 18, Nucleo Industriale di Pile, 67100 L’Aquila, Italy
University of L’Aquila, Center of Excellence for Research DEWS, Via G. Gronchi 18, Nucleo Industriale di Pile, 67100 L’Aquila, Italy
Laboratory of Signals and Systems (L2S), UMR 8506 CNRS – SUPELEC – Univ Paris–Sud, 3 rue Joliot–Curie, 91192 Gif–sur–Yvette (Paris), France E–Mail:
[email protected],
[email protected],
[email protected],
[email protected]
Abstract—Energy efficiency in cooperative spectrum sensing in cognitive radio is investigated in this paper, where a novel approach is proposed for reducing the energy consumed in spectrum sensing and improving the resultant energy efficiency of the cognitive transmission. The proposed approach is based on limiting the number of users that participate in the spectrum sensing task. The participation decision of each user is taken individually by the user itself, where each user estimates the expected amount of consumed energy based on its distance from the base station, and compares it to a predefined threshold. The user will participate only if the estimated energy is less than the threshold. Besides reducing energy consumption, our proposal increases the amount of successfully transmitted data as well. Moreover, an optimization of the threshold is carried out through simulation in order to optimize the energy efficiency. Our results show a considerable amount of reduction in energy consumption (up to 80%) compared to the conventional approach.
I. I NTRODUCTION Since energy resources are limited, especially in batterypowered mobile terminals, energy efficiency has recently gained a lot of attention. High energy consumption represents a challenge hindering wide implementation of some recent technologies [1]. A system whose characteristics imply more energy consumption than other systems is Cognitive Radio (CR). In CR, a licensed spectrum can be exploited by unlicensed users when it is unused by licensed users. This requires awareness of spectrum status, which is performed by a new pre-task, termed as spectrum sensing [2] [3]. In spectrum sensing, the unlicensed users, called cognitive users (CUs), have to sense the target spectrum for a specific period, inducing energy consumption which does not exist in the typical wireless system. Moreover, for a better performance in spectrum sensing, the local sensing results are sent to a central entity, called Fusion Center (FC), in order to process these results according to a predefined Fusion Rule (FR), and issue a final decision about spectrum status, which is known as Cooperative Spectrum Sensing (CSS) [4] [5]. Although CSS decreases the probability of erroneous decision considerably by mitigating the effects of multipath fading and shadowing, it causes extra delay, security risks [6] [7] and more energy consumption. It is normally accepted that the energy consumed during reporting sensing results to the FC is a dominant factor of the total energy consumption in CSS. Two well-known schemes ∗ This work is funded by the Research Project GREENET (PITN-GA-2010264759).
for results’ reporting [8] [9], Soft Scheme (SS), where the result of each user is quantized locally by multiple number of bits and sent to the FC, and Hard Scheme (HS), where the result is quantized by only one bit and sent to the FC. As a user employing HS reports only one bit, it is clear that the energy consumption is lower than if SS is employed [10]. Thus, in this work, we consider only HS. Several authors have investigated the energy consumption in CSS. Clustering is proposed in [11] to reduce the energy consumption during results’ reporting, where a CU is selected to forward the results in behalf of a group of users. In [12], censoring approach is proposed in order to reduce energy consumption, where CUs report to the FC only if they have informative test statistics. Although [11] and [12] reduce energy consumed during reporting, all users still consume energy in local sensing, besides, extra consumption is caused by results exchange among cluster-members in [11]. However, in our proposal, CUs are preventing from sensing and reporting, as we will see later. Optimizing sensing time is investigated in [13] in order to improve energy efficiency. An alternative approach is to optimize the FR as in [14]. Optimizing the number of participating users in CSS represents a favorite approach