Mitigating Cross-Network Interference in Cognitive ... - IEEE Xplore

IEEE ICC 2014 - Cognitive Radio and Networks Symposium

Mitigating Cross-Network Interference in Cognitive Spectrum Sharing with Opportunistic Relaying Phee Lep Yeoh∗ , Trung Q. Duong† , Maged Elkashlan‡ , Michail Matthaiou† , and Nidal Nasser§ ∗ University

of Melbourne, Melbourne, Australia University Belfast, Belfast, UK ‡ Queen Mary University of London, London, UK § Alfaisal University, Riyadh, Kingdom of Saudi Arabia Email: [email protected], [email protected], [email protected], [email protected], [email protected] † Queen’s

Abstract—We examine the impact of primary and secondary interference on opportunistic relaying in cognitive spectrum sharing networks. In particular, new closed-form exact and asymptotic expressions for the outage probability of cognitive opportunistic relaying are derived over Rayleigh and Nakagamim fading channels. Our analysis presents revealing insights into the diversity and array gains, diversity-multiplexing tradeoff, impact of primary transceivers’ positions, and the optimal position of relays. We highlight that cognitive opportunistic relaying achieves the full diversity gain which is a product of the number of relays and the minimum Nakagami-m fading parameter in the secondary network. Furthermore, we confirm that the diversity gain reduces to zero when the peak interference constraint in the secondary network is proportional to the interference power from the primary network.

I. I NTRODUCTION Opportunistic relaying is a globally optimum transmission scheme for multiple-relay networks where a single “best” relay is selected to assist the communication between the source and destination nodes [1–3]. Recently, opportunistic relaying has been examined in cognitive spectrum sharing environments to enhance the reliability of the secondary network. Cognitive opportunistic relaying is an interference-aware approach to extend the communication range of the secondary network and limit the amount of interference impinged by the relays on the primary network. In particular, it has been shown that opportunistic relaying with decode-and-forward (DF) relays can remarkably improve the performance of the secondary network [4–6]. The performance of opportunistic relaying in cognitive spectrum sharing has attracted significant interest in the recent literature (e.g., see [4–10] and references therein). Specifically, an exact closed-form expression for the outage probability (OP) of DF relaying was derived in [4, 5]. The asymptotic OP for amplify-and-forward (AF) relaying was derived in [7], where the diversity order was shown to be equal to the number of relays K. It is important to note that the analysis of opportunistic relaying in cognitive networks is non-trivial due to the statistical dependence on the common random variable of the channel gain from the SU source to the PU receiver (PU-Rx) in the end-to-end (e2e) signal-to-interference ratio (SIR) [8]. This statistical correlation is the main difference

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between the analysis of cognitive and non-cognitive relaying systems. As such, taking into account this statistical correlation is required to rigorously evaluate the secondary network performance. In this context, the performance of DF and AF relaying over Rayleigh fading channels was analyzed in [6] and [9], respectively. These works were extended to the case of Nakagami-m fading channels in [10]. However, all these works on cognitive opportunistic relaying have not considered the effect of interference from the PU transmitter (PU-Tx) on the secondary network. In fact, the aforementioned works assumed that the PU-Tx is located far away from SUs; thus, the interference from the PU-Tx on the SUs was neglected. Recently, the impact of interference from the PU-Tx has been investigated for a single-relay scenario [11–14]. In particular, a closed-form expression for the OP of Rayleigh fading channels, under a peak interference power constraint, was deduced in [11, 12]. This work has been extended to account for the joint impact of peak interference power and maximum transmit power constraint for single and multiple primary transceivers in [13] and [14], respectively. Very recently, the performance of cognitive opportunistic relaying considering the average interference power constraint in the presence of a PU-Tx was assessed in [15]. However, due to the above mentioned statistical dependence in cognitive networks, the authors of [15] provided only upper and lower bounds on the OP. Motivated by the above discussion, in this paper, we consider cognitive opportunistic relaying networks in the presence of a PU-Tx and PU-Rx. Particularly, we derive new closed-form expressions for the exact and asymptotic OP over independent Rayleigh and Nakagami-m fading channels. Our analysis takes into account the fact that a statistical dependence exists in the e2e SIR, even though the fading channels under consideration are independent. As such, our derivations provide important insights into the impact of the peak interference power constraint Ip , interference power from the PUTx γ¯I , and the number of secondary relays K on the secondary network. Specifically, we highlight the impact on the diversity gain, array gain, and diversity-multiplexing tradeoff (DMT) of cognitive opportunistic relaying. We reveal that the full diversity gain is achieved when γ¯I is fixed

