Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2013 / Article

Research Article | Open Access

Volume 2013 |Article ID 975860 | 9 pages | https://doi.org/10.1155/2013/975860

Throughput Optimization via Cooperative Spectrum Sensing with Novel Frame Structure

Academic Editor: Matjaz Perc
Received28 Aug 2013
Revised10 Nov 2013
Accepted10 Nov 2013
Published08 Dec 2013

Abstract

In cognitive radio (CR) networks, cooperation can greatly improve the performance of spectrum sensing. In this paper, we propose a novel cooperative spectrum sensing (CSS) frame structure in which CR users conduct spectrum sensing and data transmission concurrently over two different parts of the primary user (PU) spectrum band. Energy detection sensing scheme is used to prove that there exists an optimal sensing bandwidth which yields the highest throughput for the CR network. Thus, we focus on the optimal sensing settings of the proposed sensing scheme in order to maximize the throughput of the CR network under the conditions of sufficient protection to PUs and required bandwidth for potential CR user data transmission. Some algorithms are also derived to jointly optimize the sensing bandwidth and the final decision threshold. Our simulation results show that optimizing the sensing bandwidth and the final decision threshold together will further increase the throughput of the CR network as compared to that which only optimizes the sensing bandwidth or the final decision threshold.

1. Introduction

Cognitive radio is a promising technology to improve the efficiency of spectrum usage [1]. The CR users should obey the two following etiquettes [2]: they are allowed to use some unoccupied spectrum bands; they must vacate the spectrum bands quickly whenever the PUs return. In order to avoid interference with PUs, a CR user needs to efficiently and effectively detect the presence of the PUs. CR users can use one of several common detection methods [3], such as matched filter, feature detection, and energy detection. Energy detection is the most popular method addressed in the literature [48]. Measuring only the received signal power, energy detection has much lower complexity than the other two schemes. Therefore, we consider energy detection for spectrum sensing in this paper.

The detection quality of spectrum sensing easily suffers from the fading and shadowing environment, which can cause hidden terminal problem. To combat these impacts, cooperative spectrum sensing has been introduced to obtain the space diversity in multiuser CR networks [912]. Game theory is suitable for analyzing conflict and cooperation among rational decision makers [1316]. In [17], the authors focused on dynamical effects of coevolutionary rules on the evolution of cooperation. Game theory has been widely applied to study distributed optimization problems, such as power control, dynamic spectrum access and management [18, 19], and so on. In [20], the authors proposed an evolutionary game framework to answer the question of “how to collaborate” in multiuser decentralized cooperative spectrum sensing. The cooperative spectrum sensing involves sensing, reporting, and decision making steps [21]. In the sensing step, every CR user performs spectrum sensing independently using energy detection method and makes a local decision. In the reporting step, all the local sensing observations are reported to a fusion center (FC). The decision step is made to indicate the absence or the presence of the PU.

In the frame structure of periodic spectrum sensing (PSS), the CR user senses the status of the radio spectrum in the sensing slot and transmits data using the remaining frame duration [22]. Since the CR user must interrupt data transmission during the sensing slot, the CR user transmission delay will be long. Thus, in the case of delay sensitive applications, the QoS (quality of service) will not be guaranteed. In our previous work [23], we propose a novel cooperative spectrum sensing frame structure in which CR users conduct spectrum sensing and data transmission concurrently over two different parts of the primary user spectrum band. In this way, the CR users do not need to interrupt data transmission in the sensing stage, and the QoS can be guaranteed. The optimal multiminislot sensing scheme and the optimal fusion scheme that minimize the CR user transmission delay were analyzed in [23]. However, the performance of throughput with the novel CSS frame structure was not investigated. In this paper, we focus on analyzing the throughput of the CR network.

In the novel frame structure designed for CSS, one part of the PU transmission bandwidth is assigned exclusively to spectrum sensing and sensing results reporting, and the other part is assigned exclusively to potential CR user data transmission. According to this frame structure, under the condition of sufficient protection to PUs, an increase in the sensing bandwidth results in a lower false alarm probability, which leads to higher throughput of the CR network. However, the increase of the sensing bandwidth results in a decrease of the bandwidth assigned to potential CR user data transmission and hence the throughput of the CR network. Therefore, there could exist the optimal sensing bandwidth that maximizes the throughput of the CR network.

