Outage Performance of Multi-Hop Relay in Rician Fading Channel

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 5, May 2016)

Outage Performance of Multi-Hop Relay in Rician Fading

Channel

Suryakant Pathak

1

, Himanshu Katiyar

2

1_{Associate Professor & Head, Deptt of CSE Dr. K N Modi University Newai, Rajasthan, India} & Research scholar, Deptt. of CSE, BBD University, Lucknow, India

2_{Associate Professor, Deptt. of ECE, BBDNIIT, Lucknow, India}

Abstract-- The need of high-data-rate, spectrally efficient and reliable wireless communication can be met by relay-based cooperative communication. The diversity can be achieved through user cooperation, where mobile users share their physical resources to create a virtual array of relays, which eliminates the necessity of multiple-antenna on wireless terminal. In this paper outage performance of multi-hop relay link in Rician fading channel has been analyzed. Decode and forward (DF) protocol has been used for serial relay communication.

Keywords-- Cooperative communication, decode and forward, multi-hop relay, Rician fading, virtual array.

I. INTRODUCTION

In wireless communication Fading is a phenomena caused due to interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different times [1]. In Rician distribution [2] propagation paths consisting of one strong direct LOS component and many random weaker components. The equation for outage analysis is derived from [3]. Cooperative communication has been discussed in [4]. Performance analysis of cooperate relay has been discussed in [5],[6]. Optimal Power allocation for regenerative relay has been discussed in [7].Closed form expressions of BER have been established in [8] for two-hop multi-antenna cooperative relay network in Rayleigh fading channel. Here, destination performs selection combining of signals received from source, relay and relay performs selection or MRC combining of signal. Average capacity and SNR analysis of multi-antenna regenerative relay has been analyzed in [9]. Infrastructure based multi-antenna cooperative relay network has been investigated in [10]. Here, closed form expressions of outage probability and average error rate have been derived when the relay and the destination perform selection combining of the signals. Simulation studies of multi-antenna relay network have been analyzed in [11]. Here, relay performs MRC and destination performs switch and stay combining of the signal.

In [12], closed form expressions for outage probability and BER have been derived when multi-antenna cooperative relay network operates in correlated Nakagami-m fading channel and both the relay as well as destination performs MRC of signals. In [13], outage and error performance of multi-antenna relay system has been investigated with the help of simulation studies. Here, relay performs generalized selection combining and destination performs MRC of signals. Simulation studies of outage and throughput of cooperative relay network have been presented in [14] where source and relay communicate with multi-antenna destination in correlated Nakagami m fading channel. Performance of regenerative relay network operating in uplink of multi-antenna base station under Rayleigh fading channel has been presented in [15]. User cooperation in TDMA wireless system has been discussed in [16]. Various power allocation strategies for non-regenerative relay network have been studied in [17]. Simulation studies of adaptive power allocation for threshold based regenerative relay network has been done in [18]. In [19], closed form expressions of outage probability and bit error rate (BER) for binary phase shift keying (BPSK) are derived for the case where communication between source and destination is supported by multi-antenna relay and both relay and destination perform maximum ratio combining (MRC) of signals in Rayleigh fading channel. Outage probability and average error rate of two-hop multi-antenna relay based system for the case when relay performs selection combining (SC) of signals and destination performs MRC of signals are analyzed in [20] and [21], respectively. Outage performance of multi-hop relay network in Rician fading channel is analyzed in this paper.

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II. RICIAN FADING MODEL Scatterer

LOS Path Tx Rx

TX

NLOS Path

Fig 1. Rician fading model

A.

