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Journal of Communications Vol. 10, No. 6, June 2015
Opportunistic Spectrum Access in Imperfect Spectrum Sensing Cognitive Networks Yonghong Chen1, Huijian Wang2, and Shibing Zhang2 1
Xinglin College, Nantong University, China School of Electronics and Information, Nantong University, China Email: {chenyh1107, zhangshb}@ntu.edu.cn; [email protected] 2
users should access the cognitive networks with the opportunistic model [4]. The spectrum opportunity discovery and efficient channel access have been studied a lot. Zhang and Zhu used the Markov process to model the sensing activities of the secondary user (SU) and proposed an opportunistic spectrum access (OSA) algorithm which combines the physical and MAC layers [5]. Based on space division multiplexing, an OSA algorithm which makes full use of the ability of spatial signal processing was proposed [6]. The optimization of the sensing time and power allocation of SUs can also been used to improve the spectrum sensing capability and the throughput of cognitive networks [7], [8]. In fact, the spectrum sensing and spectrum access are dependent of each other instead of isolated. In order to improve spectrum efficiency, it is necessary for cognitive networks to continuously update the spectrum information in the data. Sufficient information of the spectrum access is useful to SUs to improve the efficiency and accuracy of spectrum sensing, and increase the opportunity to access the cognitive networks. El-Sherif and Liu combined the spectrum sensing with the channel access to design the multiple access protocol [9], and Liu and at el proposed a dynamic spectrum access technology by means of the prediction of the channel states based on the hidden Markov model [10]. However, the spectrum sensing may be imperfect due to the dynamic change of the multipath channels and the fading shadow of channels. In this paper, we address the opportunistic spectrum access strategies under the imperfect sensing. By setting the optimal operating point of spectrum detection and updating the confidence vector, we turn the optimizations under the imperfect spectrum sensing and fading channels into ones in the perfect spectrum sensing based on the partially observable Markov decision process (POMDP). The rest of this paper is organized as follows. Section II describes the system model. Section III presents the optimal spectrum access strategy under imperfect sensing. Some simulation results are discussed in section IV. Conclusions are stated in section V.
Abstract—Spectrum sensing strategy is key to realize cognitive radio. However, spectrum sensing error would affect the access strategy of secondary users in cognitive networks. This paper addresses the spectrum sensing strategy under imperfect spectrum sensing, and proposes opportunistic spectrum access strategies for the imperfect spectrum sensing and fading channels respectively. By setting the optimal operating point of the spectrum detection and updating the confidence vector, we turn the spectrum access optimizations under the imperfect spectrum sensing and fading channels into ones under the perfect spectrum sensing based on the partially observable Markov decision process model. Simulation results show that the strategies proposed could make the secondary users achieve about 10% margin in throughput and the cognitive networks have higher spectrum utilization. Index Terms—Opportunistic spectrum access, throughput, POMDP, sensing error, fading channel
I.
INTRODUCTION
With the increase of wireless communication business, the contradiction between the limited spectrum resources and the growing demands for spectrum resources has become a major challenge in the wireless communications [1]. Due to the intelligently sensing spectrum environment and effectively utilizing spectrum resources, cognitive radio has been widely recognized as one of the effective means to improve the idle spectrum spaces [2]. In cognitive networks, cognitive users should first sense the surrounding spectrum. When the cognitive users find there is any idle channel (spectrum hole), they would adjust their own transceiver frequencies and other parameters to access the idle channel to transmit their data [3]. At the same time, the cognitive users must constantly monitor channel states. If it is found that any authorized user begins to use the channel, cognitive users should immediately withdraw from the band to ensure that the authorized user (primary user) is not interfered by cognitive users (second users). That is to say, cognitive Manuscript received March 12, 2015; revised June 24, 2015. This work was supported by the China National Natural Science Foundation under Grant No. 61371112, the application research project of Ministry of Transport under Grant No. 2014319813220, the application research project of Nantong under Grant No. BK2013052 and the Science Foundation of Nantong University Xinglin College under Grant No. 2012K115. Corresponding author email: [email protected]. doi:10.12720/jcm.10.6.410-414 ©2015 Journal of Communications
II. SYSTEM MODEL Consider a cognitive network with N independent channels, each has the bandwidth of Bn (n = 0, 1, …, N).
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The primary user (PU) carries out data transmission synchronously [11]. In each slot, the state of every channel is denoted by “0” (busy) or “1” (idle). The busy state indicates that the channel is occupied by the PU in the current slot, and the idle state indicates the channel may be used by SUs. The channel states of the network with N channels can be modeled as a discrete-time Markov process with 2N states.
