SINR-Based Spectrum Sensing for Cognitive Radio. Networks: An Online Spectrum Monitoring Method. Ala Abu Alkheir and Mohamed Ibnkahla. Department of ...
2013 10th International Multi-Conference on Systems, Signals & Devices (SSD) Hammamet, Tunisia, March 18-21, 2013
SSD'13 1569706067 1
SINR-Based Spectrum Sensing for Cognitive Radio Networks: An Online Spectrum Monitoring Method Ala Abu Alkheir and Mohamed Ibnkahla Department of Electrical and Computer Engineering (ECE), Queen’s University, Kingston, Ontario, Canada Emails: {ala.abu.alkheir, mohamed.ibnkahla}@queensu.ca
Abstract—This article proposes a novel spectrum sensing method based on the instantaneous Signal to Interference plus Noise Ratio (SINR) of the received signal. This method allows the terminals of a Cognitive Radio Network (CRN) to momentarily detect the presence of Co-Channel Interferers (CCI), whether Primary Users (PUs) or other Cognitive Radio (CR) users without the need to schedule a Quiet Period (QP). To achieve the virtues of cooperation, three cooperative sensing protocols are proposed. The first protocol is a centralized majority-voting protocol while the other two protocols are distributed protocols that are integrated with multihop techniques, namely Amplify and Forward (AF) and Decode and Forward (DF). The proposed method and protocols were shown to achieve good detection performance under a wide range of circumstances.
performed - using the conventional sensing methods - except when the CRN terminal is not engaged in a transmit/receive process, i.e., only when the terminal is in a QP. However, since this period is consuming a valuable communication time, it is essential for the CRN terminal to minimize its duration as much as possible. Observing this, [5] has formulated an optimization problem to find the optimal QP duration to achieve a certain performance level while maximizing the throughput. Alternatively, part of the operating channel can be reserved for continuous in-band sensing [6]. However, this approach, known as partial spectrum sensing, lowers the throughput as well as complicates the in-band sensing stage. More recently, [7] has investigated a number of possible methods to achieve real-time detection of primary user based on receiver statistics. In this article, we propose an in-band spectrum sensing method that requires neither QP scheduling nor partial spectrum allocation. Furthermore, the proposed method requires no prior knowledge about the signal or the identity of the detected user, it simply treats it as a source of CCI. The proposed method uses the instantaneous SINR of the received signals to detect the presence of an arbitrary source of CCI, whether a PU or other CR users. The proposed method is extended into three cooperative spectrum sensing protocols, one centralized protocol and two distributed protocols. The distributed protocols were designed by integrating the proposed method with multihop relaying using either, Amplify and Forward (AF) or Decode and Forward (DF). The notion of exploiting multihop relaying for spectrum sensing has already been studied in the literature. In particular, [8] studied an AF cooperative spectrum sensing protocol wherein the source terminal senses the channel using the amplified transmission of the relay. This idea has been extended in [9] to DF relaying. More recently, AF, DF and Compress and Forward (CF) has been used in [10] to achieve reliable sensing by a relay-assisted terminal. Despite the achieved detection and agility gains, spectrum sensing and data communication were performed by two separate terminals. Hence, spectrum sensing exploited cooperative diversity but was not yet integrated with it. The remainder of this article is organized as follows. Section II describes the system model and the three communication patterns considered. The SINR-based sensing method is introduced in section III while the three cooperative protocols are described in section IV. Numerical and simulations results are given in section V while conclusions are drawn in section VI.
