Effect of primary network on performance of spectrum sharing AF relaying T.Q. Duong, V.N.Q. Bao, H. Tran, G.C. Alexandropoulos and H.-J. Zepernick Most of the research in spectrum sharing has neglected the effect of interference from primary users. In this reported work, the performance of spectrum sharing amplify-and-forward relay networks under interference-limited environment, where the interference induced by the transmission of primary networks is taken into account, is investigated. In particular, a closed-form expression tight lower bound of outage probability is derived. To reveal additional insights into the effect of primary networks on the diversity and array gains, an asymptotic expression is also obtained.

the fading channel coefficients h1 , h2 , g1 , g2 , f1 , f2 are complex Gaussian distributed with zero mean and variances Vh1 , Vh2 , Vg1 , Vg2 , Vf1 , Vf2 , respectively, and AWGN components nr , nd have the same variance of N0. The signal-to-interference ratio at SU-Tx is obtained as

gAF

SU

SU

SU: SU

I

SU-Tx

PU-Tx

g1

SU relay

f1

h2

2

I 2

lx u

lx u

lx u

gamma function [5, equation (8.350.2)]. As a result, the CDF of gAFup , i.e. FgAFup ( g) ¼ 1 2 [1 2 Fg1 ( g)] [1 2 Fg2 ( g)], can be written as    Vh g 1 Vh1 Vh2 g  I Vg1 Vf g g 1 e FgAFup (g) = 1 2 I Vg1 Vf 1 Vg2 Vf 2 g2 g     g  Vh 2 Vh1 g  I Vg2 Vf g g (2) 2 G 0, ×e I Vg1 Vf 1 g g   Vh2 g × G 0, I Vg2 Vf 2 g g

M −1 (−1) m! + given by [5, equation (8.357.1)] G(0, x) = x−1 e−x Sm=0 xm m

g2 f2

I 1

X where X, Y, and Z are exponentially distributed the CDF of U = YZ random variables with parameters lx , ly , and lz , respectively.  It is 1 easy to see that the CDF of U can be obtained as FU (u) ¼ 1 0 0 FX (uyz) fY ( y) fZ (z) dydz. Here, the CDF and probability density function (PDF) of W [ {X, Y, Z} are written as FW (w) ¼ 1 2 e 2lww and fW (w) ¼ lwe 2lww for lw [ {lx , ly, lz}. After some simple calculations, the CDF of U can be easily derived as ll ll ll FU (u) = 1 − y z exp y z G 0, y z , where G (., .) is the incomplete

The lower bound for OP, Pout , can be immediately obtained from (2) utilising the fact that Pout ¼ FgAFup( gth), where gth is an outage threshold. The asymptotic representation of G(a, x) for large value  of |x| can be

SU:

PU:

h1

(1)

 = Np0 and (1) is obtained by considering the interference-limited where g I = NPI0 . To start our analysis, let us introduce an upper environment, i.e. g bound for gAF given in (1) as gAF ≤ gAFup ¼ min ( g1 , g2) with 2 2 g1 = |g g|2|hg1 ||f |2 and g2 = |g g|2|hg2 ||f |2 To obtain the OP, we need to derive 1

Introduction: Spectrum sharing relay networks have recently attracted much attention for providing higher reliability over direct transmission under scarce and limited spectrum conditions [1 – 4]. Specifically, the performance of decode-and-forward (DF) relay networks in spectrum sharing environments has been reported [1 –3]. Recently, we have investigated the outage probability (OP) for spectrum sharing networks with amplify-and-forward (AF) relaying [4]. It has been shown in [1– 4] that utilising DF/AF relaying significantly enhances system performance in such constrained transmission power conditions. However, most of the previous works have neglected the effect of the primary transmitter (PU-Tx), which significantly deteriorates the performance of the secondary network. In this Letter, to evaluate this interference effect, we derive a closed-form expression for OP and further calculate an asymptotic expression. We show that under fixed interference from primary networks, the diversity order remains unchanged and the loss only occurs in the array gain, which is theoretically quantified. However, when the interference is linearly proportional to the signal-to-noise ratio (SNR) of the secondary network, the system is severely affected, leading to an irreducible error floor of OP.

|h1 |2 |h2 |2 g g 2 2 I |f1 | |g2 |2 g I |f2 |2 |g1 | g = 2 |h1 | |h2 |2 g g + +1 2 2 |g1 | g I |f1 | |g2 |2 g I |f2 |2