Rician Fading

Rician fading model is shown in fig.1, some types of scattering environment have specular or LOS components. If gI(t) and gQ(t) are Gaussian random process with non-zero mean mI(t) and mQ(t). If we again assume that these process are uncorrelated and random variable gI(t) and gQ(t) have the same variance [22]. Then magnitude of the received complex envelop at time t has a Rician distribution as

( ) ( ) ( )₍₁₎

Where

= I (t) + Q (t) (2)

is called the non-centrality parameter. This type of fading

is called Ricean fading and is very often observed in

microcellular and mobile satellite applications. The Rician

fading model is shown in fig.1. A very simple Ricean

fading model assumes that the means I (t) and Q (t)

are constants, i.e. I (t) = mI, and mQ(t) = mQ . the means

I (t) and mQ(t) corresponding to the in phase and

quadrature components of the LoS signal are given by

mI (t) = s. cos(2π fm cosθ0t +ϕ0 ) (3)

mQ(t) = s. sin(2π fm sinθ0t +ϕ0 ) (4)

Where fm cosθ0 and ϕ0 are the Doppler shift and

random phase off set associated with the LoS or specular component, respectively.

The Rice factor, K, is defined as the ratio of the

specular power to scattered power i.e. K= s2 /

, When K= 0 the channel exhibits Rayleigh fading, and

when K= ∞ the channel does not exhibit any fading at

all . The envelope distribution can be rewritten in terms of the Rice factor and the average envelope power E [ = s2 / by first noting that

=

(5)

It then follows

( ) ( ) exp { -K - ( )

I0 (2x√

( )

), x>=0

(6) = received complex envelop which is Rician distributed

= N(mI, ) + j*N(mQ, )

N = ( . , . ) Normally or Gaussian distributed random variable

= running variable = Variance

s = mI2 +mQ2

mI = mean of in phase component

mQ = mean of quadrature phase components

= zero order modified Bessel function of the first kind j = complex operator

III. COOPERATIVE COMMUNICATION A.Relaying Protocols

Cooperative communication exploits the broadcast nature of the wireless medium and allows terminals to jointly transmit information through relaying. Such intermediate relay terminals may process the signals as follows:

Amplify and forward (AF):

This is an analog scheme which works in non- regenerative mode. In this scheme, a relay receives the signal, amplifies it and then retransmits it in the next phase. Operation in this mode puts less processing burden on the relay, so it causes much smaller delay, and hence is often preferred for delay sensitive traffic such as voice and live video. Noise amplification is a major issue for such schemes.

Decode and forward (DF):

This is a digital scheme which works in regenerative mode. In this scheme, relay receives the signal, decodes it and after encoding retransmits it in the next time-slot. Noise does not prorogate to next stage, but error may propagate. Processing time is high, so it is not suitable for delay sensitive traffic.

Decode and re-encode (DR):

In this protocol, code word used to encode the message at relay may different from the source. Therefore, additional redundancy can be achieved at destination since it receives two copies of the same message encoded with different code words.

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In this paper decode and forward relaying protocol has been used.

B. Relay Transmission Topology

Serial relay transmission:

Serial relay transmission is used for long distance communication and range extension in shadowy region. It provides power gain. In this topology, signal propagates from one relay to another relay and the channels of neighboring hop are orthogonal to avoid any interference.

Parallel relay transmission:

The serial relay transmission suffers from multi-path fading. For outdoors and non-line of sight communication, signal wavelength may be large and installation of multiple antennas is not possible. To increase the robustness against multipath fading, parallel relay transmission can be used. In this topology, signal propagates through multiple relay paths in same hop and destination combines the signals received with the help of various combining schemes. It provides power gain and diversity gain simultaneously.

In this paper serial relay transmission topology has been used.