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where Ps and PRk are the transmit powers at S and Rk , respectively. Here, we denote γ¯I as the transmit power of the PU-Tx, which results in interference on the secondary receivers Rk and D. Recall that in a cognitive spectrum-sharing environment, the interference resulting on the PU-Rx from the secondary transmitters must be maintained below a maximal tolerable interference level Ip [16]. As such, we have

38 7[  N



N

N N

6HOHFWHG UHOD\ 

Ps =

N

(2)

By substituting (2) into (1), the single relay e2e SIR can be re-written as   Ip Z1k Ip Z2k γk = min , (3) , X γ¯I Z3k Z4k γ¯I Y

.

38 5[

Fig. 1.

Ip Ip , and PRk = . |g0 |2 |g1k |2

Cognitive opportunistic relaying with cross-network interference.

and independent of Ip . This diversity gain is equal to the product of the number of relays and the minimum Nakagamim fading parameter in the secondary network. Furthermore, we confirm that, when γ¯I is proportional to Ip , the diversity gain diminishes to zero and there is no benefit for the SU to access the spectrum.

where due to notational convenience we denote Z1k  |h1k |2 , Z2k  |h2k |2 , Z3k  |g1k |2 , Z4k  |g2k |2 , X  |g0 |2 , and Y  |g3 |2 . Finally, applying the max-min criterion across all the K relay links, the e2e SIR of cognitive opportunistic relaying with cross-network interference is given by γD =

γk



Ip Z2k Ip Z1k = max min , k=1,2,...,K X γ¯I Z3k Z4k γ¯I Y

II. N ETWORK AND C HANNEL D ESCRIPTION We consider a cognitive opportunistic relay network, as shown in Fig. 1, where the primary transceivers, PU-Tx and PU-Rx, coexist in the same frequency band as the SU source S, SU relays Rk , k = 1, . . . , K, and SU destination D. The SU relays play an important role in extending the range of the secondary network while satisfying the interference constraints of the primary network. The transmission in the secondary network occurs in two orthogonal time slots. In the first time slot, S transmits a signal which is received at all the K relays. In the second time slot, one of the K relays is selected to decode and then forward the received signal to D. Due to the co-existence of the primary and secondary networks, the S and Rk transmission impinges interference at the PU-Rx, whereas the PU-Tx transmission impinges interference at Rk and D. As such, we consider a cognitive opportunistic relaying scheme in which the best relay, in the max-min criterion sense, is selected by taking into account both the desired links between the SUs, and the interference links between the SUs and PUs. The channel coefficients of the desired links S → Rk , Rk → D, and interference links S → PU-Rx, Rk → PU-Rx, PU-Tx → Rk , PU-Tx → D are denoted as h1k , h2k , g0 , g1k , g2k , g3 , which follow independent Nakagami-m distributions with fading parameters mh1 , mh2 , mg0 , mg1 , mg2 , mg3 , and variances Ωh1 , Ωh2 , Ωg0 , Ωg1 , Ωg2 , Ωg3 , respectively. Based on these, the instantaneous e2e SIR for a single S → Rk → D relay link is given by [14]   Ps |h1k |2 PRk |h2k |2 γk = min , (1) , γ¯I |g2k |2 γ¯I |g3 |2

max

k=1,2,...,K

 .

(4)

In (4), we observe that there exists a statistical dependence on the common random variables (RVs) X and Y , which represent the S → PU-Rx and PU-Tx → D channel gains, respectively. III. E XACT AND A SYMPTOTIC O UTAGE P ROBABILITY In this section, we examine the impact of the coexistence of the PU-Tx and PU-Rx on the outage probability of cognitive opportunistic relay networks. Assuming independent Nakagami-m fading channels, all the RVs T ∈ {Z1k , Z2k , Z3k , Z4k , X, Y } in (4) follow a gamma distribution whose cumulative distribution function (CDF) and probability density function (PDF) can be expressed as  p T m T −1 xm mT ΩT −x FT (t) = 1 − e ΩT , (5) p! p=0 and

 fT (t) =

mT ΩT

mT

−x

mT

xmT −1 e ΩT , Γ(mT )