I. I NTRODUCTION Over the past decade, CRNs have emerged as a smart and powerful spectrum utilizing paradigm. Unlike other paradigms, like cellular or mesh networks, CRNs are license-exempt networks that intelligently coexist with licensed spectrum users. This intelligent coexistence is enabled using one of two widely studied spectrum sharing strategies, namely, spectrum overlay and spectrum underlay [1]. Despite the rich literature on both paradigms, spectrum overlay seemed more practically feasible, hence it was adopted in a number of recent CRN standards, like the IEEE 802.22 and the ECMA-392 [2] [3]. Spectrum overlay mandates that a particular spectrum channel can be accessed by a CRN terminal as long as it is not being used by its owner, i.e., the PU. Consequently, CRN terminals are expected to include a spectrum awareness engine that manages the processes of spectrum sensing, spectrum access, and spectrum evacuation [4]. The spectrum sensing process consists of two stages, these are in-band spectrum sensing and out-band spectrum sensing. As the names suggest, in-band spectrum sensing is responsible for detecting any activity of other users, PUs or other CR users, within the already accessed spectrum band, also known as the operating channel. On the other hand, out-band sensing aims at locating alternative vacant spectrum channels to be used whenever the operating channel is deemed busy or unsuitable. Upon detecting the presence of a CCI source within the operating channel, the CRN acts differently depending on the type of interferer. However, in terms of its impact on the CRN performance, all sources of CCI are equally harmful. While out-band spectrum sensing can be handled using a separate Radio Frequency (RF) unit, in-band sensing cannot be 978-1-4673-6457-7/13/$31.00 ©2013 IEEE
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II. S YSTEM M ODEL
terminal makes a local decision about the presence/absence of a CCI source and sends a one-bit decision, denoted {dk }K k=1 ∈ {0, 1}, to the FC. In turn, this latter creates a global decision metric, denoted Θ, by summing all the local decisions K and comparing the sum to a majority threshold η. If Θ k=1 dk ≥ η, the FC decides that a CCI source exists, otherwise, it decides that the channel is CCI-free. Finally, Figure1.(c) shows a K hop relay network where the k th terminal, k ≥ 2, decides whether a CCI source exists or not by examining the received signal. In the AF case, every terminal can benefit from the results of all previous hops, while in the DF case, a terminal can benefit only from the most recent hop.
Consider the two-terminals CRN shown in Figure 1.(a) where a CR transmitter S communicates with a CR destination D over a particular vacant channel. Simultaneously, another
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III. T ERMINAL -L EVEL S PECTRUM S ENSING
To examine the availability of a CCI source, D needs to decide whether it received an SNR or an SINR. To achieve this, it needs to estimate the instantaneous energies of the signal and the noise. Fortunately, since the interference term follows a Gaussian distribution just like the AWGN, D can estimate the instantaneous noise plus interference energy without perceiving the presence of an interferer. Assuming perfect estimation, D needs to decide whether the calculated ratio, denoted Λ, is an SINR or an SNR. Mathematically, D needs to solve the following binary hypothesis testing problem SINR Λ = ψ, if Λ < ϕ (3) Λ ≶ ϕ =⇒ Λ = γ, if Λ ≥ ϕ. SNR
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Fig. 1. System Model. (a) A two terminal network, (b) a centralized cooperative spectrum sensing scenario, and (c) a multihop network for distributed spectrum sensing.
where ϕ is some decision threshold to be calculated shortly. Since the SINR/SNR are suboptimal decision metrics, it is pivotal to prove that the Probability Density Functions (PDFs) of Λ in the two cases intersect at some λ0 > 0. To achieve this, let us look at the corresponding PDFs, given by