as it reduces the sensing energy and reporting energy as well [10] [15]. In this paper, a novel partial cooperative algorithm for spectrum sensing is proposed in order to reduce the energy consumed during CSS. The idea behind our proposal is to prevent the CUs which consume a larger amount of energy from participating in the CSS. The participation decision of each CU is taken individually by the CU itself, where each CU estimates the expected amount of energy that will be consumed if it participates, and compares it to a predefined threshold. Using this approach, the users that will greatly increase the energy consumption will be prevented from participating, resulting in lower energy consumption. It is worth mentioning that the proposed approach improves the energy efficiency not only by reducing energy consumption but also by increasing the amount of successfully transmitted data. The increase in amount of successfully transmitted data is due to the decrease in the overall false alarm probability, as the number of involving users in CSS decreases. As the number of the involving CUs depends on the predefined threshold, an optimization of this threshold is carried out to maximize energy efficiency. The remainder of this paper is organized as follows, Section
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II describes the system model, where in-detail discussion of energy consumption during CSS is presented. In Section III, the proposed algorithm is presented along with its mathematical formulas. Followed by performance evaluation through computer simulations in section IV. Conclusions are drawn in Section V. II. S YSTEM M ODEL We consider a cognitive network consisting of N CUs. All CUs try to access a target spectrum. All the stages of the cognitive transmission is organized by a central FC located at the base station. The channels between the CUs and the licensed users and the channels between the CUs and the FC are modeled as narrow-band Rayleigh fading with additive white Gaussian noise (AWGN). The channel variance between any CU and the target spectrum is denoted by µ2 , while the channel variance between any CU and the FC is denoted as σi2 . The CUs are distributed randomly around the FC . The distance between ith CU and the FC , denoted as (di ), is uniformly distributed di ∼ U [dmin , dmax ], where dmin and dmax are the minimum and the maximum distances, respectively. During spectrum sensing, the target spectrum is sensed for a specific time, denoted by Ts . The optimal method for spectrum sensing is energy detection method especially when no prior information is available [4]. This method implies collecting a number of samples and computing the average energy contained in these samples. According to the HS, the resultant average is compared to a predefined threshold, and a local binary decision ui {1, 0} about spectrum status is made. if ui = 1, then the ith CU decides it is used. Otherwise, the spectrum is identified as unused by the ith CU. The local performance is measured by the detection probability (Pd,i ) and the false-alarm probability (Pf,i ). The detection probability is the probability of identifying a channel as used when it is actually used. In other words, making a local decision of ui = 1, when the channel is used. The falsealarm probability is the probability of identifying a channel as used channel while it is unused, which means making a local decision of ui = 1 when the channel is unused. For simplicity, we assume an identical performance among the CUs, and hence, Pd,1 = Pd,2 = ... = Pd and Pf,1 = Pf,2 = ... = Pf . Pd and Pf for Rayleigh fading channels are given as [5], [16]: p √ 2mρ, λ (1) Pd = Qm Γ m, λ2 Pf = (2) Γ (m) where Qm (., .) is the generalized Marcum Q-function [17], m is the time-bandwidth product, ρ is the signal-to-noise ratio, λ is the energy threshold used by the energy detector and Γ (., .) is the incomplete gamma function [18]. III. C ONVENTIONAL A PPROACH OF C OOPERATIVE S PECTRUM S ENSING In the conventional approach of CSS, all CUs should participate in the spectrum sensing process. Therefore, after