indicates that transmission is successful. On the contrary, it is believed that the SU collides with the PU and has to give up transmitting. III. OPPORTUNISTIC SPECTRUM ACCESS STRATEGY A. Access Strategy under Imperfect Sensing In the cognitive networks, many factors will affect spectrum sensing, such as noise, multipath and shadow fading of channels. Therefore, the spectrum sensing may be imperfect. In the case of imperfect sensing, spectrum sensing error would occur and the collision between SU and PU would happen. On one hand, as the probability of false alarm (Pfa) increases, the probability of accessing channel by SU would decrease, which will reduce the throughput of cognitive networks. On the other hand, as the probability of miss detection (Pm) goes up, the conflict probability of the SU with PU would rise, which will deteriorate the quality of service (QoS) of cognitive networks. Therefore, the optimization of spectrum access strategy is to choose an optimal operating point for detector to make a trade-off between the probabilities of false alarm and detection, i.e., the optimal spectrum access strategy is to maximize the throughput of the cognitive networks in the premise of that the conflict probability is smaller than one allowed. The channel capacity (profit function) achieved when a SU accesses channel n is defined as
Fig. 1. Markov channel state model
Without loss of generality, it is assumed that each channel state transition is independent of each other. The channel state transition can be modeled as a discrete-time Markov process, as shown in Fig. 1. Where P01 and P10 are the channel state transition probabilities in which the channel from “0” to “1” and from “1” to “0” in one step, respectively. For convenience, we assume that the statistical characteristics of the spectrum used by PU remain unchanged in T slots. Due to the energy consumption limitations and hardware limitations, the SU cannot sense all of the N channels in each slot. It chooses only N1 channels to sense. After sensing, the SU chooses N2 channels to access according to the spectrum sensing results. It is obvious that N2 ≤N1 ≤N. Since the transition of each channel state is modeled as a discrete-time Markov process and only limited channels in the system can be observed by the SU in each slot, the spectrum sensing and access can be modeled as a POMDP. spectrum sensing
data transmision
2 Pn H n bn Bn log 2 1 K e Bn 2
(1)
where Pn is the transmitted power of the SU over the channel n, Hn is the channel gain of channel n to the SU, 2 is the additive white Gaussian noise power per unit bandwidth, and Ke is the bit error rate required by the SU (generally, it is a constant). Then the throughput achieved can be expressed as 2 P Hn Cn (t ) sn t bn =sn t Bn log 2 1 K e n Bn 2
acknowledge information
(2)
where sn(t) is the state of channel n in slot t, sn (t ) {0,1} . Let confidence vector Λ(t ) [1 (t ), 2 (t ), , M (t )] denote the set of all available channel states in slot t, 1≤t≤T, M =2N. The optimal spectrum access strategy can be presented as an optimization following
slot t0 Fig. 2. Slot structure of secondary user
When a SU wants to transmit data, it senses the spectrum at the beginning of each slot. Then, it decides whether to access the spectrum according to the result of sensing, as shown in Fig. 2. The SU will make full use of the sensing information and used information of channels to maximize its own throughput. In order to avoid the collision between the SU and PU due to the miss detection, the SU needs to design an acknowledgement (ACK) signal. When the SU transmits data, if the transmitter receives an ACK signal from the receiver, it
©2015 Journal of Communications
T
arg max E Cn t | Λ 1 Pm
s.t.
t 1 Pc
(3)
where Pm is the probability of miss detection, Pc is the probability of collision between the SU and PU, ζ is the upper limit of the conflict probability permitted, Λ(1) is the initial confidence vector in T slots. In order to find the optimal solution of the optimization with lower computational complexity, we need to
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decompose the objective function and constraint condition. It has been shown that Pm*=ζ is the optimal operating point of spectral detector [12]. When channel n is busy (Θn =0), the SU does not access channel n (Φn =0); when channel n is idle (Θn =1), the SU accesses channel n (Φn =1), i.e.
1, n 1 n 0, n 0
bn (1 Pfa )}, where, a* (t ) 1,..., N
sufficient statistic of optimal sensing and access [12], where pn(t) is the available probability of channel n at the beginning of slot t. Then, Ω(t) can be taken as the confidence vector of the cognitive network. From Fig. 1, we know that the available channel capacity of channel n is given by
In the slot t, the transmitter of the cognitive network obtains the observable information {a , Ka } and decision-making information {a , a } , where a* is the short from a*(t), Ka {0,1} represents whether the ACK signal is received by the transmitter of the cognitive network at the end of slot t. "0" indicates that the transmitter has not received the ACK signal while "1" shows that the transmitter has received the ACK signal. Since the receiver of the cognitive network only has the information of a* and Ka*, and does not know the sensing results a of the transmitter, it cannot confirm the unsuccessful to transmit data when it does not receive the data transmitted by the transmitter. In order to ensure the receiver and transmitter in the cognitive network can switch to the same channel to communicate in next slot t+1, both of them should have the same confidence vector Ω(t+1). Therefore, the confidence vector will update based on the a* and Ka* and is given by
(5)
t 1 p1 t 1 , p2 t 1 ,..., pN t 1
(8)
where pn(t+1) is given by
(6)
1 Pfa pa 1 p10 1 pa p01 pn (t 1) Pfa pa 1 p10 1 pa p01 pa p10 1 pa 1 p01 pn t 1 p10 1 pn t p01 where, the first one presents the case where the transmitter of the SU has accessed the optimal channel a* to transmit the data and received the ACK signal. At this time, the channel is not occupied by the PU, and the SU has transmitted data successfully. The second one shows the case where the transmitter of the SU has accessed the optimal channel to transmit the data but not received the ACK signal from the receiver. There are two possible scenarios. One is that the transmitter of the cognitive user selects not to access the channel a* ( a* 0 ); another is
a t n, K a t 1 a t n, K a t 0
(9)
a t n
B. Access Strategy under Fading Channel In cognitive network, the channel fading is different for different SUs. This requires SUs to adjust themselves transmitted powers to overcome the channel fading [13]. In order to save the energy of SUs, SUs don't need sense channels in the whole slot. At the beginning of each slot, each of SUs should choose the operating mode, sensing or sleep, according to the statistic information of the channel states occupied by the PU and the residual energy of the SU. If the SU selects sensing mode, it will select a best suitable channel to sense from all of the N channels according to the optimal spectrum access strategy chosen. If the SU selects sleep mode, it will do nothing until to the next slot.
that the data transmission is not successful. The third indicates the updating of non-optimal confidence vector, which is updated according to the Markov process, one step transition probability.