pair of users, PUs or other CR users, decides to use the same channel. As a result, D will experience a non-negligible level of CCI1 . In the absence of the CCI source, D receives y(n) = hsd (n) · xs (n) + w(n),
1 −λ/¯γ e , γ¯ μ(μ + λ + γ¯) 1 −λ/¯γ fΛ|H1 (λ) = · e . (μ + λ)2 γ¯ fΛ|H0 (λ) =
(1)
at the end of the nth time slot, while it receives y(n) = hsd (n) · xs (n) + hCCI (n) · xCCI (n) + w(n),
(4a) (4b)
where we have defined the hypotheses H0 and H1 to stand for ”a CCI source absent” and ”a CCI source present”, respectively. In fΛ|H1 (λ), μ is the average Signal to Interference Ratio (SIR) defined as μ γ¯ /¯ γCCI . By solving fΛ|H0 (λ) − fΛ|H1 (λ) = 0, we can readily see that the two functions intersect at the two roots of the quadratic equation
(2)
in its presence. In these two equations, hsd (n) and hCCI (n) are the coefficients of the S-D and A-D links, respectively, xs (n) and xCCI (n) are the signals of S and A, respectively, while w(n) is the Additive White Gaussian Noise (AWGN) with variance of σ 2 . In this article, all channels are modeled as flat Rayleigh fading channels, hence the corresponding Signal to Noise Ratio (SNR) and the Interference to Noise Ratio (INR) of the aforementioned links, denoted by γ and γCCI , are exponentially distributed with mean values of γ¯ and γ¯CCI , respectively. In the absence of CCI, D perceives an SNR of γ, while in its presence, it perceives an SINR of ψ γ/(γCCI + 1). At the network level shown in Figure1(b), a total of K CRN terminals receive a sensing command from a central terminal, referred as a Fusion Center (FC). Using this command, every
γ = 0, λ2 + μλ − μ¯ which are given by
(5)
μ μ ± 1 + 4¯ γ, (6) 2 2 however, since λ has to be positive, the negative root is dropped, and √ we are left with the positive root, given by = 0.5μ( 1 + 4¯ γCCI − 1) which is positive for all values λ+ 0 of γ¯ and γ¯CCI . This intersection point is shown in Figure 2. This figure also shows that fΛ|H1 (λ) ≥ fΛ|H0 (λ) for λ ≤ λ0 . Consequently, the detection and false alarm probabilities can be defined as Pd Pr[λ < ϕ|H1 ] = Fλ|H1 (ϕ) and Pf a Pr[λ < ϕ|H0 ] = Fλ|H0 (ϕ), respectively, where ϕ − λ+ 0 , λ0 = −
1 Henceforth we will refer to a PU or a CR concurrently using the channel with the CRN terminal as a CCI source.
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3
0.16
where ϕˆk is the decision of the k th terminal, then the threshold K FC can calculate Θ = k=1 dk and compare it to a decision threshold η. If Θ ≥ η, the FC decides that a CCI source exists, otherwise it declares that the band is CCI-free. Based on this cooperation scenario, the detection and false alarm probabilities were shown in [13] to be given by2
PDF of SNR PDF of SINR
0.14 0.12
PDF
0.1 0.08
Qd =
Intersection point at λ = 7.9 dB
0.06
bk K
U1,l V1,l ,
(11a)
U0,l V0,l ,
(11b)
k=η l=1
0.04
Qf a =
0.02
bk K k=η l=1
0 0
2
4
6
8
10 λ in dB
12
14
16
18
where bk = K!/[(K − k)!k!] is the number of possible permutations of K elements taken k at a time. U1,l is the lth permutation consisting of the product of k out of the K possible Pd,k terms while V1,l is the lth permutation forming the complements’ product of the remaining K − k terms, i.e., (1 − Pd,k ). Similarly, U0,l and V0,l are defined using the false alarm probabilities, Pf a,k , of the various terminals.
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Fig. 2. A plot of fΛ|H0 (λ) and fΛ|H1 (λ) as a function of λ where γ ¯= 10dB and γ ¯CCI = 0dB.
is chosen according to the Neyman-Pearson criterion [11] while Fλ|H1 (λ) and Fλ|H1 (λ) are the Cumulative Distribution Functions (CDFs) of Λ under the two hypotheses, which are given by FΛ|H0 (λ) = 1 − e
−λ/¯ γ
, μ −λ/¯γ e FΛ|H1 (λ) = 1 − . μ+λ
B. Distributed Cooperative Sensing: Multihop AF Case In distributed cooperation, every terminal is responsible for making its own decision using some of the available sensing information. Consider the multihop network shown in Figure 1.(c) above. In this figure, S communicates with D through the help of a number of relay terminals. The total number of hops between S and D is K ≥ 2. Every relay terminal uses an amplification factor, Gk , given by [14]