a local decision is issued individually by each CU, all local decisions should be reported to the FC. The general FR to process the received local decisions in HS is called K-out-ofN rule [9], where N denotes the total number of reporting users and K the number of users who detect a signal in the target spectrum, i.e., have obtained a local decision of 1. K-out-of-N rule implies comparing K with a predefined threshold (K 0 ). If K > K 0 , then the spectrum is identified as used. Otherwise, the spectrum is identified as unused. Mathematically, the function of K-out-of-N rule is written as follows: used if K ≥ K 0 F inal Decision = (3) unused if K < K 0 Some popular rules are derived from this rule like OR-rule (K 0 = 1), AND-rule (K 0 = N ). Without loss of generality, we consider only OR-rule (K 0 = 1). The overall performance is measured by the overall detection probability and the overall false alarm probability, which are given as [9] [5]: PD = 1 − (1 − Pd )N
(4)
PF = 1 − (1 − Pf )N
(5)
Regarding the total energy consumed in this approach, if we denote the energy consumed by the ith CU during sensing and reporting by Es,i , Er,i , respectively, and the energy consumed by the scheduled user is Et , the total energy consumed is given as: N N X X Etot = Es,i + Er,i + Punused Et (6) i=1
i
where Punused is the probability of identifying the spectrum as unused, and is given as: Punused = 1 − P0 PF − P1 PD
(7)
where P0 and P1 are the probabilities that the spectrum is actually unused and used, respectively. Notice that the sensing energy is identical for all CUs and equal to Es , thus, (6) can be simplified as: Etot = N Es +
N X
Er,i + Punused Et
(8)
i
As the energy is defined as the consumed power multiplied by the time, (8) can be rewritten as: Etot = N αs Ts +
N X
αr,i Tr + Punused αt Tt
(9)
i=1
where Ts , Tr , and Tt are the time consumed by a CU in sensing, reporting and transmission, respectively. αs , αr and αt are the consumed power during sensing, reporting and transmission, respectively. Another important quantity that should be defined is the amount of the successfully transmitted data (D) measured in bits. Notice that D depends on the correct identification of the unused spectrum. D is given as: D = P0 (1 − PF )RTt
(10)
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where R is the data rate in bps, and the factor P0 (1 − PF ) represents the probability of the correct identification of the unused spectrum. From (10), it is also clear that the D increases as PF decreases. Finally, for the purpose of assessing the energy efficiency in [Joule/bit], we define the consumed energy per bit (EpB) as follows: Etot (11) EpB = D IV. T HE P ROPOSED A PPROACH Motivated by improving the energy efficiency in cognitive radio systems, we propose a novel approach for spectrum sensing which reduces energy consumption during this process with a constraint on the achievable detection accuracy. The idea is to reduce the number of users participating in spectrum sensing, which results in a partial cooperative spectrum sensing. The novelty of our proposal is that the participation decision is taken individually by each CU, and on a base of expected energy consumption. In other words, each CU calculates its expected energy consumption in case of participating in spectrum sensing, and compares it to a predefined threshold (γ). If it is lower than γ, the CU will participate. Otherwise, the CU will not participate. By such mechanism, we try to reduce energy consumption by an effective way that implies preventing the CUs who will consume large amount of their energy in spectrum sensing from participation. If we denote the estimated energy consumed during spectrum sensing by the ith CU by Ei , the following equation describes the participation decision (Si ) 1 (P articipate) if Ei < γ Si = (12) 0 (Don0 t participate) if Ei ≥ γ Next, we discuss the calculation of Ei , the resulting performance based on our proposal, and finally, we address the energy efficiency improvement achieved by the proposed approach. A. Calculating of Ei Ei includes the energy consumed during local sensing and decision reporting by the CU. Thus, Ei is given as: Ei = Es + Er,i
(13)
as Es is identical for all CUs, then the determinant factor in Ei is Er,i that can be written as a product of the reporting time Tr and the power consumed during reporting αr,i , as follows: Eri = αr,i Tr
(14)
In results’ reporting, the user is in transmission status, and hence, αr,i mainly depends on the distance from the FC and the desired bite error rate. αr,i is given as [19]: αr,i = αc + αiP A
