Exact outage probability of cognitive AF relaying with underlay spectrum sharing T.Q. Duong, V.N.Q. Bao and H.-J. Zepernick The exact closed-form expression for the outage probability (OP) of cognitive radio dual-hop amplify-and-forward (AF) relay networks is derived. The tractable expression of the OP, given in the form of elementary functions, readily enables evaluating the effect of primary users on the secondary system performance. It has been shown that the use of AF relaying significantly improves the performance of cognitive radio networks compared to its direct transmission counterpart.

Introduction: Cognitive radio with spectrum sharing has significantly improved spectrum efficiency by allowing secondary users (SUs) to simultaneously share the frequency band licensed to primary users (PUs) without causing any harmful interference on PUs. The performance analysis for cognitive radio with applications to relay networks has gained much attention in the research community [1–8]. In particular, the outage probability for cognitive decode-and-forward (DF) relay networks has been presented in [1–3]. Recently, the issue of relay selection for cognitive DF relay networks has been addressed in [4–7]. It is important to note that all of the above-mentioned works, i.e. [1–7], only considered DF relays. Very recently, the authors in [8] have taken into account the amplify-and-forward (AF) relays to investigate the performance of cognitive relay networks. However, this analysis utilised the bounded signal-to-noise ratio (SNR), i.e. the end-to-end SNR for AF relays is approximated as the minimum SNR among the two hops. As a result, the problem to investigate cognitive AF relay networks equivalently becomes opportunistic DF relays. More importantly, the analysis in [8] has been conducted for the high SNR regime, which is not appropriate for cognitive networks with underlay spectrum sharing (requiring an acceptable level of interference on PUs). To the best of our knowledge, there has been no previous works considering the performance of cognitive AF relay networks. Inspired by all of the above, in this Letter, we derive the exact outage probability for cognitive AF relay networks over non-identical Rayleigh fading channels. Our final outage expression is given in a compact form and validated by Monte-Carlo simulations. Utilising the analytical expression, we can evaluate the impact of PUs on SUs’ systems and highlight the advantage of using AF relays for cognitive radio networks over direct transmission. interference link

data link PU

h s,p

SUTx

h s,r

h r,p SURelay

h r,d

SURx

Fig. 1 System model for cognitive amplify-and-forward relay networks

System and channel model: We consider a dual-hop spectrum-sharing system with the coexistence of PUs and SUs by sharing the same narrowband frequency as shown in Fig. 1. In the secondary network, for the first hop transmission, the SU transmitter (SU-Tx) sends signal x to the SU relay (SU-Relay). To ensure that the SU transmission does not cause any harmful interference on PUs, the transmit power at SU-Tx Ps is set at Ps = I p /|hs,p |2 , where I p is the maximum tolerable interference power at PU and hs,p is the channel coefficient of the link from SU-Tx to PU. As a result, the received signal at the SU-Relay is given by yr = hs,r x + nr , where hs,r is the channel coefficient for the link from SU-Tx to SU-Relay and nr is additive white Gaussian noise (AWGN). Then, the received signal at SU-Relay is amplified with variable gain G and forwarded to the SU receiver (SU-Rx). Due to power constraint, the SU-Relay should limit its transmitted power to PR = I p /|hr,p |2 , where hr,p is the channel coefficient from SU-Relay to PU. The received signal at SU-Rx is given by yd = Ghr,d hs,r x + Ghr,d nr + nd , where nd is AWGN at the SU-Rx. In this Letter, we consider non-identical Rayleigh fading for all links in which the channel power gain |hu,v|2 is exponentially distributed with E{|hu,v|2} ¼ Vu,v, where u [ {s, r}, v [ {r, p, d}, and

E{.} denotes the expectation. We further assume that all AWGN components have zero mean and variance N0. To derive the amplifying gain G, we utilise the fact that PR = G2 (|hs,r |2 PS + N0 ). Since PS = I p /|hs,p |2 and PR = I p /|hr,p |2 , we can obtain G from the following   |hs,r |2 N0 + . The end-to-end SNR at SU-Rx expression 1/G2 = |hr,p |2 |hs,p |2 I p after the maximum likelihood decoding can be expressed as

gd =

I p |hs,r |2 I p |hr,d |2 N0 |hs,p |2 N0 |hr,p |2

G |hr,d | |hs,r | PS = G2 |hr,d |2 N0 + N0 I p |hs,r |2 I p |hr,d |2 + +1 N0 |hs,p |2 N0 |hr,p |2 2