In this paper, we study the tradeoff problem for cooperative spectrum sensing with novel frame structure. We are interested in the problem of designing the sensing bandwidth to maximize the throughput of the CR network under the conditions of sufficient protection to PUs and required bandwidth for potential CR user data transmission. When energy detection is utilized for spectrum sensing, we prove that there indeed exists one optimal sensing bandwidth which yields the highest throughput for the CR network.

In the cooperative spectrum sensing with novel frame structure, we employ the counting rule as the fusion rule at the FC since it requires the least communication overhead and is easy to implement. Since CR is originally designed to improve the spectrum efficiency, maximizing the CR users’ throughput is one of the most practical interests. Our object is to find the optimal sensing settings to maximize the throughput of the CR network under the conditions of sufficient protection to PUs and required bandwidth for potential CR user data transmission. To achieve that, we propose an efficient search algorithm that jointly optimizes the sensing bandwidth and the final decision threshold. Computer simulations show that optimizing the sensing bandwidth and the final decision threshold together will further increase the throughput of the CR network as compared to that which only optimizes the sensing bandwidth or the final decision threshold.

The rest of this paper is organized as follows. The cooperative spectrum sensing with novel frame structure is analyzed in Section 2. The optimization problem of maximizing the throughput with sensing bandwidth and final decision threshold as the optimization variables is formulated in Section 3. Optimal sensing settings of throughput are analyzed in detail in Section 4. Simulation results are presented in Section 5, followed by concluding remarks in Section 6.

2. Cooperative Spectrum Sensing with Novel Frame Structure

We consider a CR network, with a number of CR users and a fusion center. The size of the secondary network is small compared with the distance between the primary network and the secondary network to ensure the QoS of primary link. Then the path loss of each CR user is almost identical and the primary signals received at the CR users are considered to be independent and identically distributed (i.i.d.) [24]. In cooperative spectrum sensing, local CR users individually sense the channels and then send information to the fusion center, and the fusion center will make the final decision.

Figure 1 illustrates the novel frame structure designed for cooperative spectrum sensing. In the frequency domain, considering the case that the CR users know the PU transmission bandwidth , is divided into two parts, namely, and (). is assigned exclusively to spectrum sensing and sensing results reporting, which means that the status of PU can be decided by sensing a portion of PU bandwidth, and we do not need to sense the whole PU bandwidth. The other part is assigned exclusively to potential CR user data transmission. The CR users conduct spectrum sensing and data transmission concurrently over two different parts of the primary user spectrum band.

In the time domain, it is assumed that the frame duration is and the individual reporting duration is . Since each CR user continues the spectrum sensing after sending its sensing result to the fusion center, the sensing duration for each CR user is .

The essence of spectrum sensing is a binary hypothesis-testing problem [25]:

The received signal at the th CR user can be formulated as where is the received signal at the th CR user, is the noise and , is the signal of PU and , and is the channel gain between PU and the th CR user. The power spectrum density (PSD) of the noise and the PSD of the primary signal are evenly distributed, with values of and , respectively. The SNR (signal-to-noise ratio) of PU’s signal at the th CR user is .

Since the primary signals received at the CR users are considered to be i.i.d., we can omit the subscript “.” Suppose the sampling frequency is and the decision statistic of energy detection at each CR user is given by . It is shown in [26] that when is large enough, according to central limit theorem, we have The probability density function (PDF) of can then be written as

For a nonfading environment, the probability of false alarm and the probability of detection at each CR user can be computed by where denotes the threshold of the energy detection and is the -function defined as .

By (5), we have

In CSS, each CR user makes a “one bit” local decision (1 standing for the presence of PU and 0 standing for the absence of PU) on the primary user activity and then sends the individual decision to the fusion center over a reporting channel. Let denote the number of CR users reporting presence of PU. In the FC, the final decision strategy is given by [27] where is an integer, and , is the final decision threshold at FC. It is seen that OR rule corresponds to the case of , AND rule corresponds to the case of , and Majority rule corresponds to the case of . The final false alarm probability and final detection probability can be calculated as [27] Lets define and . Then, we have , , , and .

3. Optimization Problem Formulation

In our proposed novel cooperative spectrum sensing frame structure, the CR user transmits data over the bandwidth only when the PU is sensed to be absent. Suppose that the power spectrum density of the CR user signal is evenly distributed, with the value of . Then, . There are two scenarios for the CR users to transmit data.

(1) The PU Is Correctly Detected to Be Absent. The probability of this scenario happening is , where denotes the prior probability of the absence of the PU. In this case, the achievable throughput of the CR network is where is the SNR for the secondary link, and where is the channel gain of the secondary link.