(15)
where αiP A is the power consumed in the power amplifier stage of the ith user, and αc is the power consumed by the other circuit elements. αc is identical in all users and can be modeled as: αc = αDAC + αf ilt + αmix + αsyn
(16)
where αDAC , αf ilt , αmix , and αsyn are the power consumption at the digital-to-analog converter (DAC), the transmit filters, the mixer, and the frequency synthesizer, respectively. αf ilt , αmix , and αsyn can be modeled as constants, while αDAC can be approximated as: 1 n1 2 DAC Vdd I0 (2 − 1) + n1 Cp (2B + fcor )Vdd (17) α = 2 where I0 is the current supply, n1 is the number of bits in the DAC, Cp is the parasitic capacitance, Vdd is the voltage supply, fcor is the corner frequency, and B is the symbol bandwidth. The second part of (15), αiP A is given as: ζ out α (18) δ i where δ is the drain efficiency of the RF power amplifier, ζ is the Peak-to-Average Ratio (PAR) which is dependent on the modulation scheme and the constellation size, and αiout is the transmitted power from the amplifier. When the channel only experiences a square-law path loss we have: αiP A =
αiout = E¯b Rb
(19)
where E¯b is the required energy per bit at the receiver for a given BER requirement, and Rb is the bit rate. Under Rayleigh fading, E¯b in (19) for BPSK modulation can be given as follows: No (1 − 2Pe )2 (20) E¯b = 4σi2 Pe (1 − Pe ) where Pe is the BER and σi2 is channel variance that is given as: (4πdi )2 Ml Nf (21) σi2 = Gt Gr λ2 where Gt is the transmitter antenna gain, Gr is the receiver antenna gain, λ is the carrier wavelength, Ml is the link margin compensating the hardware process variations and other additive background noise or interference, and Nf is the receiver r noise figure defined as Nf = N No with No = 171 dBm/Hz the single-sided thermal noise Power Spectral Density (PSD) at room temperature and Nr is the PSD of the total effective noise at the receiver input. B. The achievable performance Let us consider the estimated energy of each CU (Ei ) as a random variable with a Probability Density Function (pdf), fe , and Cumulative Distribution Function (CDF), FE . Therefore, for any CU, the probability of participation in the spectrum sensing equals to FE (γ). Also, the number of CUs who have decided to participate (N ∗ ) follows a binomial distribution described as: N −n N P rob.(N ∗ = n) = (FE (γ))n 1 − FE (γ) (22) n where the average number of sensing users N ∗ is given by N ∗ = N FE (γ)
(23)
After reporting the local decisions made by N ∗ CUs, OR-rule is applied and a final decision is made. In case of N ∗ = 0, i.e., no users have participated, a random final decision is made at
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the FR. Therefore, the average overall detection probability ∗ (PD ) and the average overall false alarm probability (PF∗ ) can be written as: ∗ 1 − (1 − Pd )N if N ∗ ≥ 1 ∗ PD = (24) 0.5 if N ∗ = 0 ∗ 1 − (1 − Pf )N if N ∗ ≥ 1 ∗ PF = (25) 0.5 if N ∗ = 0 where N ∗ = 1, 2, ..., N . C. Energy Efficiency Optimization The total energy consumed by the whole system by follow∗ ing the proposed approach (Etot ) can be written as follows: ∗ Etot =
N X
∗ Si Ei + Punused Et∗
(26)
i=1
where the first term represents the consumed energy during spectrum sensing process, which equals to 0 for the CUs who have not participated because it is multiplied by Si = 0. The second term represents the energy consumed during data ∗ ∗ transmission (Et∗ ) which is conditioned by Punused . Punused is the probability of identifying the spectrum as unused in our ∗ approach, which can be obtained by substituting PD and PF∗ instead of PD and PF in (7). Regarding the calculation of Et∗ , we assume that a CU is randomly scheduled for data transmission. Therefore, the calculation of Et∗ follows the same procedure as Er with a proper substitution of the values of fcor , B, and Pe . The amount of successfully transmitted data in bits, D∗ depends mainly on the performance of the spectrum sensing, and can be given as: ∗ ∗ D = RTt P0 (1 − PF ) (27) Hence,the total energy consumed per successfully transmitted bit based in the proposed approach (EpB ∗ ) is given as: ∗ Etot (28) D∗ Remember that the resulting EpB depnds mainly on the number of participating users which is a function of γ. Therefore, in order to minimize EpB ∗ , an optimization of γ is highly motivated.