IV. OUTAGE PERFORMANCE IN MULTI-HOP RELAY NETWORK

In this paper multi-hop relay communication technology is used. Serial relay transmission topology is used for long distance communication and range extension in shadowy region. It provides power gain. In this, signal propagates from one relay to another relay and the channels of neighboring hop are orthogonal to avoid any interference. In this system model n-1 relay has been used between source and destination so there are n hops between source to destination. The system model in shown in Fig.2

Source Relay1 Relay2 Relayn-1

Destination

Fig.2 Multi-hop relaying in Rician fading channel

Outage Probability Pout in cooperative communication for n number of link

( )

( ) ̅

̅ [∑ ( ̅ )

( _̅)

(_̅) ] (7)

(γ) = 1 [{ ( )} ] [see appendix] (8) Where Eq.(8) can be evaluated using [3, Eq. (1.111)]

(γ) = [ *∑ ( ) ( ( )) +]

(γ) = * *∑ ( ) ( * ( )

̅

̅ [∑ ( ̅ )

( ̅)

(_̅) ]+)

_]

]

(γ) = * *∑ ( ) ( * ( )

̅

̅ [∑ ( ̅ )

* ̅_(∑ ( ̅)

)+

(_̅)

]_]₎ _] ]

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Outage Probability Pout = (χ) Where χ= 1 is Outage threshold

(χ) == * *∑ ( ) ( * ( )

̅

̅ [∑ ( ̅ )

* ̅_(∑ (̅)

)+

(_̅)

]_]₎ _] ]

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V. SIMULATION AND RESULTS

Outage probability for multi-hop relay network communication system over Rician fading channel is analyzed. Fig.3 shows Outage probability of multi-hop relay network with respect to SNR for two Relays. Fig. 4 shows outage probability of multi-hop relay network with respect to SNR for three relay links. Fig. 5 and fig.6 shows outage probability of multi-hop relay networks with respect to threshold for unity SNR. After analyzing above results it is concluded that outage probability with respect to SNR and threshold both increases when the number of relay links increases.

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Fig.3 Outage probability of multi-hop relay network with respect to SNR for two Relays.

Fig.4 Outage probability of multi-hop relay network with respect to SNR for three Relays.

Fig.5 Outage probability of multi-hop relay network with Respect to threshold for two Relays and unity SNR

Fig.6 Outage probability of multi-hop relay network with respect to threshold for three Relays and unity SNR

VI. CONCLUSION

In this paper outage probability of multi-hop relay based wireless system has been analyzed for decode and forward protocol over Rician fading channel. After analysis it is observed that the outage increases with number of relay links. In this results Rice factor K also plays vital role when the value of K increases outage probability improves.

APPENDIX

The Minimum of n IID Random Variables

Suppose that , ,…. . are independent and identically distributed (iid) continuous random variables. By independent, we mean that

P { ∈ , ∈ ,… ∈ } = P{ ∈ } P{

∈ }…….. P{ ∈ } (11)

For any ⊆ R , ⊆ R, ⊆ R. By identically distributed we mean that , each have the same distribution function F (and therefore the same density function f).

nth quantities of interest are the minimum of and . It turns out to be surprisingly easy to

determine the distribution and density functions of the minimum. The key observations are that

min{ , } > x if and only if > x, > x ….

Distribution of min { , }

Suppose that Y = min { , }.By definition, the distribution function of Y is

( ) = P {Y ≤ y} = P {min{ , }≤ y} .

( ) = P {Y ≤ y} = 1 − P {Y > y} (12)

= 1 − P {min{ , }> y}

0 2 4 6 8 10 12 14 16 18 20

10-2 10-1 100

SNR (dB)

O

u

ta

g

e

P

ro

b

a

b

ili

ty

Outage Probability of multi-hop relay network

K=0 K=1

0 2 4 6 8 10 12 14 16 18 20

10-2 10-1 100

SNR (dB)

O

u

ta

g

e

P

ro

b

a

b

ili

ty

K=0 K=1

0 0.5 1 1.5 2 2.5 3

10-0.7 10-0.6 10-0.5 10-0.4 10-0.3 10-0.2 10-0.1

Threshold

O

u

ta

g

e

P

ro

b

a

b

ili

ty

K=0 K=1

0 1 2 3 4 5 6 7

100

Threshold

O

u

ta

g

e

P

ro

b

a

b

ili

ty

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This is useful to us since

P{min{ , }> y} = P { , > y , > y,

> y}

= P { , > y} P { > y} …P { > y} (13) Using the fact that ….. are independent. However, have the same distribution function i.e.