(2) The PU Is Falsely Detected to Be Absent. The probability of this scenario happening is , where denotes the prior probability of the presence of the PU. In this case, the primary signal is considered as an interference to the secondary receiver, and the achievable throughput of the CR network is where is the signal-to-noise and interference ratio for the secondary link, and where is the channel gain between the PU and the CR user.

Then, the achievable throughput of the CR network can be computed by

Considering the fact that the priority of a CR system is the protection of the QoS of the primary link, a high probability of detection is required to ensure that no harmful interference is caused by the CR network. Our object is to find the optimal sensing settings to maximize the CR users’ throughput under the condition of sufficient protection to PUs. To satisfy the required bandwidth for potential CR user data transmission, we set ; namely, . Mathematically, the optimization problem can be stated as where is the target detection probability with which the PUs are defined as being sufficiently protected. In the second scenario, the primary signal is considered as an interference with the secondary receiver, and we have . Suppose that the prior probability of the presence of the PU is small; say less than 0.3; thus it is economically advisable to explore the secondary usage for PU spectrum band. Since is a decreasing function of , according to (5), we have . Furthermore, since for , is an increasing function of for ; thus and . Therefore, the optimization problem can be approximated by maximizing subject to (16).

Theorem 1. is a decreasing function of .

Proof. For a given and , we have where Since and , it is derived that . Thus, is a decreasing function of . Theorem 1 is proved.

Therefore, the optimal solution must occur when the following equation stands: To get the optimal solution of (15), we need to calculate the root of numerically. Newton-Raphson algorithm can be employed to find the root of [28]. The process of the Newton-Raphson algorithm is stated as follows.(1)Choose tolerance and initial guess ; let .(2)If , stop; otherwise, go to step .(3)Let ; let ; go to step .

The optimization problem is reduced to

In the next section, we will find the optimal solutions of and to maximize the throughput of the CR network.

4. Optimal Sensing Settings of Throughput

First we will prove that, for any target detection probability and the final decision threshold , there exists an optimal value of that maximizes the throughput of the CR network for the CSS with novel frame structure. The derivative of with respect to is where Obviously,

Equation (24) means that increases when is small and decreases when approaches . Hence, there must be a maximum point of for . Next we will prove that the maximum point of is unique in this range; that is, there is a unique where such that . Setting and after some algebraic manipulations, it is derived that , where

If functions and intersect each other only once for , we can conclude that the root of is unique. The derivative of with respect to is

Since and for , and , we can obtain that for . Thus, is a decreasing function of for . The derivative of with respect to is

Case 1. If , we have for . According to (27), we can obtain that . In this case, is an increasing function of for . Thus, and can intersect at most once. Therefore, there is only one intersection between and for . The root of is unique in this case.

Case 2. If , when , we have + and . Thus, is a decreasing function of for . When , we have + and . Thus, is an increasing function of for . In this case, we will prove that and can intersect each other only once for .

Theorem 2. for .

Proof. For , we have and . Thus, .
For , we have and . We first prove that, when , . According to (26), when , we have According to (27) and (28), is given as
For , +. Let +. Substituting into (29), it is derived that
Since for [29], the inequality at (30) is verified. Thus, has been proved. Next we will prove that for . Since for , we have
According to (26), (28), and (31), we obtain . Therefore, for . Theorem 2 is proved.

In Case 2, there are two possible scenarios for the intersection between and .(i) and intersect each other in the region of . Since , it is impossible for them to intersect more than once because decreases at a faster rate than for . For , is always larger than since is an increasing function of while is a decreasing function of . It is impossible for them to intersect each other for . Therefore, in this scenario, there is only one intersection between and , and it occurs in the region of .(ii) and do not intersect each other in the region of . In this scenario, they must intersect in the region of since there must be at least one intersection in the entire range of . For , is a decreasing function of and is an increasing function of . Thus, they can intersect each other at most once. Therefore, in this scenario, there is only one intersection between and , and it occurs in the region of .

From the analysis above, one can conclude that there is a unique where such that . Bisection method can be used to find the root of [28]. The process of bisection method is stated as follows.(1)Choose lower guess and upper guess for the root such that the function changes sign over the interval. This can be checked by ensuring that .(2)An estimate of the root is determined by .(3)Make the following evaluations to determine in which subinterval the root lies.If , the root lies in the lower subinterval. Therefore, set and return to step .If , the root lies in the upper subinterval. Therefore, set and return to step .If , the root equals ; terminate the computation.