©2015 Journal of Communications
(7)
transmitter does not access the channel a* ( a* 0 ) or is
When SUs find that the channel n is idle, one of the SUs will accesses the channel n. Then, at the beginning of slot t, the throughput achieved by accessing channel n can be expressed as
Cn (t ) ( pn (t )(1 p10 ) (1 pn (t )) p01 )bn (1 Pfa )
a* (t ) arg max { pn (t )(1 p10 ) (1 pn (t )) p01 n 1,..., N
(4)
where Θn is the sensing result of channel n. The probability of miss detection Pm is set as ζ. So, the maximum conflict probability allowed by PU is ζ, which meet the requirements of collision restrictions when the SU selects the optimal channel to access. Therefore, the optimization above can be transformed into the problem of POMDP based on the imperfect spectrum sensing, which objective is to find the optimal channel selection strategy to achieve the maximum throughput when Pm = ζ. Related study has shown that when all channels are independent of each other, Ω(t ) p1 (t ),..., pN (t ) is the
Cn (t ) ( pn (t )(1 p10 ) (1 pn (t )) p01 )bn
where Pfa is the probability of false alarm of the channel n in slot t. When we use the greedy algorithm to achieve the optimization, the optimal spectrum access strategy can be simplified as to find a optimal channel a*(t) to access to maximize the throughput as follows
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Suppose the SU divides its transmission energy into J energy levels according to the degrees of channel fading. The maximum throughput achieved by selecting channel n to access is given by Vn t arg max Cn t
access strategy [13]. In order to simplify the simulation, we suppose that there are only one PU and three SU, the channel bandwidth is 1 unit. The data is transmitted with binary over and 30 slots (T = 30). We simulate each one for 10000 times. The channel state transition probabilities shown in the simulation figures are the means of the uniform distribution functions with variance 0.001 respectively.
(10)
n0,1,..., N
where Cn(Ω(t)) is the throughput achieved by a SU accessing channel n, n=0 denotes the SU selects sleep mode, n=1,...,N denotes the SU selects channel n to access. When the SU selects sleep mode, it does not generate any revenues. Therefore, the throughput achieved at the slot t is the same as last slot as follows
0.7
Throughput of SUs(bit/s)
C0 t Vn t 1
0.8
(11)
When the SU selects sensing mode, it will sense and access channel n. Right now, the throughput achieved will be changed as follows
0.6 0.5 0.4
0.2 0.1 0
J
Cn t pn t 1 P10 1 pn t P01 bn n j
where n(j) , j = 1, ..., J, denote the probability of the jth energy level with which the SU selects channel n to transmit the data. If Cn(Ω(t))>C0(Ω(t)), the SU will select the sensing mode; otherwise it will select sleep mode. Therefore, the optimal mode selection strategy for channel n can be expressed as follows (13)
In the sleep mode, the confidence vector is updated according to the Markov chain as follows
pn t 1 pn t 1 P10 1 pn t P01
(14)
While in the sensing mode, the confidence vector is updated as follows
0.3
0.4
0.5
0.6
0.7
(15)
a (t ) n, a*(t ) 0 a (t ) n IV. SIMULATION RESULTS
0.6 0.5 0.4
Case Case Case Case Case Case
0.3 0.2
In this section, we provide some simulation results of the optimal spectrum access strategy (OSAS) under imperfect sensing and fading channels proposed in this paper, and compare it with the conventional spectrum ©2015 Journal of Communications
0.2
0.8
Throughput of SUs(bit/s)
1 P10 , pn t 1 P01 , p t 1 P 1 p t P , 10 n 01 n a (t ) n, a*(t ) 1
0.1
OSAS Conventional OSAS Conventional OSAS Conventional
Fig. 3 depicts the effect of imperfect spectrum sensing on the normalized throughput when there are 3 channels. We compare the throughputs in three different cases. The first one is the case where the difference between the transition probability of different channel states and the transition probability of same channel states is 0.8 (p01=0.1, p10=0.1); the second is the case where the difference is 0.6 (p01=0.2, p10=0.2); the final one is the case where the difference is 0.2 (p01=0.6, p10=0.6). As the probability of collision allowed between the PU and SUs, ζ, increases, the throughput obtained is improved. Due to the limitation of capacity themselves, the throughput obtained cannot continue to rise with the increase of ζ. When ζ is larger than 0.3, the throughput will be basically stable. On the other hand, it is clearly seen from Fig. 3 that the difference between the transition probability of different channel states and the transition probability of same channel states is also the main factor to affects the throughput besides the probability of collision. The more the difference is, the larger the throughput is. However, the throughputs achieved by the optimal spectrum access strategy we proposed are always larger than conventional ones.