(6)

respectively, with mT ∈ {mh1 , mh2 , mg1 , mg2 , mg0 , mg3 }, and ΩT ∈ {Ωh1 , Ωh2 , Ωg1 , Ωg2 , Ωg0 , Ωg3 }. Note that in the subsequent analysis we will assume mT to be an integer for the sake of analytical tractability. Although we consider independent fading channels in all the links, we note that the RVs γ1 , . . . , γK are correlated due to the common RVs X and Y in each γk . As such, the e2e SIR in (4) represents the maximum selection criterion among multiple

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correlated RVs, which is a tedious mathematical problem. To circumvent this, we first derive the CDF of γk conditioned on X and Y as follows:  

   Ip Z2k Ip Z1k  γ Pr >γ , X γ¯I Z3k Z4k γ¯I Y       Z2k γX γY Z1k 1 − Pr < < , = 1 − 1 − Pr Z3k ρ Z4k ρ

 

  I1

I2

(7) where ρ 

Ip γ ¯I .

 I1 = 1 −  = 

mg2 Ωg2

The first term I1 is evaluated as

∞ 0

 fZ3k (y) FZ1k

mg2

∞

m h1 −1 1 Γ(mg2 ) p =0 −y

m

γyX ρ 

γXmh1 g2 Ωg2 + ρΩh1

j

Ωg0

Ωg3

Γ(mg0 )Γ(mg3 )(Γ(mg1 )Γ(mg2 ))j

⎤  jp −1   Γ(p1 + mg2 ) jp1 −jp1 +1 1 ⎣ ⎦ × j Γ(p + 1) p 1 1 p1 =1 jp =0 ⎡ 1 ⎤ jp2 −1  m −1 h2  jp −1   Γ(p2 + mg1 ) jp2 −jp2 +1 2 ⎣ ⎦ × j Γ(p2 + 1) p2 p2 =1 jp2 =0 jmg1  jmg2  mg2 ρΩh1 mg1 ρΩh2 × mh2 Ωg1 γ mh1 Ωg2 γ × Jjm ,σ ,m ,Ω , mg1 ρΩh2  Jjm ,σ ,m ,Ω , mg2 ρΩh1  . m h1 −1

jp1 −1

p2

g3

g3 m h2 Ωg1 γ

g2

p1

g0

g0 m h1 Ωg2 γ

(13)

p1 ! 

Similarly, the second term I2 is evaluated as  mg1 mg1 ρΩh2 1 I2 = Γ(mg1 ) mg1 ρΩh2 + γ|g3 |2 mh2 Ωg1  p2 m h2 −1 γY mh2 Ωg1 Γ(p2 + mg1 ) × . (9) Γ(p2 + 1) mg1 ρΩh2 + Ωg1 γY mh2 p =0 2

We derive the conditional CDF of the e2e SIR, γD , as shown in (10) on the next page, by substituting (8) and (9) into (7) and applying the binomial expansion [17, eq. (1.111)] and the multinomial expansion of [18] j p

x Γ(p + 1) ⎡ ⎤ jp −jp+1  p−1  N −1 j  N −1 jp−1 Γ(p + m) ⎣ ⎦ x p=1 jp = jp Γ(p + 1) p=1 j =0 p=0

p

(11) where j0 = a and jN = 0. Based on (6) and (10), the unconditional CDF of γD is derived according to  ∞ FγD (γ) = FγD (γ|X, Y ) fX (x) fY (y) dx dy. (12) 0

j=0

K  mg0 mg0  mg3 mg3

mh1 −1

dy p 1

1

N −1  Γ(p + m)

K (−1)j 

⎡

g1

y p1 +mg2 −1 e dy 0  mg2 mg2 ρΩh1 1 = Γ(mg2 ) mg2 ρΩh1 + γXmh1 Ωg2  p1 m h1 −1 γXmh1 Ωg2 Γ(p1 + mg2 ) × . (8) Γ(p1 + 1) mg2 ρΩh1 + Ωg2 γXmh1 p =0