EpB ∗ =
V. S IMULATION R ESULTS In this section, we present some simulation results in order to illustrate the advantage of the proposed partial-cooperative spectrum sensing scheme. In particular, we are interested in finding an optimal value of the energy threshold, γ, which minimizes the total energy consumed per successfully transmitted bit in partial CSS, EpB ∗ . Table V lists the simulation parameters used in this section. Fig.1 shows the achievable amount of successfully transmitted data versus the threshold γ. The x-axis is shown in terms of Emin , Emax and ∆, where Emin and Emax are the energy consumed in spectrum sensing by a CU at a distance equals to dmin and dmax , respectively. ∆ is the step between each two consecutive lines equals to
1 × 10−14 . For low values of γ, all CUs will not participate in CSS since they have Ei larger than γ, which results in PF∗ = 0.5, according to (25). Hence, D∗ is constant since it depends mainly on PF∗ , as stated in (27). When γ increases so that the number of sensing users equals 1, PF∗ improves, and consequently, the transmitted data increases. As γ increases, D∗ decreases since PF∗ increases. For comparative purposes, Fig.1 also shows the plot for the achievable amount of successfully transmitted data using the conventional approach, D, where all the users take part in CSS. Since in conventional approach, D is independent of the value of γ, the plot will be a constant with respect to γ. In Fig. 2, the total energy consumed by the system in partial CSS, ∗ Etot over different values of γ is plotted. We can see that, as ∗ γ increases, Etot first remains the same, but then decreases and then gradually becomes stable for larger values of γ. The initial flat region in the plot is due to the fact the estimated energy, Ei of all the CU’s is above γ. Hence, all the CU’s will not participate in spectrum sensing, and energy is consumed ∗ decreases even only in transmission. As γ is increased, Etot though more CUs participate in CSS. This is due to the decrease in Punused . The plot for total energy consumed by the system in conventional approach, is also shown in Fig. 2. From the previous figures, it is clear that increasing γ lowers the energy consumption but with lower transmitted data. Thus, in order to find the optimal value of γ that balances the two contrasting effects, the total energy consumed per successfully transmitted bit in partial CSS, EpB ∗ versus different values of γ is plotted in Fig. 3. As γ increases, EpB ∗ first remains the same, but then decreases and then increases after a particular value of γ. The value of γ, where EpB ∗ is minimum gives the optimal value of γ. The plot for total energy consumed per successfully transmitted bit is also shown in Fig. 3. The results in Fig. 3 clearly shows the potential gain of using the proposed partial-CSS scheme over the conventional approach. More precisely, when the optimal value of γ is used, partial CSS provides a Relative Average Energy Reduction(RAER) per successfully transmitted bit of approximately 80% with respect to the conventional approach.
Parameter
Value
Parameter
value
N Pd Ts Tt
10 0.8 3 ms 40 ms 7Km 50.0mW 30.3mW 3V 10Kbps 1pF 10dB 0.35 10−5
P0 Pf Tr dmin αs αf ilt I0 fr n1 Gt Gr Ml fcor ζ
0.5 0.2 0.01 ms 100m 106 mW 2.5mW 3µA 2.5GHz 10 5dBi 40dB 1KHz 514 × 10−3
dmax αsyn αmix Vdd Rb Cp Nf δ Pe
Table I: Simulation Parameters
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Fig. 1.