2

2

(1)

Exact outage probability analysis: It is important to note that the exact SNR expression given in (1) has not appeared in the literature. For g1 g2 , where notational simplification, we write (1) as gd = g + g2 + 1 1 I p |hs,r |2 I p |hr,d |2 g1 = and g2 = . To obtain the statistical characterN0 |hs,p |2 N0 |hr,p |2 istics of gd , we need to find the probability density function (PDF) fgn( g) and cumulative distribution function (CDF) Fgn ( g) for n [ X {1, 2}. In other words, we need to find the PDF and CDF of Z = a , Y where a is a positive constant; X and Y are two exponentially distributed random variables with parameters Vx and Vy , respectively. The CDF of 1 yz fY (y)dy = 1 − (1 + lz)−1 , Z can be obtained from FZ (z) = 0 FX a Vy where l = . Taking the derivative of Fz (z) with respect to z aVx yields fZ (z) = l(1 + lz)−2 . to derive the CDF With the obtained statistics for gn , we  are now able  1 gg2 + g of gd as Fgd (g) = Fg2 (g) + g Pr g1 ≤ fg2 (g2 )d g2 . By g2 − g applying the change of variable t = g2 − g for the integral, after some algebraic manipulations, the CDF of gd can be given by 1 l2 tdt (2) F gd (g ) = 1 − 2 0 [l1 g(g + 1) + (1 + l1 g)t](1 + l2 g + l2 t) where l1 = (I p Vs,p )/(Vs,r N0 ) and l2 = (I p Vr,p )/(Vr,d N0 ). To proceed further the calculation, we need to solve the following integral 1 w(x)dx I= 0 , where w(x) = b4 x, c(x) = (b2 + b1 x)(b3 + b4 x)2 , and c(x) b1 , b2 , b3 , b4 . 0. To do so, let us rewrite the integrand of I into the partial expansion as follows:

w(x) 1 A1 B1 B2 = + + (3) c(x) b1 b4 (x + b2 /b1 ) (x + b3 /b4 ) (x + b3 /b4 )2 where A1 , B1 , and B2 are partial coefficients given by −b2 /b1 b2 /b1 b3 /b4  A1 =   , B1 =   , B2 =  b3 b2 b3 b2 2 b3 b2 2 − − − b4 b1 b4 b1 b4 b1 which then yields,   bb b2 b4 ln 2 4 1 b1 b3 + I= b1 b3 − b2 b4 (b1 b3 − b2 b4 )2

(4)

Finally, from (4) and (2), the CDF of gd can be obtained in closed-form expression as follows: Fgd (g) = 1 −

1 (1 + l1 g)(1 + l2 g) − l1 l2 g(g + 1)

l1 l2 g(g + 1) [(1 + l1 g)(1 + l2 g) − l1 l2 g(g + 1)]2

l1 l2 g(g + 1) × ln (1 + l1 g)(1 + l2 g)



(5)

The outage probability Pout is defined as the probability that the endto-end SNR gd falls below a given threshold gth. As a result, we have Pout ¼ Fgd ( gth), which immediately follows from (5).

ELECTRONICS LETTERS 18th August 2011 Vol. 47 No. 17

Numerical results: We consider a linear dual-hop AF relay network in a 2D plane, where all SUs are located in a straight line. Furthermore, the SU-Tx and SU-Rx are located at co-ordinates (0,0) and (1,0), respectively, and their distance is normalised to one. The SU-Relay node is placed half-way between SU-Tx and SU-Rx, i.e. ds,r = dr,d = 1/2. The pass loss of each link follows an exponential-decay model. In other words, the average channel power for the transmission between e node u and node v is modelled as Vu,v = 1/du,v where e denotes the path loss exponent with u [ {s, r} and v [ {p, r, d}. For a typical non-line-of-sight propagation model, we can set e ¼ 4. To evaluate the effect of PU on SU’s networks, we consider three different scenarios in which PU is located at different co-ordinates (0.44, 0.44), (0.55, 0.55), and (0.66, 0.66). We also compare the performance of cognitive AF relay networks and conventional cognitive radio networks, i.e. only direct transmission from SU-Tx to SU-Rx. Hence, it is convenient to provide the outage probability for cognitive radio with direct transmission as (detailed derivations are omitted here due to space limitation) (DT) = Pout

gth I p Vs,d gth + N0 Vs,p

(6)

100

outage probability

PU(0.55,0.55) exact closed-form simulation direct transmission

10–1 PU(0.66,0.66)