(12)
Vn t 1
J b n k Vn t 1 sensing mode n j 1 sleep mode otherwise
0
1: 1: 2: 2: 3: 3:
Fig. 3. Throughput under different scenarios
j 1
1 pn t 1 P10 1 pn t P01
Case Case Case Case Case Case
0.3
0.1
0
5
10
15 Slot
Fig. 4. Throughput under fading channel
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1: 1: 2: 2: 3: 3:
OSAS Conventional OSAS Conventional OSAS Conventional
20
25
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[8]
Fig. 4 shows the throughput in the Rayleigh fading channel when the channel number N = 3. We compare the throughputs in three different cases respectively. The first one is the case when p01=0.05, p10=0.05; the second is the case when p01=0.1, p10=0.1; the final one is the case when p01=0.2, p10=0.2. It shows that both would achieve the stable throughputs. It means that the fading of the channels only affect the throughput at the beginning of the communication. However, OSAS will reach the stable throughput in 10 slots, but the conventional one will need 15 slots to reach the stable throughput. That is to say, OSAS has faster convergence than conventional one. Similar to the Fig. 3, the more the difference between the transition probability of different states and the transition probability of same state in the same channel is, the greater the throughput achieved. The difference of transition probabilities is still the main factor to affect the throughput.
[9]
[10]
[11]
[12]
[13]
V. CONCLUSIONS This paper proposes opportunistic spectrum access strategies which consider the sensing error and channel fading. By setting the optimal operating point of the spectrum detection and updating the confidence vectors, we turned the imperfect spectrum sensing into one under the perfect spectrum sensing based on the POMDP model. Simulation results show that the difference of transition probabilities is an important factor which affects the throughput. The more the difference is, the greater the throughput achieved is. In the fading channel, the SU will quickly achieve the stable throughput. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
Y. Song and J. Xie, “A proactive spectrum handoff framework for cognitive radio Ad hoc networks without common control channel,” IEEE Transactions on Mobile Computing, vol. 11, no. 7, pp. 1127-1139, 2012. M. Hasegawa, H. Hirai, K. Nagano, H. Harada, and K. Aihara, “Optimization for centralized and decentralized cognitive radio networks,” Proc. IEEE, vol. 102, no. 4, pp. 574-584, 2014. J. Noh and S. Oh, “Cognitive radio channel with cooperative multi-antenna secondary systems,” IEEE Journal on Selected Areas in Communications, vol. 32, no. 3, pp. 539-549, 2014. A. Bourdena, E. Pallis, G. Kormentzas, and G. Mastorakis, “Efficient radio resource management algorithms in opportunistic cognitive radio networks,” Transactions on Emerging Telecommunications Technologies, vol. 25, no. 8, pp. 785-797, 2014. J. Zhang and H. B. Zhu, “Opportunistic spectrum access algorithm based on cross-layer optimization,” Journal on Communications, vol. 31, no. 11, pp. 188-194, 2010. Z. Li, L. J. Zhao, and Q. Liu, “Space division multiplexing based on opportunistic spectrum access in cognitive radio network,” Journal of Electronics & Information Technology, vol. 33, no. 5, pp. 1172-1177, 2011. S. Stotas and A. Nallanathan, “Optimal sensing time and power allocation in multiband cognitive radio networks,” IEEE Transactions on Communications, vol. 59, no. 1, pp. 226-235, 2011.
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S. Stotas and A. Nallanathan, “On the throughput and spectrum sensing enhancement of opportunistic spectrum access cognitive radio networks,” IEEE Transactions on Communications, vol. 11, no. 1, pp. 97-107, 2012. A. A. El-Sherif and K. J. Liu, “Joint design of spectrum sensing and channel access in cognitive radio networks,” IEEE Trans. Wireless Communications, vol. 10, no. 6, pp. 1743-1753, 2011. Y. N. Liu, J. G. Yang, H. L. Yang, and H. Hai, “Hidden markov model-based joint probability channel prediction dynamic spectrum access in cognitive radio,” Journal of Shanghai University(Natural Science), vol. 17, no. 5, pp. 581-585, 2011. D. V. Djonin, Q. Zhao, and V. Krishnamuurthy, “Optimality and complexity of opportunistic spectrum access: A truncated Markov decision process formulation,” in Proc. IEEE International Conference on Communications, Glasgow, June 24-28, 2007, pp. 5787-5792. Park Sungsoo and H. Daesik, “Optimal spectrum access for energy harvesting cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 12, pp. 6166–6179, 2013. Q. Zhao, Y. X. Chen, and A. Swami, “Distributed spectrum sensing and access in cognitive radio networks with energy constraint,” IEEE Transactions on Signal Processing, vol. 57, no. 2, pp. 783-797, 2009.
Yonghong Chen was born in Jiangsu Province, China, in 1981. She received the B.S. degree in electronic information science and technology from Zhengzhou University of Light Industry, in 2004 and the M.S. degree in signal and information processing from Nanjing University of Posts and Telecommunications in 2007. She is currently a lecturer of Nantong University. Her research interests include communication signal processing and cognitive wireless networks. Huijian Wang was born in Taizhou, China in 1987. He received his B. S. degree in communications engineering from Nantong University China in 2011. He is currently a graduate student of Nantong University. He is engaged in the research activities in the areas of communication signal processing and cognitive wireless networks.