SU-Rx

PU-Rx

Fig. 1 System model for spectrum sharing AF relay network considering interference from PU-Tx

System model and outage probability analysis: Consider an underlay cognitive network where a secondary transmitter (SU-Tx) communicates with a secondary receiver (SU-Rx) through the assistance of a secondary relay (SU-relay) in co-existence with a primary network, as shown in Fig. 1. The transmit powers at the SU-Tx and the SU-relay are constrained so that their transmission will not cause any harmful interference to the PU-Rx, which is defined by the maximum tolerable interference power Ip. In the first hop, the SU-Tx transmits its signal, I s, to the SU-relay under the power constraint that Ps = |g p|2 , where g1 is 1 the channel coefficient for the link SU-Tx  PU-Rx. The received by the transmission of the PU-Tx, signal at the SU-relay, √ yr , impaired √ is given by yr = Ps h1 s + P1 f1 x1 + nr , where h1 is the channel coefficient for the link SU-Tx  SU-relay, PI is the average transmit power at the PU-Tx, x1 is the transmitted signal of the PU-Tx in the first time slot, and nr is additive white Gaussian noise (AWGN) at the SU-relay. Without loss of generality, we assume that E{|s|2 } = E{|x1 |2 } = 1, where E{·} is the expectation. Then, the SU-relay amplifies yr with an amplifying gain G and transmits the resulting signal to the SU-Rx I with the average power PR = |g p|2 , where g2 is the channel coefficient 2 for the link SU-relay  PU-Rx. Owing to the concurrent transmission of the√ PU-Tx, the received signal can be written as √at the SU-Rx√ yd = Ps Gh2 h1 s + Gh2 nr + Gh2 PI f1 x1 + nd + PI f2 x2 , where h2 and f1 are the channel coefficients for the links SU-relay  SU-Rx and PU-Tx  SU-Rx, respectively, x2 is the transmitted signal of the PU-Tx with E{|x2 |2 } = 1, and nd is AWGN at the SU-Rx. In this work, we consider non-identical Rayleigh fading in which all

O(|x|−M )], M = 1, 2, . . . , 1. By substituting this result into (2) and neglecting small terms, we obtain   1 Vg Vf 1 g Vg Vf g I gth 1 + 2 2 (3) Pout ≃  Vh1 Vh2 g For comparison, we also derive an asymptotic expression for the case of neglecting the effect of the PU-Tx in [4], i.e. in the absence I , Vf 1 , and Vf 2 . The lower bound for OP is shown as (detailed of g proof is omitted here due to space limitation)  −1  −1 Vg1 Vg2 1 + Vh g gth . Then, applying the Pout = 1 − 1 + Vh g gth 1

2

k k k McLaurin series expansion for (1 + ax)21 ¼ S1 k¼0(21) a x , after some manipulations and ignoring small terms, the asymptotic OP of the system in [4] is shown as   g 1 Vg Vg gth 1 + 2 (4) Pout ≃  Vh1 Vh2 g

From (3), i.e. in the presence of the PU-Tx, and (4), i.e. in the absence of the PU-Tx, we observe that under a fixed g I , the two systems have the same diversity order. However, the array gain   is reduced by an amount of G1 = 10 log10

(Vg1 Vf 1 Vh2 +Vg2 Vf 2 Vh1 ) gI Vg1 Vh2 +Vg2 Vh1

. When the inference

I , is linearly proportional to the average SNR, i.e. from the PU-Tx, g g  where r is a positive constant, the OP in (2) becomes  I = rg  g 1, g I =r g   Vg Vf V V . This ≃ r V1 h 1 + gV2 h f 2 gth , which is independent of g Pout 1

2

causes an error floor in the OP for the whole SNR range yielding zero diversity order. Numerical results: Similarly as in [4], a linear network topology is assumed here where the SU-Tx, the SU-relay, and the SU-Rx are located at co-ordinates (0,0), and (1,0), respectively. The average channel power for the link between node A and B, V0 , is inversely proportional to the distance from A to B, d0 , i.e. V0 = d14 for a shadowed 0