Note that the second constraint of the optimization problem is . If , is monotonically increasing in the range of . In this case, choose ; the optimization is achieved. If , is monotonically increasing in the range of and is monotonically decreasing in the range of . In this case, choose ; the optimization is achieved.

For the third constraint of the optimization problem, , no closed-form solution for the optimal is available. However, since is an integer, it is not computationally expensive to search through from to to obtain the optimal that maximizes (20). Therefore, the process to achieve the maximum throughput for the CSS with novel frame structure is listed as follows.(1)For each , calculate the root of by using the Newton-Raphson algorithm.(2)For each , calculate the root of by using the bisection method. If is satisfied, choose ; otherwise, choose .(3)For each , calculate the corresponding individual false alarm probability by (6), the final false alarm probability by (8), and the throughput by (10).(4)Compare and choose the maximum one.

5. Simulation Results

To get insight into the effectiveness of the proposed sensing methods and validate some related theorems, computer simulations have been conducted to evaluate the performance of throughput for various spectrum sensing schemes. In the simulations, we set the bandwidth of PU as  Hz; the frame duration is  ms; the individual reporting duration is  ms; the target detection probability is ; the SNR for the secondary link is  dB; the prior probability of the absence of PU is and . To satisfy the required bandwidth for potential CR user data transmission, we set .

Figure 2 compares the throughput of the CR network when the novel CSS frame structure is employed to the case when the previous frame structure is employed. For the previous frame structure, we can refer to Figure 1 in [25]; for the novel CSS scheme, the number of CR users is ; the SNR of the PU’s signal at the CR user is  dB. It is seen that using the novel CSS frame structure can achieve a much higher throughput than that using the previous frame structure, especially when the final decision threshold is optimized. For the previous frame structure, the maximum achievable throughput is approximately bits/s. However, when our proposed novel CSS frame structure is employed and is optimized, the maximum achievable throughput is approximately bits/s. From this figure, it can be seen that, for a given sensing bandwidth, the optimal sensing settings improve the throughput of the CR network. When  kHz, Majority rule () is suboptimal. However, OR rule () outperforms Majority rule when  kHz. It is also observed that there exists an optimal sensing bandwidth which yields the highest throughput for the secondary network. The optimal sensing bandwidth varies with different values of .

In Figure 3, it is also observed that the throughput of the novel CSS scheme is much higher than that of the previous scheme. For the novel CSS scheme, optimal values are used for each fixed . The optimal sensing settings can achieve a higher throughput than that using fixed sensing bandwidth. In addition, one can clearly see that the disadvantage with a fixed sensing bandwidth is that, at high SNR levels where the PU can be easily detected, the throughput of the CR network is bounded by the percentage of the total PU transmission bandwidth that is assigned to spectrum sensing. For the novel CSS scheme, by comparing the curves of and , we can see that, in low SNR region,  dB, the throughput of the former scheme () is lower than that of the latter scheme (). However, when SNR is larger than  dB, the two curves approach constants and the throughput of the former scheme is larger than that of the latter scheme. This indicates that no fixed is optimal for all SNR values. Thus, there is a need to optimize the value of to enhance the throughput of the CR network.

Figure 4 illustrates the maximum throughput of the CR network versus the average SNR for the novel CSS scheme with various counting rules. Optimal sensing bandwidth is used in each of the counting rules. One can see clearly that the optimal sensing settings can achieve a higher throughput than that using uniform thresholds. It is seen that, when  dB, Majority rule () is suboptimal and AND rule () performs the worst. In particular, at  dB SNR, the optimal sensing settings can achieve almost times throughput than that when AND rule is used. However, when SNR is lower than  dB, AND rule outperforms Majority rule and OR rule (). And it achieves the same throughput as the optimal setting when SNR is extremely weak. Therefore, there is no single decision threshold that is optimal for all cases. To maximize the throughput of the CR network, different SNR levels require different optimal values.

Figure 5 is simulated to show the maximum throughput of the CR network versus number of CR users for various sensing schemes with different values of , in which optimal values are used for each fixed . The SNR of PU’s signal at the CR user is  dB. It has been shown that the throughput with optimal sensing settings is larger than that using fixed sensing bandwidth and grows as the number of CR users increases. For the sensing scheme with fixed sensing bandwidth, the throughput of the CR network approaches constants when the number of CR users is extremely large and is bounded by the percentage of the total PU transmission bandwidth that is assigned to spectrum sensing. By comparing the curves of the sensing schemes with different values of , we can also find that no fixed is optimal for all cases. To enhance the throughput of the CR network, the value of needs to be optimized.