Shibing Zhang was born in Haimen, China in 1962. He received his B.S. degree in wireless communications from Dalian Maritime University, China in 1983, M.S. degree and Ph.D. degree in wireless communications from Nanjing University of Posts and Telecommunications, China in 1989, 2007 respectively. He worked as an associate engineer in the Nantong Changjiang Communication and Navigation Management Section from Sept. 1983 to Aug. 1986, engineer in the Yancheng Electronic Equipment Manufactory from Feb. 1989 to Apr. 1997 and senior engineer in the Haimen Economical Information Centre from May. 1997 to Mar. 2001 respectively. Since Apr. 2001, he has been working in Nantong University as a professor. His current research interests include wireless communications and networking, OFDM system, especially on ultrawideband communications, cognitive radio. From Jul. 2009 to Mar. 2010, Dr. Zhang was a visiting scholar with the Department of Electrical and Computer Engineering, University of Victoria.
414
Opportunistic Spectrum Access in Imperfect Spectrum Sensing Cognitive Networks Yonghong Chen1, Huijian Wang2, and Shibing Zhang2 1
Xinglin College, Nantong University, China School of Electronics and Information, Nantong University, China Email: {chenyh1107, zhangshb}@ntu.edu.cn; [email protected] 2
users should access the cognitive networks with the opportunistic model [4]. The spectrum opportunity discovery and efficient channel access have been studied a lot. Zhang and Zhu used the Markov process to model the sensing activities of the secondary user (SU) and proposed an opportunistic spectrum access (OSA) algorithm which combines the physical and MAC layers [5]. Based on space division multiplexing, an OSA algorithm which makes full use of the ability of spatial signal processing was proposed [6]. The optimization of the sensing time and power allocation of SUs can also been used to improve the spectrum sensing capability and the throughput of cognitive networks [7], [8]. In fact, the spectrum sensing and spectrum access are dependent of each other instead of isolated. In order to improve spectrum efficiency, it is necessary for cognitive networks to continuously update the spectrum information in the data. Sufficient information of the spectrum access is useful to SUs to improve the efficiency and accuracy of spectrum sensing, and increase the opportunity to access the cognitive networks. El-Sherif and Liu combined the spectrum sensing with the channel access to design the multiple access protocol [9], and Liu and at el proposed a dynamic spectrum access technology by means of the prediction of the channel states based on the hidden Markov model [10]. However, the spectrum sensing may be imperfect due to the dynamic change of the multipath channels and the fading shadow of channels. In this paper, we address the opportunistic spectrum access strategies under the imperfect sensing. By setting the optimal operating point of spectrum detection and updating the confidence vector, we turn the optimizations under the imperfect spectrum sensing and fading channels into ones in the perfect spectrum sensing based on the partially observable Markov decision process (POMDP). The rest of this paper is organized as follows. Section II describes the system model. Section III presents the optimal spectrum access strategy under imperfect sensing. Some simulation results are discussed in section IV. Conclusions are stated in section V.
Abstract—Spectrum sensing strategy is key to realize cognitive radio. However, spectrum sensing error would affect the access strategy of secondary users in cognitive networks. This paper addresses the spectrum sensing strategy under imperfect spectrum sensing, and proposes opportunistic spectrum access strategies for the imperfect spectrum sensing and fading channels respectively. By setting the optimal operating point of the spectrum detection and updating the confidence vector, we turn the spectrum access optimizations under the imperfect spectrum sensing and fading channels into ones under the perfect spectrum sensing based on the partially observable Markov decision process model. Simulation results show that the strategies proposed could make the secondary users achieve about 10% margin in throughput and the cognitive networks have higher spectrum utilization. Index Terms—Opportunistic spectrum access, throughput, POMDP, sensing error, fading channel
I.
INTRODUCTION
With the increase of wireless communication business, the contradiction between the limited spectrum resources and the growing demands for spectrum resources has become a major challenge in the wireless communications [1]. Due to the intelligently sensing spectrum environment and effectively utilizing spectrum resources, cognitive radio has been widely recognized as one of the effective means to improve the idle spectrum spaces [2]. In cognitive networks, cognitive users should first sense the surrounding spectrum. When the cognitive users find there is any idle channel (spectrum hole), they would adjust their own transceiver frequencies and other parameters to access the idle channel to transmit their data [3]. At the same time, the cognitive users must constantly monitor channel states. If it is found that any authorized user begins to use the channel, cognitive users should immediately withdraw from the band to ensure that the authorized user (primary user) is not interfered by cognitive users (second users). That is to say, cognitive Manuscript received March 12, 2015; revised June 24, 2015. This work was supported by the China National Natural Science Foundation under Grant No. 61371112, the application research project of Ministry of Transport under Grant No. 2014319813220, the application research project of Nantong under Grant No. BK2013052 and the Science Foundation of Nantong University Xinglin College under Grant No. 2012K115. Corresponding author email: [email protected]. doi:10.12720/jcm.10.6.410-414 ©2015 Journal of Communications
II. SYSTEM MODEL Consider a cognitive network with N independent channels, each has the bandwidth of Bn (n = 0, 1, …, N).