ELECTRONICS LETTERS 5th January 2012 Vol. 48

No. 1

urban cellular radio, where A, B [ {SU-Tx, SU-relay, SU-Rx, PU-Tx, PU-Rx}. The outage threshold gth is set to 3 dB for all examples. Fig. 2 displays the OP performance for PU-Rx(0.5,0.5) and g¯ I ¼ 2 dB. Here, we consider three different scenarios where the location of the PU-Tx is set to (0.7, 0.7), (0.8, 0.8), and (0.9, 0.9). As expected, the performance increases when the PU-Tx moves away from the secondary network, i.e. (0.7, 0.7)  (0.8, 0.8)  (0.9, 0.9). The analysis matches very well with the simulation and the asymptotic result tightly converges to the exact value, which validates the proposed analysis. To understand the impact of the PU-Tx on the system performance I . better, Fig. 3 shows OP for different values of the interference power g I being independent of the average SNR g , i.e. g I = 2, 4 In the case of g I degrades the array gain but not the diversity gain. 6 dB, increasing g The PU-Tx has a major impact on the secondary network since the performance loss of more than 10 dB is observed in the case of the interferI = 2 dB compared to the scenario without the PU-Tx. More ence of g I = 0.5 I = 0.1 g and g g, the performance is significantly severely, as g reduced owing to the error floor for the considered SNR range.

Conclusion: The effect of the primary network on spectrum sharing AF relaying has been investigated in this Letter. Closed-form and asymptotic expressions for OP have been derived for non-identical Rayleigh fading channels. It has been shown that under a fixed interference from the primary network, the diversity order of the secondary network is not affected but only the array gain. However, when the interference power is dependent on the average SNR of the secondary network, it is infeasible to operate the secondary system as an irreducible error floor exists for the whole SNR regime. # The Institution of Engineering and Technology 2012 13 October 2011 doi: 10.1049/el.2011.3151 T.Q. Duong, H. Tran and H.-J. Zepernick (Blekinge Institute of Technology, Sweden) E-mail: [email protected] V.N.Q. Bao (Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam) G.C. Alexandropoulos (Athens Information Technology, Athens, Greece)

100 Pu-Tx(0.7,0.7)

References

outage probability

gth = 3 dB 10–1

Pu-Rx(0.5,0.5)

Pu-Tx(0.8,0.8) 10–2

analysis simulation asymptotic 0

5

10

Pu-Tx(0.9,0.9) 15 SNR, g, dB

20

25

30

Fig. 2 Performance comparison for different positions of PU-Tx

1 Costa, D.da, Ding, H., and Ge, J.: ‘Interference-limited relaying transmissions in dual-hop cooperative networks over Nakagami-m fading’, IEEE Commun. Lett., 2011, 15, (5), pp. 1 –3 2 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 3 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 4 Duong, T.Q., Bao, V.N.Q., and Zepernick, H.-J.: ‘Exact outage probability of cognitive AF relaying with underlay spectrum sharing’, Electron. Lett., 2011, 47, (17), pp. 1001– 1002 5 Gradshteyn, I.S., and Ryzhik, I.M.: ‘Table of integrals, series, and products’ (Academic Press, San Diego, CA, USA, 2000, 6th edn.)

outage probability

100

gth = 3 dB 10–1 Pu-Rx(0.5,0.5)

gI = 2 dB gI = 4 dB

Pu-Tx(0.6,0.6)

gI = 6 dB gI = 0.5 dB g

10–2

gI = 0.1 dB g no Pu-Tx signal 0

5

10

15 SNR, g, dB

20

25

30

Fig. 3 Performance comparison for different average powers from PU-Tx g¯ I

ELECTRONICS LETTERS 5th January 2012 Vol. 48 No. 1

Effect of primary network on performance of spectrum ...

10–2. SNR, γ, dB. Fig. 2 Performance comparison for different positions of PU-Tx ... G.C. Alexandropoulos (Athens Information Technology, Athens,. Greece).

191KB Sizes 2 Downloads 257 Views

Recommend Documents

The spectrum of Internet performance
of these metrics are quite simple and show power-law tails. ...... analyses of the infrastructure: measurement and visualization of Internet connectivity and ...

The Effect of Team Production on Individual Performance
and individual exploitation for overtime-work and long-hour reductions. Variation .... the late work shift, and from 10:00 pm until 6:30 am in the night work shift.

The Effect of the Internet on Performance, Market ...
May 19, 2017 - are not the most popular ones, without affecting other movies. .... studies the impact of various policy, economic, and social changes, .... net users–where Internet users are people with access to the worldwide network. ..... on the

The effect of management structure on the performance ...
Mar 4, 2009 - procedure. In a multi-domain network a particular network management/controller may have complete information about its own domain but ...