P { , > y} = 1 − FX1 (y) P { > y} = 1 − FX2 (y) …….

P { > y} = 1 − FXn (y) Therefore,

( ) = 1 − P {Y > y}

= 1 − [1 − FX1(y) ] · [1 − FX2(y) ]…….[1 − FXn(y) ] For independent and n identically distributed random variables

( = = …….= )

( ) = 1 − ( ) . (14)

REFERENCES

[1] Rappaport T.S.,”Wireless Communications Principles and Practice” (Prentice Hall, 2011 2nd_edn.).

[2] Simon, M.K., Alouini, M.-S., “Digital communication over fading channels” (John Wiley and Sons, Inc., Hoboken, 2005, 2nd edn.) [3] Gradshteyn, I.S., Ryzhik, I.M., “Table of integrals, series and

products” (Academic Press Inc., 2007, 7th revised edn.)

[4] Katiyar H, Rastogi A and Agrawal R, “Cooperative communication: A review”. IETE Technical Review Journal. 28(5),409-417,2011

[5] Dharmraj and Katiyar Himanshu, “ Performance Analysis of Cooperative Relaying over α-μ Fading Channel” International Journal of Innovative Research in Computer and Communication Engineering(IJIRCCE), ISSN 2320-9801 Vol.3, Issue 8, pp.7204-7213, 2015.

[6] Dharmraj and Katiyar Himanshu, “ Performance Analysis of Multi-Hop Relay- Network over α-μ Fading Channel” International Journal of Research in Electronics and Communication Technology (IJRECT), Vol.2, Issue 3, pp 22-28, Jul-Sep, 2015.

[7] Dharmraj and Katiyar Himanshu, “ Optimal Power allocation for regenerative relay over α-μ Fading Channel” International Journal of Computer and Communication Technologies (IJCCTS), Vol.3,No.11, Issue 6 pp 761-766, Sep, 2015.

[8] H. Katiyar, and R. Bhattacharjee. “BER performance of regenerative multi-antenna cooperative relay network in Rayleigh fading channel”, In Proc. of UKIWCWS 2009, IIT Delhi, India, Dec. 11-12, 2009.

[9] H. Katiyar, and R. Bhattacharjee. "Average capacity and SNR analysis of multi-antenna regenerative cooperative relay in Rayleigh fading channel", IET Communications, Accepted for Publication. doi: 10.1049/iet-com.2010.0969

[10] H. Katiyar, and R. Bhattacharjee. "Performance of two-hop infrastructure based multi-antenna regenerative relaying in Rayleigh fading channel", Physical Communication (Elsevier),vol. 4, no. 3, pp. 190-5, Sept. 2011.

[11] H. Katiyar, R. Bhattacharjee, and Samdarshi. "Outage performance of switch and stay combining scheme for multi- antenna relay network", In Proc. of UKIWCWS 2010, IIT New Delhi, India. pp. 1-5, Dec. 2010.

[12] H. Katiyar, and R. Bhattacharjee. “Performance of two-hop regenerative relay network under correlated Nakagami-m fading at multi-antenna relay”, IEEE Communications Letters, Vol. 13, no. 11. pp. 820-2, Nov. 2009

[13] H. Katiyar, R. Jana, and R. Bhattacharjee. “Performance analysis of two-hop regenerative relay network with generalized selection combining at multi-antenna relay”, In Proc. of INDICON Kolkata, India: Jadavpur University; 2010.

[14] H. Katiyar, and R. Bhattacharjee. “Performance of regenerative relaying at uplink of multi-antenna access point in Nakagami-m fading”, In Proc. of NCC 2009, IIT Guwahati, pp. 165-9, Jan. 16-18, 2009.