×

FγD (γ) =



γXmh1 ρΩh1

1

which results in

mh2 −1

We define σp1  p1 =1 jp1 and σp2  p2 =1 jp2 and J(j,k,a,b,c) is given by  ∞ a+k−1 −at/b t e J(j,k,a,b,c)  dt, (14) j+k (t + c) 0 which can be evaluated as J(j,k,a,b,c) ⎧  b a Γ(a), ⎪ a ⎨ a−j  c Γ(−a+j)Γ(a+k) ac = 1 F1 a + k, 1 + a − j, b Γ(j+k) ⎪  ⎩ a−a+j Γ(a−j) ac + b−a+j 1 F1 j + k, 1 − a + j, b ,

j = 0, j ≥ 1, (15)

where Γ(a, x) is the upper incomplete gamma function [17, eq. (8.350.2)], and 1 F1 (a; b; z) is the hypergeometric function [17, eq. (9.100)]. Finally, our new expression for the CDF of the e2e SIR of cognitive opportunistic relay networks is given by (16) on the m m ρΩh1 m m ρΩh2 next page, where α1  mg2h1 Ωg0 and α2  mg1h2 Ωg3 . g0 Ωg2 g1 Ωg3 For the case of Rayleigh fading, the exact CDF of γD simplifies to   2  αn αn αγn FγD (γ) = 1 − K e E1 γ γ n=1     j   K 2  (−1)j αn K  αn αn j−1 γ (−1) + e E1 2 j γ γ n=1 j=2 (j − 1)!   i+1 j−2  αn i + , (17) (−1) (j − i − 2)! γ i=0 where E1(·) is the exponential integral function defined as ∞ −xt E1 (x) = 1 e t dt. With the CDF of γD in (16) and (17), we can easily calculate the exact outage probability, Pout , which is defined as the probability that γD falls below a predetermined threshold γth , i.e., Pout = Pr (γD < γth ) = FγD (γth ). To obtain deeper insights, we proceed to derive the asymptotic outage probability as Ip → ∞ and to examine the impact of the number of relays K, the PU-Tx transmit power γ¯I , and the PU-Rx interference power constraint Ip , on the system

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Fγ D

K    γ X, Y =

(−1)j

K



j

mg1 ρΩh2 mg1 ρΩh2 + γY mh2 Ωg1

jmg1 

mg2 ρΩh1 mg2 ρΩh1 + γXmh1 Ωg2

jmg2

(Γ(mg1 )Γ(mg2 ))j ⎡ ⎤ h1 −1 j jp1 −1   m m h1 −1 p1 p1 =1  jp −1   Γ(p1 + mg2 ) jp1 −jp1 +1  Ω γXm h1 g2 1 ⎣ ⎦ × jp1 Γ(p1 + 1) mg2 ρΩh1 + Ωg2 γXmh1 p1 =1 jp =0 ⎡ 1 ⎤ h2 −1 j jp2 −1  m m h2 −1 p2 p2 =1  jp −1   Γ(p2 + mg1 ) jp2 −jp2 +1  Ω γY m h2 g1 2 ⎣ ⎦ × jp2 Γ(p2 + 1) mg1 ρΩh2 + Ωg1 γY mh2 p =1 j =0 j=0

2

(10)

p2

K 

K

(α1 /γ)mg0 (α2 /γ)mg3 mh1 −1 mh2 −1 j p1 =1 jp1 )Γ(jmg1 + p2 =1 jp2 ) j=1 Γ(mg0 )Γ(mg3 )(Γ(mg1 )Γ(mg2 )) Γ(jmg2 + ⎡ ⎤ ⎡ ⎤ jp1 −1  jp2 −1  m h1 −1 h2 −1  jp −1   Γ(p1 + mg2 ) jp1 −jp1 +1 m  jp −1   Γ(p2 + mg1 ) jp2 −jp2 +1 1 2 ⎣ ⎦ ⎣ ⎦ × j Γ(p + 1) j Γ(p + 1) p 1 p 2 1 2 p1 =1 p =1 jp1 =0 jp2 =0 2      m m h1 −1 h1 −1 α1 × Γ mg0 + jp1 Γ(jmg2 − mg0 )1 F1 mg0 + jp1 ; 1 + mg0 − jmg2 ; γ p1 =1 p1 =1    jmg2 −mg0 m h1 −1 α1 α1 Γ(mg0 − jmg2 )1 F1 jmg2 + jp1 ; 1 + jmg2 − mg0 ; + γ γ p1 =1      m m h2 −1 h2 −1 α2 jp2 Γ(jmg1 − mg3 )1 F1 mg3 + jp2 ; 1 + mg3 − jmg1 ; × Γ mg3 + γ p2 =1 p2 =1    jmg1 −mg3 m h2 −1 α2 α2 (16) Γ(mg3 − jmg1 )1 F1 jmg1 + jp2 ; 1 + jmg1 − mg3 ; + γ γ p =1

FγD (γ) =1 +

(−1)j

j

2

FγD (γ) =

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

Γ(Kmh1 +mg0 ) Γ(mg0 )

 

(mg2 +mh1 −1)! mh1 !(mg2 −1)!