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Journal of Communications Vol. 10, No. 6, June 2015
The primary user (PU) carries out data transmission synchronously [11]. In each slot, the state of every channel is denoted by “0” (busy) or “1” (idle). The busy state indicates that the channel is occupied by the PU in the current slot, and the idle state indicates the channel may be used by SUs. The channel states of the network with N channels can be modeled as a discrete-time Markov process with 2N states.
indicates that transmission is successful. On the contrary, it is believed that the SU collides with the PU and has to give up transmitting. III. OPPORTUNISTIC SPECTRUM ACCESS STRATEGY A. Access Strategy under Imperfect Sensing In the cognitive networks, many factors will affect spectrum sensing, such as noise, multipath and shadow fading of channels. Therefore, the spectrum sensing may be imperfect. In the case of imperfect sensing, spectrum sensing error would occur and the collision between SU and PU would happen. On one hand, as the probability of false alarm (Pfa) increases, the probability of accessing channel by SU would decrease, which will reduce the throughput of cognitive networks. On the other hand, as the probability of miss detection (Pm) goes up, the conflict probability of the SU with PU would rise, which will deteriorate the quality of service (QoS) of cognitive networks. Therefore, the optimization of spectrum access strategy is to choose an optimal operating point for detector to make a trade-off between the probabilities of false alarm and detection, i.e., the optimal spectrum access strategy is to maximize the throughput of the cognitive networks in the premise of that the conflict probability is smaller than one allowed. The channel capacity (profit function) achieved when a SU accesses channel n is defined as
Fig. 1. Markov channel state model
Without loss of generality, it is assumed that each channel state transition is independent of each other. The channel state transition can be modeled as a discrete-time Markov process, as shown in Fig. 1. Where P01 and P10 are the channel state transition probabilities in which the channel from “0” to “1” and from “1” to “0” in one step, respectively. For convenience, we assume that the statistical characteristics of the spectrum used by PU remain unchanged in T slots. Due to the energy consumption limitations and hardware limitations, the SU cannot sense all of the N channels in each slot. It chooses only N1 channels to sense. After sensing, the SU chooses N2 channels to access according to the spectrum sensing results. It is obvious that N2 ≤N1 ≤N. Since the transition of each channel state is modeled as a discrete-time Markov process and only limited channels in the system can be observed by the SU in each slot, the spectrum sensing and access can be modeled as a POMDP. spectrum sensing
data transmision
2 Pn H n bn Bn log 2 1 K e Bn 2
(1)
where Pn is the transmitted power of the SU over the channel n, Hn is the channel gain of channel n to the SU, 2 is the additive white Gaussian noise power per unit bandwidth, and Ke is the bit error rate required by the SU (generally, it is a constant). Then the throughput achieved can be expressed as 2 P Hn Cn (t ) sn t bn =sn t Bn log 2 1 K e n Bn 2
acknowledge information
(2)
where sn(t) is the state of channel n in slot t, sn (t ) {0,1} . Let confidence vector Λ(t ) [1 (t ), 2 (t ), , M (t )] denote the set of all available channel states in slot t, 1≤t≤T, M =2N. The optimal spectrum access strategy can be presented as an optimization following
slot t0 Fig. 2. Slot structure of secondary user
When a SU wants to transmit data, it senses the spectrum at the beginning of each slot. Then, it decides whether to access the spectrum according to the result of sensing, as shown in Fig. 2. The SU will make full use of the sensing information and used information of channels to maximize its own throughput. In order to avoid the collision between the SU and PU due to the miss detection, the SU needs to design an acknowledgement (ACK) signal. When the SU transmits data, if the transmitter receives an ACK signal from the receiver, it
©2015 Journal of Communications
T
arg max E Cn t | Λ 1 Pm
s.t.
t 1 Pc
(3)
where Pm is the probability of miss detection, Pc is the probability of collision between the SU and PU, ζ is the upper limit of the conflict probability permitted, Λ(1) is the initial confidence vector in T slots. In order to find the optimal solution of the optimization with lower computational complexity, we need to
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decompose the objective function and constraint condition. It has been shown that Pm*=ζ is the optimal operating point of spectral detector [12]. When channel n is busy (Θn =0), the SU does not access channel n (Φn =0); when channel n is idle (Θn =1), the SU accesses channel n (Φn =1), i.e.
1, n 1 n 0, n 0
bn (1 Pfa )}, where, a* (t ) 1,..., N
sufficient statistic of optimal sensing and access [12], where pn(t) is the available probability of channel n at the beginning of slot t. Then, Ω(t) can be taken as the confidence vector of the cognitive network. From Fig. 1, we know that the available channel capacity of channel n is given by
In the slot t, the transmitter of the cognitive network obtains the observable information {a , Ka } and decision-making information {a , a } , where a* is the short from a*(t), Ka {0,1} represents whether the ACK signal is received by the transmitter of the cognitive network at the end of slot t. "0" indicates that the transmitter has not received the ACK signal while "1" shows that the transmitter has received the ACK signal. Since the receiver of the cognitive network only has the information of a* and Ka*, and does not know the sensing results a of the transmitter, it cannot confirm the unsuccessful to transmit data when it does not receive the data transmitted by the transmitter. In order to ensure the receiver and transmitter in the cognitive network can switch to the same channel to communicate in next slot t+1, both of them should have the same confidence vector Ω(t+1). Therefore, the confidence vector will update based on the a* and Ka* and is given by
(5)
t 1 p1 t 1 , p2 t 1 ,..., pN t 1
(8)
where pn(t+1) is given by
(6)
1 Pfa pa 1 p10 1 pa p01 pn (t 1) Pfa pa 1 p10 1 pa p01 pa p10 1 pa 1 p01 pn t 1 p10 1 pn t p01 where, the first one presents the case where the transmitter of the SU has accessed the optimal channel a* to transmit the data and received the ACK signal. At this time, the channel is not occupied by the PU, and the SU has transmitted data successfully. The second one shows the case where the transmitter of the SU has accessed the optimal channel to transmit the data but not received the ACK signal from the receiver. There are two possible scenarios. One is that the transmitter of the cognitive user selects not to access the channel a* ( a* 0 ); another is
a t n, K a t 1 a t n, K a t 0
(9)
a t n
B. Access Strategy under Fading Channel In cognitive network, the channel fading is different for different SUs. This requires SUs to adjust themselves transmitted powers to overcome the channel fading [13]. In order to save the energy of SUs, SUs don't need sense channels in the whole slot. At the beginning of each slot, each of SUs should choose the operating mode, sensing or sleep, according to the statistic information of the channel states occupied by the PU and the residual energy of the SU. If the SU selects sensing mode, it will select a best suitable channel to sense from all of the N channels according to the optimal spectrum access strategy chosen. If the SU selects sleep mode, it will do nothing until to the next slot.