10–2

–15

γ th = 1 dB

PU(0.44,0.44) exact closed-form simulation direct transmission

–10

–5

5 0 Ip /N0, dB

Acknowledgment: This research was supported by the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) (No. 102.99-2010.10). # The Institution of Engineering and Technology 2011 25 May 2011 doi: 10.1049/el.2011.1605 One or more of the Figures in this Letter are available in colour online. T.Q. Duong and H.-J. Zepernick (Blekinge Institute of Technology, Karlskrona, Sweden) E-mail: [email protected]

As can be observed from Fig. 2, the analytical results obtained from the exact closed-form outage probability given in (5) match very well with simulations, which validates our analysis. For comparison, the performance of cognitive AF relaying substantially outperforms that of direct transmission for all three examples. Approximately, by using the AF relay, a gain of 4.5 dB can be obtained compared to the direct transmission. In addition, the position of PU significantly affects the performance of SU’s networks. The best performance can be achieved for the case when PU is located at co-ordinate (0.66,0.66), in which the minimum interference power on PU is satisfied among the three representative scenarios.

exact closed-form simulation direct transmission

Conclusion: We have derived the exact closed-form expression for the outage probability of cognitive AF relay networks under interference power constraint. Our analytical results are valid for non-identical Rayleigh fading channels and provide a powerful tool to assess the effect of PU on the performance of cognitive radio networks with relaying assistance. It has been certified that the dual-hop relaying is a promising candidate for cognitive radio networks since its performance surpasses the conventional cognitive radio direct transmission.

10

15

20

V.N.Q. Bao (Posts and Telecommunications Institute of Technology, Vietnam) References 1 Luo, L., Zhang, P., Zhang, G., and Qin, J.: ‘Outage performance for cognitive relay networks with underlay spectrum sharing’, IEEE Commun. Lett., 2011, 15, (7), pp. 710–712 2 Guo, Y., Kang, G., Zhang, N., Zhou, W., and Zhang, P.: ‘Outage performance of relay-assisted cognitive-radio system under spectrumsharing constraints’, Electron. Lett., 2010, 46, (2), pp. 182 –184 3 Yan, S., Wang, X., and Zhang, H.: ‘Performance analysis of the cognitive cooperative scheme based on cognitive relays’. IEEE Int. Conf. on Communications Workshops, (ICC), Cape Town, South Africa, May 2010 4 Lee, J., Wang, H., Andrews, J.G., and Hong, D.: ‘Outage probability of cognitive relay networks with interference constraints’, IEEE Trans. Wirel. Commun., 2011, 10, (2), pp. 390– 395 5 Li, L., Zhou, X., Xu, H., Li, G.Y., Wang, D., and Soong, A.: ‘Simplified relay selection and power allocation in cooperative cognitive radio systems’, IEEE Trans. Wirel. Commun., 2011, 10, (1), pp. 33– 36 6 Si, J., Li, Z., Chen, X., Hao, B., and Liu, Z.: ‘On the performance of cognitive relay networks under primary user’s outage constraint’, IEEE Commun. Lett., 2011, 15, (4), pp. 422–424 7 Asghari, V., and Aissa, S.: ‘Cooperative relay communication performance under spectrum-sharing resource requirements’. IEEE Int. Conf. on Communications, (ICC), Cape Town, South Africa, May 2010 8 Ding, H., Ge, J., Costa, D.B.d., and Jiang, Z.: ‘Asymptotic analysis of cooperative diversity systems with relay selection in a spectrum sharing scenario’, IEEE Trans. Veh. Technol., 2011, 60, (2), pp. 457–472

Fig. 2 Outage probability of cognitive amplify-and-forward relay networks

ELECTRONICS LETTERS 18th August 2011 Vol. 47 No. 17

Exact outage probability of cognitive AF relaying with ...

Foundation for Science and Technology Development (NAFOSTED). (No. ... V.N.Q. Bao (Posts and Telecommunications Institute of Technology,. Vietnam).

217KB Sizes 0 Downloads 216 Views

Recommend Documents

Exact outage probability of cognitive AF relaying with ...
harmful interference on PUs, the transmit power at SU-Tx Ps is set at. Ps = Ip/|hs,p|2, where Ip is the maximum tolerable interference power at PU and hs,p is the ...