[15] H. Katiyar and R. Bhattacharjee. “Performance of regenerative relay network operating in uplink of multi-antenna base station under Rayleigh fading channel”, In Proc. of TENCON 2009, IEEE Region 10 Conference, Singapore, pp. 1-5, Nov. 23-26, 2009.

[16] H. Katiyar, B.S. Paul, and R. Bhattacharjee. “User cooperation in TDMA wireless system”, IETE Technical Review Journal, Vol. 25. pp. 270-6, Sep.-Oct. 2008.

[17] H. Katiyar, and R. Bhattacharjee. “Power allocation strategies for non-regenerative relay network in Nakagami-m fading channel”, IETE Journal of Research, Vol. 55, no. 5. pp. 205-11, Nov. 2009. [18] H. Katiyar, and R. Bhattacharjee. “Adaptive power allocation for

repetition based cooperative relay in Nakagami-m fading channel”, In Proc. of TENCON 2008, IEEE Region 10 Conference, Hyderabad, India, Nov. 19-21, 2008.

[19] H. Katiyar, and R. Bhattacharjee. “Performance of MRC combining multi-antenna cooperative relay network”, AEU (Elsevier) -International Journal of Electronics and Communications, Vol. 64, no. 10. pp. 988-91, 2010.

[20] H. Katiyar, and R. Bhattacharjee. “Outage performance of two-hop multi-antenna co-operative relaying in Rayleigh fading channel”, IET Electronics Letters, Vol. 45, no.17. pp. 881-3, Aug. 2009.

[21] H. Katiyar, and R. Bhattacharjee. “Average error rate of multi-antenna decode and forward cooperative relay network”, In Proc. of IEEE INDICON 2009, DAIICT Ahmedabad, India, Dec. 18-20, 2009.

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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 5, May 2016) AUTHOR’S BIOGRAPHY

Suryakant Pathak received his MCA, M.Tech in Computer Science & Engineering and pursuing Ph.D. in Wireless Communication from BBD University Lucknow, India. He had worked in Indian Air Force, 1983-2003. Faculty at DOEECC Centre, Madan Mohan Malviya University of Technology campus Gorakhpur (U.P.), India, 2004-2006. Lecturer at Amity University Lucknow (U.P.), India, 2007-2008. Assistant Professor at Sagar Institute of Technology & Management Barabanki (U.P.), India, 2009-2013. At present he is Associate Professor & Head of Department Computer Science & Engineering Dr. KN Modi University Newai, Rajasthan, India. His research interests include almost all aspects of wireless communications with a special emphasis on MIMO systems, MIMO-OFDM, spread spectrum system, cooperative diversity schemes.

Himanshu Katiyar received his B.E. degree in Electronics and Communication Engineering from M.I.T. Moradabad (M.J.P. Rohilkhand University, Bareilly) in 2001, M.Tech degree from Madan Mohan Malviya Engineering College, Gorakhpur (U.P. Technical University, Lucknow) in2004 and Ph.D. degree in the area of wireless communication at the Indian Institute of Technology, Guwahati, Assam India in 2011. From2004–2005 he was lecturer of Electronics and Communication Engineering Dept. at SRMSCET, Bareilly, Uttar Pradesh, India and from 2005–2006 he was lecturer of Electronics and Communication Engineering Dept. at NIEC, Lucknow, and Uttar Pradesh, India. At present he is Associate Professor of the Electronics and Communication Engineering Dept. at BBDNIIT, Lucknow, and Uttar Pradesh, India. He was awarded from IETE research fellowship and he was project investigator (from September, 2009 to December, 2010) of an IETE sponsored research project. He has published over thirteen research papers in SCI journals, twelve research papers in non SCI journals and ten national/ international conference papers. His research interests include almost all aspects of wireless communications with a special emphasis on MIMO systems, MIMO-OFDM, spread spectrum system, channel modelling, infrastructure-based multi-hop and

relay networks, cognitive radio communication,