(7a) (7b)
Finally, according to the aforementioned criterion, ϕ is chosen to meet a certain false alarm probability, Pˆf a , hence ˆ γ Pˆf a = 1 − e−ϕ/¯ =⇒ ϕˆ = −¯ γ ln(1 − Pˆf a ),
using this threshold, Pd can be written as μ ˆ γ e−ϕ/¯ Pd = FΛ|H1 (ϕ) ˆ =1− . μ + ϕˆ
(8)
G2k =
Ek−1 |hk
|2
Ek , + Eik |hik |2 + σk2
(12)
when the CCI source is present and
(9)
G2k =
IV. N ETWORK - LEVEL S PECTRUM S ENSING
Ek , Ek−1 |hk |2 + σk2
(13)
when it it absent. In these two equations, Ek−1 and Ek are the transmission energies of the (k − 1)th and k th terminals, respectively, while hk is the channel coefficient between the two terminals and σk2 is the variance of the AWGN at the k th terminal. Observe that the k th terminal does not need to know whether a CCI source is present or not to calculate Gk because it simply calculates the energy of the received signal regardless of its content. Using MRC, the end-to-end SNR/SINR can be approximated by [15] K −1 1 , (14) Λeq ≈ Λk
Regardless of how excellent the performance of a spectrum sensing method is, it is well known that cooperative sensing can make it even better [12]. It can also mitigate the various channel impairments, like deep fading and shadowing, and in particular it can mitigate the hidden terminal problem. To achieve the cooperation advantages, this section considers two types of cooperation scenarios, a centralized scenarios and a distributed scenario. In the latter, the proposed SINR based sensing method is integrated with a multihop relaying network. A. Centralized Cooperative Sensing A straightforward cooperation scenario occurs when all network terminals, say K, pass their local decisions to a FC that makes the final decision. This scenario is shown in Figure 1.(b). In particular, if every terminal makes a local decision {dk }K k=1 ∈ {0, 1} using the rule 1 if Λk ≤ ϕˆk , dk = (10) 0 if Λk > ϕˆk ,
k=1
where λk is the SNR/SINRs of the k th link. The detection and ˆ 1] false alarm probabilities, denoted by Qd Pr[Λeq < ϕ|H 2 These two expressions assume perfect reporting channels. However, a more practical situation would require eliminating the faulty reporters and to account for the possible decoding errors. Nevertheless, these two issues are not considered here due to space limitations.
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4
and Qf a Pr[Λeq < ϕ|H ˆ 0 ], respectively, can be written as
M1/ψeq (−s)
−1 Qd = 1 − L , (15a)
s 1/ψeq =1/ϕ ˆK
M1/γeq (−s)
−1 . (15b) Qf a = 1 − L
s
Mathematically speaking, Qd and Qf a of the k th terminal can be written as
1/γeq =1/ϕ ˆK
−1
where L {·} is the inverse Laplace transform operation and M1/ψeq (−s) and M1/γeq (−s) are the Moment Generating Functions (MGFs) of 1/ψeq and 1/γeq , respectively. These two functions can be written as the product of the MGFs of the K individual hops, i.e.,{1/ψk }K k=1 and {1/γk }k=1 , respectively, which are given by s s/μk s , (16a) e E1 M1/ψk (−s) = 1 − μk μk
s s M1/γk (−s) = 2 K1 2 . (16b) γ¯k γ¯k
Qd = Pr[ψk,1 < ϕˆk , ψk,2 < ϕˆk ] + Pr[ψk−1,1 < γth , ψk,2 < ϕˆk ],
(17a)
Qf a = Pr[γk,1 < ϕˆk , γk,2 < ϕˆk ] + Pr[γk−1,1 < γth , γk,2 < ϕˆk ],
(17b)
where the subscripts (·)1 and (·)2 correspond to the first and second time slots, respectively. By exploiting the independence between the various terms, Qd and Qf a can be rewritten as 2 + Pout,k−1 Pd,k , Qd = Pd,k
Qf a =
Pf2a,k
+ Pout,k−1 Pf a,k ,
(18a) (18b)
where Pd,k , Pf a,k and Pout,k−1 are the detection, false alarm and outage probabilities of the k th and (k − 1)th terminals, respectively.
where K1 (·) is the first order modified Bessel function of the second kind and E[·] is the exponential integral. It should be remarked, however, that evaluating the exact MGF of 1/ψk is an involved problem, hence we resorted to use the MGF of the approximation ψk ≈ γ/γCCI [16]. Finally, using the numerical technique described in [17] to calculate the inverse Laplace transform in (13), the detection and false alarm probabilities can be easily evaluated.