Effect of Schizotypy on Cognitive Performance and Its ...
spatial n-back tests; and cognitive performance speed, which reflects a reduction of the ..... scription of a functional polymorphism and its potential application to.

Effect of Cost and differentiation strategies on firm performance ...
Effect of Cost and differentiation strategies on firm performance article.pdf. Effect of Cost and differentiation strategies on firm performance article.pdf. Open.

Effect of initial configuration on network-based ...
published online 13 February 2008. PACS 89.75 ... tigated in the engineering community [3]. Various ... recommendation algorithm with degree-dependent initial.

Topology on Spectrum of Modules.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. Topology on ...

Towards Reproducible Performance Studies Of Datacenter Network ...
Data Storage Institute ... codes for our simulation set- ups are publicly available at http://code.google.com/p/ntu-dsi- dcn/. ... fully functional datacenter network of 50,000 servers [5], with .... such as as higher network capacity and graceful pe

The Effect of a Varying Solar Spectrum on Solar Cells Energy ...
The Iranian solar powered car called Persian Gazelle II made by students of ...... Figure 8.5, Screen-dump of the Spectral Response Source File. ..... renamed to National Renewable Energy Laboratory, NREL) by Richard Bird and Carol ...

Geometric Scale Effect of Flow Channels on Performance of Fuel Cells
This paper studies the effect of flow channel scaling on fuel cell performance. In particular, the impact of dimensional scale on the order of 100 micrometers and below has been investigated. A model based on three-dimensional computational flow dyna

Effect of Path Diversity on the loss performance of UDP ...
number of relay nodes that are positioned around the Internet. ... Service Provider (ISP)) internal network and find that for a ... networks in the wireless environment. ..... [10] S. Wu and S. Banerjee, “An area-based feedback implosion control.

The Effect of a Varying Solar Spectrum on Solar Cells ...
Dec 5, 2006 - Copernicus Institute for Sustainable Development and Innovation. The Effect of a Varying Solar Spectrum on Solar Cells Energy Performance. A Comparison between Simulated Actual and Air Mass 1.5 Standard Spectra by. Modeling Spectra Usin

The Effect of Crossflow on Vortex Rings
The trailing column enhances the entrainment significantly because of the high pressure gradient created by deformation of the column upon interacting with crossflow. It is shown that the crossflow reduces the stroke ratio beyond which the trailing c

Effect of Salinity on Biduri.pdf
There was a problem previewing this document. Retrying... Download. Connect more apps... Try one of the apps below to open or edit this item. Effect of Salinity ...

The Effect of Crossflow on Vortex Rings
University of Minnesota, Minneapolis, MN, 55414, USA. DNS is performed to study passive scalar mixing in vortex rings in the presence, and ... crossflow x y z wall. Square wave excitation. Figure 1. A Schematic of the problem along with the time hist

High‐Performance Monolayer WS2 Field‐Effect Transistors on High‐κ ...
Aug 10, 2015 - E-mail: [email protected]; [email protected]. Y. Pan, Prof. B. Wang. National Laboratory of Solid State Microstructures. School of Physics.

the effect of pellet feed on the performance and ...
The main objective of this study was to investigate the effects of pellet and meal feed on performance parameters: body weight (BW), daily weight gain (DWG), feed conversion ration (FCR) and apparent nutrient digestibility. (AND) of weaned piglets. F

Effect of earthworms on the community structure of ...
Nov 29, 2007 - Murrell et al., 2000). The development and application of suitable molecular tools have expanded our view of bacterial diversity in a wide range ...

Effect of Dual Fullerenes on Lifetimes of Charge ...
Compared with the SubPc-TPA dyad, a long-lived .... distance between the lowest unoccupied molecular orbital ... The nearest distance between the LUMO.

The effect of Quinine on Spontan.Rhythmic contrac. of Rabbit Ileal ...
The effect of Quinine on Spontan.Rhythmic contrac. of Rabbit Ileal smoot. musc..pdf. The effect of Quinine on Spontan.Rhythmic contrac. of Rabbit Ileal smoot.

Effect Of Acidic Treatment On Metal Adsorptions Of Sugarcane ...
Two pH systems were tested that are pH 3 and pH 5. The range ..... Adsorption of mercury, lead and cadmium ions on modified activated carbon”, Adsorption ...