In Figure 6, the maximum throughput of the CR network is presented versus the number of CR users for the novel CSS scheme with various counting rules. Optimal sensing bandwidth is used in each of the counting rules. The SNR of PU’s signal at the CR user is  dB. It is observed that the optimal sensing settings can achieve a higher throughput than that using uniform thresholds. Majority rule () is suboptimal and AND rule () always performs the worst. It is also seen that the throughput of the CR network increases as the number of CR users increases. However, the complexity of our proposed algorithm grows approximately linearly with the number of cooperating CR users.

6. Conclusions

In this paper, we propose a novel frame structure for cooperative spectrum sensing. It has been proved that there exists an optimal sensing bandwidth which yields the highest throughput for the CR network. The optimal sensing settings to maximize the throughput of the CR network under the conditions of sufficient protection to PUs and required bandwidth for potential CR user data transmission have been proposed. The proposed optimal sensing settings are analyzed and calculated in detail by using some simple but reliable methods. Computer simulations have shown that significant improvement in the throughput of the CR network has been achieved when the sensing bandwidth and the final decision threshold are jointly optimized.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

This work is supported by the National Fundament Research of China (973 no. 2009CB3020400) and the Jiangsu Province Natural Science Foundation under Grant BK2011002.

References

  1. P. P. Chen and Q. Y. Zhang, “Joint temporal and spatial sensing based cooperative cognitive networks,” IEEE Communications Letters, vol. 15, no. 5, pp. 530–532, 2011. View at: Publisher Site | Google Scholar
  2. Y.-J. Choi, Y. Xin, and S. Rangarajan, “Overhead-throughput tradeoff in cooperative cognitive radio networks,” in Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC '09), pp. 1–6, April 2009. View at: Publisher Site | Google Scholar
  3. D. Cabric, S. M. Mishra, and R. W. Brodersen, “Implementation issues in spectrum sensing for cognitive radios,” in Conference Record of the 38th Asilomar Conference on Signals, Systems and Computers, pp. 772–776, November 2004. View at: Google Scholar
  4. Z. Quan, S. Cui, and A. H. Sayed, “Optimal linear cooperation for spectrum sensing in cognitive radio networks,” IEEE Journal on Selected Topics in Signal Processing, vol. 2, no. 1, pp. 28–40, 2008. View at: Publisher Site | Google Scholar
  5. Z. Quan, S. Cui, A. H. Sayed, and H. V. Poor, “Optimal multiband joint detection for spectrum sensing in cognitive radio networks,” IEEE Transactions on Signal Processing, vol. 57, no. 3, pp. 1128–1140, 2009. View at: Publisher Site | Google Scholar | MathSciNet
  6. G. Ganesan, Y. Li, B. Bing, and S. Li, “Spatiotemporal sensing in cognitive radio networks,” IEEE Journal on Selected Areas in Communications, vol. 26, no. 1, pp. 5–12, 2008. View at: Publisher Site | Google Scholar
  7. J. Jafarian and K. H. Hamdi, “Throughput optimization in a cooperative double-threshold sensing scheme,” in Proceedings of the IEEE Wireless Communications and Networking Conference, pp. 1034–1038, 2012. View at: Google Scholar
  8. J. Jafarian and K. H. Hamdi, “Non-cooperative double-threshold sensing scheme: a sensing-throughput tradeoff,” in Proceedings of the IEEE Wireless Communications and Networking Conference, pp. 3405–3410, 2013. View at: Google Scholar
  9. G. Ganesan and Y. Li, “Cooperative spectrum sensing in cognitive radio, part I: two user networks,” IEEE Transactions on Wireless Communications, vol. 6, no. 6, pp. 2204–2212, 2007. View at: Publisher Site | Google Scholar
  10. G. Ganesan and Y. Li, “Cooperative spectrum sensing in cognitive radio, part II: multiuser networks,” IEEE Transactions on Wireless Communications, vol. 6, no. 6, pp. 2214–2222, 2007. View at: Publisher Site | Google Scholar
  11. Q. Wu, G. Ding, J. Wang, and Y.-D. Yao, “Spatialtemporal opportunity detection for spectrum-heterogeneous cognitive radio networks: two-dimensional sensing,” IEEE Transactions on Wireless Communications, vol. 12, pp. 516–526, 2013. View at: Google Scholar