V. N UMERICAL
AND
S IMULATIONS R ESULTS
Let us now investigate the performance of the proposed method and protocols under various circumstances. In the following simulations, an arbitrary SNR/INR γk is expressed as γk SNRk (d/dk )n , where SNRk is the transmission SNR/INR, d is a normalizing distance measure, dk is the distance between the transmitter and the receiver, and n = 4 is the path loss exponent. All figures show the complementary receiver operating characteristics which are plots of the probability of miss-detection, defined as Pm = 1 − Pd versus the probability of false alarms P − f a. To start with, we shall consider the single terminal case as shown in Figure 3. This figure shows that the proposed method can accurately detect the presence of a CCI source whenever this source is transmitting with a high SNR. However, as expected, this accuracy is gradually lost when this source transmits at a lower SNR or is farther away from the receiving CRN terminal. Nonetheless, this may not be a drawback from the CRN perspective since the resulting CCI will be less harmful. Next, let us see the performance of this method when used in a centralized cooperative sensing scenario. Figure 4 illustrates the effect of increasing the distance between the various terminals and the CCI source. It can be readily seen that a closer CCI source can be accurately detected compared to a distant source. The performance of the AF case is illustrated in Figure 5 for different number of hops. It illustrates that the larger the number of hops, the better the detection performance. Finally, the performance of the DF case is illustrated in Figure 6. This figure shows that increasing the distance between the CCI source and the CRN terminal reduces the detection accuracy, while when the source is within the transmission range of the CRN terminal, a high level of detection accuracy can be achieved.
C. Distributed Cooperative Sensing: Multihop DF case Unlike the AF case, DF case does not carry the information of the individual hops to the destination. Hence, designing a cooperative sensing protocol for the DF case is not as straightforward as it was in the AF case. In particular, since the k th relay terminal regenerates the signal before forwarding it to the following hop, we mandate that it regenerates the signal only when the received SNR/SINR exceeds the outage threshold, denoted by γth 2Q − 1, where Q is the spectral efficiency measured in bits per second per Hertz. If this condition is violated, the relay terminal requests a retransmission from the (k − 1)th terminal. This request is overheard by the (k + 1)th relay terminal. When the retransmission occurs, the k th terminal examines the same channel condition again to decide whether to regenerate the signal or to go to another retransmission. The (k + 1)th terminal, in turn, examines the same channel quality condition. If the channel passes the quality test, then the message is forwarded to the following hop. Otherwise, the (k + 1)th declares - without asking for a retransmission- that a CCI source is present. Consequently, the k th terminal can declare the presence of a CCI source if one of the following two conditions is met3 • If the received SNR/SINR of the original as well as the repeated transmission falls below the decision threshold ϕˆk , or th • If the (k − 1) terminal receives a successful retransmission while the k th terminal receives a failed transmission.
VI. C ONCLUSIONS This article proposed an SINR based spectrum detection method that achieves real-time sensing of an arbitrary source of CCI. The proposed method has been extended into three
3 It
should be remarked here that other definitions of a detection event are possible as well.
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0
0
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Simulation Analytical
Simulation Analytical
−1
10
−1
d
= 1−Q
−2
10
K=2
m
SNRCCI = 10dB, 5dB, and 0 dB
Q
Pm = 1−Pd
10
−2
10
K=4 −3
10
K=8 −3
10 −4
10 −2 10
−1
10 P
0
−3
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−2
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fa
0
10
fa
Fig. 3. Complementary receiver operating characteristics of the proposed method for SNRCCI = 10, 5, and 0 dBs where SNRs = 10dB and dsd , dcci ∈ [0.5d, d].
Fig. 5. Complementary receiver operating characteristics of the AF distributed cooperative spectrum sensing protocol where SNRs = 5dB, SNRCCI = 10dB, and dk , dcci ∈ [0.5d, d].
0
0
10
10
Simulations Analytical
Simulation Analytical
−1
10
−2
10
Qm = 1−Qd
Qm = 1−Qd
−1
10
Q
dCCI ∈ [0.5d, d], [0.75d,2d], and [d,1.5d]
−3
10
−1
10
dCCI ∈ [ 0.5 d, d], [ 0.75 d, 1.5d] , and [ d, 2d]
−4
10
−2
−2
10
−1
10 Q
10 −3 10
0
10
−2
10
−1
Q
10
0
10
fa
fa
Fig. 4. Complementary receiver operating characteristics of the centralized cooperative spectrum sensing protocol using the OR rule where SNRs = SNRCCI = 10 dBs, K = 10, and dsd ∈ [0.5d, d].