K  K 

mh1 Ωg2 Ωg0 mg2 Ωh1 mg0

Kmh1  Kmh2 

γγ ¯I Ip

Kmh1 Kmh2

 + o Ip−Kmh1 ,  + o Ip−Kmh2 ,

Γ(Kmh2 +mg3 ) (mg1 +mh2 −1)! mh2 Ωg1 Ωg3 γγ ¯I Γ(mg3 ) mh2 !(mg1 −1)! mg1 Ωh2 mg3 Ip  Kmh1  K K Γ(mh1 j+mg0 )Γ(mh2 (K−j)+mg3 ) γγ ¯I j=0 j Ip Γ(mg0 )Γ(mg3 )  mh1 j   mh2 K−j  (mg2 +mh1 −1)! mh1 Ωg2 Ωg0 (mg1 +mh2 −1)! mh2 Ωg1 Ωg3 × mh1 !(mg2 −1)! mg2 Ωh1 mg0 mh2 !(mg1 −1)! mg1 Ωh2 mg3

I

performance. To do so, we first substitute ρ = γ¯Ip into the conditional CDF in (10) and thereafter apply the McLaurin series ∞  expansion for polynomials, e.g., (1+βx)−1 = (−1)k β k xk . k=0

We then substitute the asymptotic conditional CDF into (12) and after some mathematical manipulations, we derive a new simple closed-form expression for the asymptotic CDF of γD given in (18). For Rayleigh fading, the asymptotic CDF of γD reduces to K  K   γ¯ γI Ωg2 Ωg0 Ωg1 Ωg3 FγD (γ) = K! + + o Ip−K . Ωh1 Ωh2 Ip (19) From the asymptotic expressions in (18) and (19), we can

mh1 < mh2 , mh1 > mh2 ,

 + o Ip−Kmh1 , mh1 = mh2 (18)

extract the diversity gain, Gd , and array gain, Ga , of cognitive opportunistic relaying as:  −G Pout = (Ip Ga ) d + o Ip−Gd . (20) Remark 1: When the PU-Tx interference power γ¯I is fixed and independent of Ip , we observe that cognitive opportunistic relaying achieves a full diversity order which is equal to the product of the number of relays and the minimum fading parameter between the S → Rk and Rk → D links, i.e., Gd = K min(mh1 , mh2 ). Remark 2: When the PU-Tx interference power γ¯I is proportional to Ip , i.e., γ¯I = Ip with  being a fixed constant 0 <  < 1, the diversity gain diminishes to zero and the network exhibits an error floor across the whole range of Ip .

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0

0

10

10

−1

10

−1

10

K

mh1= mh2 = 1 2 3

−2

10 −2

10

−3

10

−3

−4

10

10

−5

10

−4

10

−6

10

Asymptotic Exact

−5

10

Simulation −6

10

0

Asymptotic Exact

−7

10

Simulation

−8

5

10

15

IP

20

25

10

30

5

10

15

20

25

30

IP

Fig. 2. Outage probability of opportunistic relaying versus Ip with K = 1, 2, 3, and γ ¯I = 5 dB.

Lemma 1: Based on our asymptotic CDF, we derive the DMT of cognitive opportunistic relay networks as − log Pout Gd (r) = lim Ip →∞ log Ip

K min(mh1 , mh2 )(1 − 2r), = 0,

0

γ¯I =  Ip , γ¯I = Ip ,

(21)