that the data transmission is not successful. The third indicates the updating of non-optimal confidence vector, which is updated according to the Markov process, one step transition probability.
©2015 Journal of Communications
(7)
transmitter does not access the channel a* ( a* 0 ) or is
When SUs find that the channel n is idle, one of the SUs will accesses the channel n. Then, at the beginning of slot t, the throughput achieved by accessing channel n can be expressed as
Cn (t ) ( pn (t )(1 p10 ) (1 pn (t )) p01 )bn (1 Pfa )
a* (t ) arg max { pn (t )(1 p10 ) (1 pn (t )) p01 n 1,..., N
(4)
where Θn is the sensing result of channel n. The probability of miss detection Pm is set as ζ. So, the maximum conflict probability allowed by PU is ζ, which meet the requirements of collision restrictions when the SU selects the optimal channel to access. Therefore, the optimization above can be transformed into the problem of POMDP based on the imperfect spectrum sensing, which objective is to find the optimal channel selection strategy to achieve the maximum throughput when Pm = ζ. Related study has shown that when all channels are independent of each other, Ω(t ) p1 (t ),..., pN (t ) is the
Cn (t ) ( pn (t )(1 p10 ) (1 pn (t )) p01 )bn
where Pfa is the probability of false alarm of the channel n in slot t. When we use the greedy algorithm to achieve the optimization, the optimal spectrum access strategy can be simplified as to find a optimal channel a*(t) to access to maximize the throughput as follows
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Suppose the SU divides its transmission energy into J energy levels according to the degrees of channel fading. The maximum throughput achieved by selecting channel n to access is given by Vn t arg max Cn t
access strategy [13]. In order to simplify the simulation, we suppose that there are only one PU and three SU, the channel bandwidth is 1 unit. The data is transmitted with binary over and 30 slots (T = 30). We simulate each one for 10000 times. The channel state transition probabilities shown in the simulation figures are the means of the uniform distribution functions with variance 0.001 respectively.
(10)
n0,1,..., N
where Cn(Ω(t)) is the throughput achieved by a SU accessing channel n, n=0 denotes the SU selects sleep mode, n=1,...,N denotes the SU selects channel n to access. When the SU selects sleep mode, it does not generate any revenues. Therefore, the throughput achieved at the slot t is the same as last slot as follows
0.7
Throughput of SUs(bit/s)
C0 t Vn t 1
0.8
(11)
When the SU selects sensing mode, it will sense and access channel n. Right now, the throughput achieved will be changed as follows
0.6 0.5 0.4
0.2 0.1 0
J
Cn t pn t 1 P10 1 pn t P01 bn n j
where n(j) , j = 1, ..., J, denote the probability of the jth energy level with which the SU selects channel n to transmit the data. If Cn(Ω(t))>C0(Ω(t)), the SU will select the sensing mode; otherwise it will select sleep mode. Therefore, the optimal mode selection strategy for channel n can be expressed as follows (13)
In the sleep mode, the confidence vector is updated according to the Markov chain as follows
pn t 1 pn t 1 P10 1 pn t P01
(14)
While in the sensing mode, the confidence vector is updated as follows
0.3
0.4
0.5
0.6
0.7
(15)
a (t ) n, a*(t ) 0 a (t ) n IV. SIMULATION RESULTS
0.6 0.5 0.4
Case Case Case Case Case Case
0.3 0.2
In this section, we provide some simulation results of the optimal spectrum access strategy (OSAS) under imperfect sensing and fading channels proposed in this paper, and compare it with the conventional spectrum ©2015 Journal of Communications
0.2
0.8
Throughput of SUs(bit/s)
1 P10 , pn t 1 P01 , p t 1 P 1 p t P , 10 n 01 n a (t ) n, a*(t ) 1
0.1
OSAS Conventional OSAS Conventional OSAS Conventional
Fig. 3 depicts the effect of imperfect spectrum sensing on the normalized throughput when there are 3 channels. We compare the throughputs in three different cases. The first one is the case where the difference between the transition probability of different channel states and the transition probability of same channel states is 0.8 (p01=0.1, p10=0.1); the second is the case where the difference is 0.6 (p01=0.2, p10=0.2); the final one is the case where the difference is 0.2 (p01=0.6, p10=0.6). As the probability of collision allowed between the PU and SUs, ζ, increases, the throughput obtained is improved. Due to the limitation of capacity themselves, the throughput obtained cannot continue to rise with the increase of ζ. When ζ is larger than 0.3, the throughput will be basically stable. On the other hand, it is clearly seen from Fig. 3 that the difference between the transition probability of different channel states and the transition probability of same channel states is also the main factor to affects the throughput besides the probability of collision. The more the difference is, the larger the throughput is. However, the throughputs achieved by the optimal spectrum access strategy we proposed are always larger than conventional ones.