Fig. 6. Complementary receiver operating characteristics of the DF distributed cooperative spectrum sensing protocol where SNRs = SNRCCI = 10dB, and dk ∈ [0.5d, d], while γth ≈ 4.77dB.
cooperative sensing protocols. The proposed method and protocols were shown to achieve high level of accuracy when detecting nearby sources of CCI. In our future work, we are investigating the integration of the proposed method with other cooperative diversity protocols. In addition, the impact of imperfect channel estimation on the performance of the proposed method/protocols will be addressed.
[2] “IEEE draft standard for information technology–telecommunications and information exchange between systems–Local and Metropolitan Area Networks– specific requirements–part 22.1: Standard to enhance harmful interference protection for low power licensed devices operating in the tv broadcast bands,” IEEE Unapproved Draft Std P802.22.1/D6, Feb 2009. [3] “MAC and PHY for operation in TV white space,” ECMA International, Tech. Rep., Dec. 2009. [4] G. Ko, A. Franklin, S.-J. You, J.-S. Pak, M.-S. Song, and C.-J. Kim, “Channel management in IEEE802.22 WRAN systems,” Communications Magazine, IEEE, vol. 48, no. 9, pp. 88 –94, Sep. 2010. [5] Y.-C. Liang, Y. Zeng, E. Peh, and A. T. Hoang, “Sensing-throughput tradeoff for cognitive radio networks,” Wireless Communications, IEEE Transactions on, vol. 7, no. 4, pp. 1326 –1337, Apr. 2008. [6] D. Willkomm and A. Wolisz, “Efficient QoS support for secondary users in cognitive radio systems [dynamic spectrum management],” Wireless
R EFERENCES [1] B. Wang and K. Liu, “Advances in cognitive radio networks: A survey,” Selected Topics in Signal Processing, IEEE Journal of, vol. 5, no. 1, pp. 5 –23, Feb. 2011.
5
6
Communications, IEEE, vol. 17, no. 4, pp. 16 –23, Aug. 2010. [7] S. Boyd, J. Frye, M. Pursley, and T. Royster, “Spectrum monitoring during reception in dynamic spectrum access cognitive radio networks,” Communications, IEEE Transactions on, vol. 60, no. 2, pp. 547 –558, Feb. 2012. [8] G. Ganesan and Y. Li, “Agility improvement through cooperative diversity in cognitive radio,” in IEEE GLOBECOM, vol. 5, Dec. 2005, pp. 1–5. [9] M. Zou, C. Zhao, B. Shen, and K. Kwak, “Cooperative spectrum sensing using DF cooperative diversity protocol in cognitive radio,” in International Symposium on Communications and Information Technologies, Oct. 2008, pp. 604 –608. [10] S. Astaneh and S. Gazor, “Relay assisted spectrum sensing in cognitive radio,” in Systems, Signal Processing and their Applications (WOSSPA), 2011 7th International Workshop on, May. 2011, pp. 163 –166. [11] S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Englewood Cliffs, NJ, USA: Printice Hall, 1998. [12] A. Ghasemi and E. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in First IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), 8-11 Nov. 2005, pp. 131 –136. [13] A. Abu Alkheir and M. Ibnkahla, “Selective cooperative spectrum sensing in cognitive radio networks,” in Global Telecommunications Conference (GLOBECOM 2011), 2011 IEEE, Dec. 2011, pp. 1 –5. [14] S. Ikki and S. A¨ıssa, “Performance analysis of dual-hop relaying systems in the presence of co-channel interference,” in GLOBECOM 2010, 2010 IEEE Global Telecommunications Conference, Dec. 2010, pp. 1 –5. [15] M. Hasna and M.-S. Alouini, “Outage probability of multihop transmission over Nakagami fading channels,” Communications Letters, IEEE, vol. 7, no. 5, pp. 216 – 218, May 2003. [16] T. Soithong, V. A. Aalo, G. P. Efthymoglou, and C. Chayawan, “Outage analysis of multihop relay systems in interference-limited nakagami- m fading channels,” Vehicular Technology, IEEE Transactions on, vol. 61, no. 3, pp. 1451 –1457, Mar. 2012. [17] Y.-C. Ko, M.-S. Alouini, and M. Simon, “Outage probability of diversity systems over generalized fading channels,” Communications, IEEE Transactions on, vol. 48, no. 11, pp. 1783 – 1787, Nov. 2000.
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