The amount of transmitted data versus γ. (∆ = 1 × 10−14 ) Fig. 3. Total energy consumed per successfully transmitted bit versus γ. (∆ = 1 × 10−14 )
Fig. 2. Total consumed energy of the whole system versus γ. (∆ = 1 × 10−14 )
VI. C ONCLUSIONS A partial cooperative spectrum sensing approach is presented in this paper, which aims to reduce the energy consumption in cognitive radio. The proposed approach is based on reducing the number of sensing users. Each user decides to participate in spectrum sensing if its expected energy consumption during this process is less than a threshold. The threshold is optimized to minimize the energy consumption through computer simulations. R EFERENCES [1] G. Fettweis and E. Zimmermann, ”ICT Energy Consumption - Trends and Challenges, WPMC Conference, Lapland-Finland, 2008. [2] J. Mitola and G.Q. Maguire, ”Cognitive radio: Making software radios more personal,” IEEE Personal Communications, vol. 6, no. 4, pp. 13-18, August 1999. [3] S. Haykin, ”Cognitive radio : Brain-empowered wireless communications,” IEEE Journal on Selected Areas in Communications, vol.23, no.2, pp. 201-220, February 2005. [4] S. M. Mishra, A. Sahai and R. Brodersen, ”Cooperative Sensing among Cognitive Radios”, IEEE ICC, Istanbul-Turkey, June 2006.
[5] A. Ghasemi and S. Sousa, ”Opportunistic Spectrum Access in Fading Channels Through Collaborative Sensing”, Journal of Communications, vol. 2, no. 2, pp. 71-82, March 2007. [6] I.F. Akyildiz, B.F. Lo and R. Balakrishnan, ”Cooperative spectrum sensing in cognitive radio networks: A survey”, Physical Communication (Elsevier), vol. 4, no. 1, pp. 40-62, March 2011. [7] M. Di Renzo, F. Graziosi, F. Santucci, ”Cooperative Spectrum Sensing in Cognitive Radio Networks over Correlated Log-Normal Shadowing”, IEEE Vehicular Technology Conference Spring, Barcelona, Spain, April 2009. [8] S. Chaudhari, J. Lunden, V. Koivunen, and H. V. Poor, ”Cooperative Sensing With Imperfect Reporting Channels: Hard Decisions or Soft Decisions?”, IEEE Transactions on Signal Processing, vol.60, no. 1, January 2012. [9] R. Viswanathan and P.K. Varshney, ”Distributed detection with multiple sensors, Proceedings of the IEEE, vol. 85, no. 1, pp. 54-63, January 1997. [10] S. Maleki, S.P. Chepuri, G. Leus, ”Energy and Throughput Efficient Strategies for Cooperative Spectrum Sensing in Cognitive Radios”, IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications, San Francisco-CA, June 2011. [11] C. Sun, W. Zhang, K.B. Letaief, ”Cluster-based cooperative spectrum sensing in cognitive radio systems, IEEE ICC, June 2007. [12] J. Lunden, V. Koivunen, A. Huttunen, H.V. Poor, ”Censoring for Collaborative Spectrum Sensing in Cognitive Radios”, ACSSC, April 2007. [13] H.N. Pham, Y. Zhang, P.E. Engelstad, T. Skeie and F. Eliassen, ”Energy Minimization Approach for Optimal Cooperative Spectrum Sensing in Sensor-Aided Cognitive Radio Networks, ICST WICON, 2010. [14] S. Althunibat, S. Narayanan, M. Di Renzo and F. Granelli, ”On the Energy Consumption of the Decision-Fusion Rules in Cognitive Radio Networks”, IEEE CAMAD, Barcelona-Spain, September 2012. [15] E.C.Y. Peh, Y.C. Liang, Y.L. Guan and Y. Pei, ”Energy-Efficient Cooperative Spectrum Sensing in Cognitive Radio Networks, IEEE GlobeCom, 2011. [16] F.F. Digham, M.S. Alouini, and M.K. Simon, ”On the energy Detection of Unknown signals Over Fading Channels”, IEEE Transactions on Communications, vol. 55, no. 1, pp. 21-24, January 2007. [17] A. H. Nuttall, ”Some integrals involving the QM function”, IEEE Transactions on Information Theory, vol. 21, no. 1, pp. 9596, January 1975. [18] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. Academic Press, 1994. [19] S. Cui, A. Goldsmith, and A. Bahai, ”Energy-efficiency of MIMO and Cooperative MIMO Techniques in Sensor Networks”, IEEE Journal on Selected Areas in Communications, vol. 22, no. 6, pp. 1089-1098, 2004