where r denotes the normalized transmission rate with respect to the channel capacity (the proof is omitted here due to space limits). Based on (21), we see that cognitive opportunistic relaying achieves the maximum diversity of Gd = K min(mh1 , mh2 ) when r → 0 and γ¯I is independent of Ip . Moreover, the maximum normalized transmission rate of r = 1/2 is obtained when Gd → 0, which is the direct consequence of the halfduplex relay mode. When γ¯I is directly proportional to Ip , we note that the DMT is zero due to the loss of diversity gain. IV. N UMERICAL E XAMPLES Numerical examples are provided to highlight the impact of key system parameters and the user locations on the outage probability of cognitive opportunistic relay networks. In the examples, we consider a simple two dimensional network topology where the SUs, S, Rk , and D are placed along the x-axis, with S located at (0, 0), D located at (1, 0), and the relays Rk clustered between S and D at (dR , 0) with 0 < dR < 1. We assume an exponential decay path loss model where the channel mean power is proportional to d−ν with d denoting the distance between the transceivers, ν = 3 denoting the path loss coefficient, and the variance of the S → D link is normalized to unity. The variance of the remaining links are determined by their respective user locations, e.g., Ωg1 = ((dP Rx − dR )2 + d2P Ry )−3/2 and Ωg2 = ((dP Tx − dR )2 + d2P Ty )−3/2 , where (dP Tx , dP Ty ) and

Fig. 3. Outage probability of opportunistic relaying versus Ip with mh1 = ¯I = 5 dB. mh2 = 1, 2, 3 and γ

(dP Rx , dP Ry ) are the coordinates of the PU-Tx and PU-Rx, respectively. The outage threshold is set to γth = 10 dB. In the plots, the solid lines represent the exact outage probability derived in (16), the dashed lines represent the asymptotic outage probability derived in (18), and ‘+’ denote the simulation points. We see in all the figures that there is a good agreement between our analytical results and the simulations. Figs. 2 and 3 plot the outage probability versus the peak interference constraint at the PUs, Ip . We set the coordinates of the PU-Tx, PU-Rx, and relay cluster to (1, 1), (0, 1), and (0.5,0), respectively. In Fig. 2, we consider the scenario where the fading in the secondary network is more severe than the fading between the SUs and the PUs, with mh1 = mh2 = 1 and mg0 = mg1 = mg2 = mg3 = 2. The figure clearly illustrates the impact of the number of relays on the outage probability which decreases with increasing K. In Fig. 3, we consider the scenario where the fading between the SUs and the PUs is more severe than the fading in the secondary network with mg0 = mg1 = mg2 = mg3 = 1. We see that the outage probability also decreases with increasing mh1 and mh2 . Based on Figs. 2 and 3, we can conclude that the diversity order is determined by the number of relays, K, and the secondary network fading parameters mh1 and mh2 . Figs. 4 and 5 plot the outage probability versus the distance between the source and the relays, dR . In Fig. 4, we set the coordinates of the PU-Tx and PU-Rx to (1, 1), and (0, 1), respectively, and examine the impact of different mh1 and mh2 . We see that the outage probability varies considerably depending on the location of the relay. Interestingly, we observe that the optimal relay location for the case (mh1 = 1, mh2 = 3) is symmetrical to the case (mh1 = 3, mh2 = 1) around dR = 0.5. In Fig. 5, we set mh1 = mh2 = 2 and examine the impact of different PU-Tx and PU-Rx locations.

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10

−1

Exact



Simulation

 10

−2

10

−3

10

−4

PU-Tx = (1, 1) PU-Rx = (0, 1)

   


   

   

PU-Tx = (2, 1) PU-Rx = (1, 1)

PU-Tx = (0, 1) PU-Rx = (-1, 1)





























10




−5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

dR

Fig. 4. Outage probability of opportunistic relaying versus dR with K = 3, ¯I = 5 dB. mg0 = mg1 = mg2 = mg3 = 1, Ip = 10 dB, and γ

Fig. 5. Outage probability of opportunistic relaying versus dR with K = 3, ¯I = 5 dB. Ip = 10 dB, and γ

We conclude that the optimal relay location is determined by the secondary network fading parameters mh1 and mh2 , and the location of the primary transceivers relative to the secondary users. V. C ONCLUSIONS We derived new closed-form expressions for the exact and asymptotic outage probability of opportunistic relaying in cognitive spectrum sharing networks. We examined the impact of primary and secondary interference where the PU-Tx and PU-Rx co-exist in the same frequency band as the SU source, SU relays, and SU destination. Our results are valid for independent Nakagami-m fading in the primary and secondary networks. The presented analytical results allow us to investigate the diversity gain, array gain, and DMT of cognitive opportunistic relaying. An important result of our analysis is that, when the primary interference power γ¯I is fixed and independent of the peak interference constraint Ip , a full diversity order of Gd = K min(mh1 , mh2 ) is achieved.

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