  12. G. Ding, J. Wang, Q. Wu, F. Song, and Y. Chen, “Spectrum sensing in opportunity-heterogeneous cognitive sensor networks: how to cooperate?” IEEE Sensors Journal, vol. 13, pp. 4247–4255, 2013. View at: Google Scholar
  13. M. Perc, J. Gómez-Gardeñes, A. Szolnoki, L. M. Floría, and Y. Moreno, “Evolutionary dynamics of group interactions on structured populations: a review,” Journal of the Royal Society Interface, vol. 10, no. 80, Article ID 20120997, 2013. View at: Publisher Site | Google Scholar
  14. M. Perc and P. Grigolini, “Collective behavior and evolutionary games—an introduction,” Chaos, Solitons & Fractals, vol. 56, pp. 1–5, 2013. View at: Publisher Site | Google Scholar | MathSciNet
  15. A. Szolnoki, M. Perc, and G. Szabó, “Accuracy in strategy imitations promotes the evolution of fairness in the spatial ultimatum game,” Europhysics Letters, vol. 100, no. 2, Article ID 28005, 2012. View at: Publisher Site | Google Scholar
  16. A. Szolnoki, M. Perc, and G. Szabó, “Defense mechanisms of empathetic players in the spatial ultimatum game,” Physical Review Letters, vol. 109, Article ID 078701, 2012. View at: Google Scholar
  17. M. Perc and A. Szolnoki, “Coevolutionary games-A mini review,” BioSystems, vol. 99, no. 2, pp. 109–125, 2010. View at: Publisher Site | Google Scholar
  18. Y. Xu, J. Wang, Q. Wu, A. Anpalagan, and Y.-D. Yao, “Opportunistic spectrum access in cognitive radio networks: global optimization using local interaction games,” IEEE Journal on Selected Topics in Signal Processing, vol. 6, no. 2, pp. 180–194, 2012. View at: Publisher Site | Google Scholar
  19. W. Zhong, Y. Xu, and H. Tianfield, “Game-theoretic opportunistic spectrum sharing strategy selection for cognitive MIMO multiple access channels,” IEEE Transactions on Signal Processing, vol. 59, no. 6, pp. 2745–2759, 2011. View at: Publisher Site | Google Scholar | MathSciNet
  20. B. Wang, K. J. Ray Liu, and T. Charles Clancy, “Evolutionary cooperative spectrum sensing game: how to collaborate?” IEEE Transactions on Communications, vol. 58, pp. 890–900, 2010. View at: Google Scholar
  21. H. Vu-Van and I. Koo, “Cooperative spectrum sensing with collaborative users using individual sensing credibility for cognitive radio network,” IEEE Transactions on Consumer Electronics, vol. 57, no. 2, pp. 320–326, 2011. View at: Publisher Site | Google Scholar
  22. S. Stotas and A. Nallanathan, “On the throughput and spectrum sensing enhancement of opportunistic spectrum access cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 11, no. 1, pp. 97–107, 2012. View at: Publisher Site | Google Scholar
  23. H. Hu, H. Zhang, and H. Yu, “Delay QoS guaranteed cooperative spectrum sensing in cognitive radio networks,” International Journal of Electronics and Communications, vol. 67, pp. 804–807, 2013. View at: Google Scholar
  24. H. Yu, W. Tang, and S. Li, “Optimization of cooperative spectrum sensing with sensing user selection in cognitive radio networks,” EURASIP Journal on Wireless Communications and Networking, vol. 208, article 208, 2011. View at: Google Scholar
  25. W. Zhang, R. K. Mallik, and K. Ben Letaief, “Optimization of cooperative spectrum sensing with energy detection in cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 8, no. 12, pp. 5761–5766, 2009. View at: Publisher Site | Google Scholar
  26. W. Yin, P. Ren, Q. Du, and Y. Wang, “Delay and throughput oriented continuous spectrum sensing schemes in cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 11, no. 6, pp. 2148–2159, 2012. View at: Publisher Site | Google Scholar
  27. W. Han, J. Li, Z. Tian, and Y. Zhang, “Efficient cooperative spectrum sensing with minimum overhead in cognitive radio,” IEEE Transactions on Wireless Communications, vol. 9, no. 10, pp. 3006–3011, 2010. View at: Publisher Site | Google Scholar
  28. C. Steven Chapra and P. Raymond Canale, Numerical Methods for Engineers, McGraw-Hill, 6th edition, 2010.
  29. N. Kingsbury, “Approximation Formulae for the Gaussian Error Integral, Q(x),” June 2005, Connexions, http://cnx.org/content/m11067/2.4/. View at: Google Scholar

Copyright © 2013 Hang Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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