(12)
Vn t 1
J b n k Vn t 1 sensing mode n j 1 sleep mode otherwise
0
1: 1: 2: 2: 3: 3:
Fig. 3. Throughput under different scenarios
j 1
1 pn t 1 P10 1 pn t P01
Case Case Case Case Case Case
0.3
0.1
0
5
10
15 Slot
Fig. 4. Throughput under fading channel
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1: 1: 2: 2: 3: 3:
OSAS Conventional OSAS Conventional OSAS Conventional
20
25
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[8]
Fig. 4 shows the throughput in the Rayleigh fading channel when the channel number N = 3. We compare the throughputs in three different cases respectively. The first one is the case when p01=0.05, p10=0.05; the second is the case when p01=0.1, p10=0.1; the final one is the case when p01=0.2, p10=0.2. It shows that both would achieve the stable throughputs. It means that the fading of the channels only affect the throughput at the beginning of the communication. However, OSAS will reach the stable throughput in 10 slots, but the conventional one will need 15 slots to reach the stable throughput. That is to say, OSAS has faster convergence than conventional one. Similar to the Fig. 3, the more the difference between the transition probability of different states and the transition probability of same state in the same channel is, the greater the throughput achieved. The difference of transition probabilities is still the main factor to affect the throughput.
[9]
[10]
[11]
[12]
[13]
V. CONCLUSIONS This paper proposes opportunistic spectrum access strategies which consider the sensing error and channel fading. By setting the optimal operating point of the spectrum detection and updating the confidence vectors, we turned the imperfect spectrum sensing into one under the perfect spectrum sensing based on the POMDP model. Simulation results show that the difference of transition probabilities is an important factor which affects the throughput. The more the difference is, the greater the throughput achieved is. In the fading channel, the SU will quickly achieve the stable throughput. REFERENCES [1]
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S. Stotas and A. Nallanathan, “On the throughput and spectrum sensing enhancement of opportunistic spectrum access cognitive radio networks,” IEEE Transactions on Communications, vol. 11, no. 1, pp. 97-107, 2012. A. A. El-Sherif and K. J. Liu, “Joint design of spectrum sensing and channel access in cognitive radio networks,” IEEE Trans. Wireless Communications, vol. 10, no. 6, pp. 1743-1753, 2011. Y. N. Liu, J. G. Yang, H. L. Yang, and H. Hai, “Hidden markov model-based joint probability channel prediction dynamic spectrum access in cognitive radio,” Journal of Shanghai University(Natural Science), vol. 17, no. 5, pp. 581-585, 2011. D. V. Djonin, Q. Zhao, and V. Krishnamuurthy, “Optimality and complexity of opportunistic spectrum access: A truncated Markov decision process formulation,” in Proc. IEEE International Conference on Communications, Glasgow, June 24-28, 2007, pp. 5787-5792. Park Sungsoo and H. Daesik, “Optimal spectrum access for energy harvesting cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 12, pp. 6166–6179, 2013. Q. Zhao, Y. X. Chen, and A. Swami, “Distributed spectrum sensing and access in cognitive radio networks with energy constraint,” IEEE Transactions on Signal Processing, vol. 57, no. 2, pp. 783-797, 2009.
Yonghong Chen was born in Jiangsu Province, China, in 1981. She received the B.S. degree in electronic information science and technology from Zhengzhou University of Light Industry, in 2004 and the M.S. degree in signal and information processing from Nanjing University of Posts and Telecommunications in 2007. She is currently a lecturer of Nantong University. Her research interests include communication signal processing and cognitive wireless networks. Huijian Wang was born in Taizhou, China in 1987. He received his B. S. degree in communications engineering from Nantong University China in 2011. He is currently a graduate student of Nantong University. He is engaged in the research activities in the areas of communication signal processing and cognitive wireless networks.
Shibing Zhang was born in Haimen, China in 1962. He received his B.S. degree in wireless communications from Dalian Maritime University, China in 1983, M.S. degree and Ph.D. degree in wireless communications from Nanjing University of Posts and Telecommunications, China in 1989, 2007 respectively. He worked as an associate engineer in the Nantong Changjiang Communication and Navigation Management Section from Sept. 1983 to Aug. 1986, engineer in the Yancheng Electronic Equipment Manufactory from Feb. 1989 to Apr. 1997 and senior engineer in the Haimen Economical Information Centre from May. 1997 to Mar. 2001 respectively. Since Apr. 2001, he has been working in Nantong University as a professor. His current research interests include wireless communications and networking, OFDM system, especially on ultrawideband communications, cognitive radio. From Jul. 2009 to Mar. 2010, Dr. Zhang was a visiting scholar with the Department of Electrical and Computer Engineering, University of Victoria.
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