Outage Probability of Selection Relaying Networks with ...
Email: [email protected], [email protected]. Vo Nguyen Quoc Bao. Wireless Communication ... incremental relaying, decode-and-forward, Rayleigh fading, out- age probability. I. INTRODUCTION. It is well ... ing techniques at relays, including

Cognitive Multiple-Antenna Network with Outage and Rate Margins at ...
Content may change prior to final publication. Citation information: DOI. 10.1109/TVT.2014.2345588, IEEE Transactions on Vehicular Technology. 1. Cognitive Multiple-Antenna Network with Outage and Rate Margins at the Primary System. Behrouz Maham, Me

Cognitive Amplify-and-Forward Relaying with Best ...
community with the aim to alleviate the spectrum scarcity problem and, at the same time, to support the fast growing demand for wireless applications. ... This research was supported by Vietnam's National Foundation for Science and Technology Develop

On the performance of Outage Probability in Underlay ...
are exponential random variables. (RVs) with parameter ij. For example, the data link between. S and D denoted by ℎsd has the parameter sd. To facilitate.

On Outage and Interference in 802.22 Cognitive Radio ... - Leeds
works(CRNs) are capable of utilizing the scarce wireless specturm ... for profit or commercial advantage and that copies bear this notice and the full citation.

On Outage and Interference in 802.22 Cognitive Radio ...
interference free transmission. This is .... Or an alternative definition can be given as,. PP N ... tually generated by MATLAB simulation of expression derived in.

Relaying with Selection Combining
idea is that relay terminals in a rnulti-user network effectively form a virtual multiple-input multiple-output (MIMO) channel to assist the source-destination ...

Relaying with Selection Combining
protocol offers remarkable diversity advantage over direct trans- mission as well as .... We consider a wireless relay network consisting of one source. K relays ...

Isotropic Remeshing with Fast and Exact Computation of ... - Microsoft
ρ(x)y−x. 2 dσ. (4). In practice we want to compute a CVT given by a minimizer of this function instead of merely a critical point, which may be a saddle point. If we minimize the same energy function as in .... timization extra computation is nee

New Exact Solution of Dirac-Coulomb Equation with ... - Springer Link
Sep 19, 2007 - brings on that the solutions of the Klein-Gordon equation and the Dirac ... and its magnetic moment in a completely natural way and so on.

Exact Bit Error Probability of Multi-hop Decode-and ...
sion for M-PSK is presented for multi-hop Decode-and-Forward Relaying. (MDFR) scheme, in ... and transmit jointly as a virtual antenna array. This enables them ... (MRC) or selection combining (SC) have been published [2-9]. In particular, in.

Incremental Relaying with Partial Relay Selection - Semantic Scholar
May 5, 2010 - fer from one disadvantage—a loss in spectral efficiency as multiple orthogonal ... We consider a wireless relay network consisting of one source (S), N relays .... communication link whose equivalent SNR is written as fol- lows: .....

Zero-Forcing-Based Two-Phase Relaying with Multiple Mobile Stations
where hk is an (N × tk)-dimensional channel matrix or a vector between the kth MS and the BS. Here, tk denotes the number of data streams that is allocated to ...

Outage Performance of Multi-Antenna Cooperative Incremental ...
Email: [email protected] ... the link from source to destination while the other locates near ... as an incremental link, and this system is referred to as.

Incremental Relaying with Partial Relay Selection - Semantic Scholar
May 5, 2010 - 2. System Model. We consider a wireless relay network consisting of one ..... schemes, the advantage of IRPRS schemes is the improve-. Fig. 2.

Buffer-Aided Two-Way Relaying with Lattice Codes - IEEE Xplore
relaying with lattice codes to improve the sum-rate in asymmetric SNR two-way relay channels (TWRCs). Specifically, the relay can store some amount of data.

tower - af -
Reticulated gas system. Laundromats ... Fiber to Home (FTTH) system for telephone connectivity ... CCTV monitoring in basements car park and at entry levels in ...

Zero-Forcing-Based Two-Phase Relaying with Multiple ...
†Institute for Information Technology Convergence. Korea Advanced Institute of Science and Technology, Daejeon, Korea. Email: [email protected].

On Uplink Virtual MIMO with Device Relaying Cooperation ...
autonomously punish malicious MTs, the malicious MTs cannot gain by defecting from relaying other MTs' data. Index Terms—5G cellular network, virtual MIMO, ...

Two-Way Relaying with Multiple Antennas using ...
and-forward relaying using physical layer network coding. So far, the design of the relay .... Computer simulations are used to compare the performance of the ...