International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 154

ISSN 2229-5518

Outage Analysis of Coded Cooperation with Full

Duplex Relay

Jyoti Yadav

Abstract - In this paper we propose analyse the outage behaviour of a coded cooperative communication system with one full duplex relay. The full duplex relay listens to source and transmits to the destination simultaneously. The expression for the outage probability is derived, and the effect of loop interference (that exists between the transmitting and receiving antennas of the relays) over the outage performance is investigated. The channel coefficients are assumed to be modelled as Nakagami-m distribution.

Cooperative communication is the new communication technology which allows multiple transceivers combine as a form of clusters for the data transmission and combination of transceivers could greatly improve the transmission quality among the signals[1]. To provide the transmit diversity in the wireless communication there is cooperation among the wireless users to enhance the system capacity. Cooperation means two single user antennas form a partnership and their partner’s antennas as a relay and both user and relay generate diversity [2,

3].

Earlier different cooperative communication methods were introduced [4, 5]. In Amplify and Forward relay amplified the original signal and transmits this amplified signal to the destination. The main drawback of this method is noise is also amplified and transmits to destination. Later Decode and Forward method were introduced, relay decode the original information and the transmits the decode version of information. The drawback of this method is original information is changed. In this paper we introduced a new technology of cooperative

We have taken a simple model which consists of source (S), relay(R) and the destination (D) as shown in Fig. 1. The fading characteristics in all the links in our model are assumed to be flat and distributed as Nakagami- m distribution. We divide the whole information of user into several blocks, each of N bits encoded with rate R. We partitioned the information in such a way that N1 contain the information part and N2 contain the additional parity bits, hence N1+N2=N. The N1 and N2 bits are getting from length N codeword by partitioning it with rates R1 and R2 by using a rate compatible punctured convolutional code (RCPC). The relay supports the full duplex capabilities i.e. receives and transmits simultaneously. At first time instant user transmit x out of N bits to relay and the destination. At the second time instant user transmits xR out of N bits which are received by the relay and destination and relay receive and transmit the xR bits to destination also. Now here loop interference exists between the receiving and transmitting bits at the relay i.e. interference between the x bit and xR of previous

message bit. We define the cooperation ratio (α) as

communication: coded cooperation. A significant improvement α = N

N

from the earlier methods of cooperative communication. Coded

cooperation based on the concept of coordinate the user

cooperation with channel coding. Apart from repeating the same

(1)

information received by the user, it also transmits the additional parity symbols (i.e. incremental redundancy) by using some coding scheme. The coding mechanism in the coded cooperation is managed automatically without any need of feedback between users. The user and relay transmit their information to the destination and generate independent fading path. Coded cooperation helps to maintain the same information rate, bandwidth, code rate and also transmit power as compare to other on cooperative communication.

We are consider four channels hSR , hRD , hRR , h SD these are channel coeffiencients for the channel from source to relay, relay to destination, relay to relay, and source to destination respectively. Here hRR represents the echo interfering channel between the transmitting and receiving antennas of the relay. All the channels are modelled with Nakagami-m fading distribution. In general Nakagami-m fading can be characterised for the node i to node j channel hij by the following expression

In most of earlier work on the cooperative communication relay work on the half duplex mode i.e. at one instant of time relay can

fhij (p) =

2

⎾�mij �

�m__ __ ij

Ωij

mij

�

p2mij−1

exp �−__ __mij

Ωij

p2 � (2)

2

either listen the user or transmit to the destination [6, 7]. But to

provide higher processing efficiency to the future generation and

also provide them high data rate relay must operate in full

duplex mode (FDR). In this paper relay work on the full duplex mode i.e. relay receives the information from the user and transmits to the destination simultaneously.

Where {ij} = {SR, RD, RR, SD}, and Ωij = E {�hij � }. Where E is the expectation operator and mij is the Nakagami parameter and

⎾(m) is the gamma function.

On the relay interference will occur via hRR . The equivalent

signal to interference noise ratio (SINR) at the relay will be represents as

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International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 155

ISSN 2229-5518

δR =

|hSR|2

|hRR|2 +1

(3)

In first time slot when the user transmit their message to the relay and to the destination. The overall equation will be

All the channels are distributed as Nakagami- m distribution the

terms |hSR |2 , |hRR|2,|hRD |2 , |hSD |2 will follow the gamma

distribution as

YD = hSD x + n

YR = hSR x + n

f

�hij�

2 (p) = 1

⎾�mij �

�mij

Ωij

mij

�

pmij−1 exp �

−mij

Ωij

p� (4)

Where n is the Gaussian noise and we considered Gaussian noise will be 1.

Further we consider the two cases, case 1: relay decodes correctly, case 2: relay fails to decode correctly. We assume throughout the analysis the threshold power (Pth ) is same for all the links. The validation of relay receive correctly depend on the basis of cyclic redundancy checks (CRCs). We assume that the relay receive correctly only if the received power over its link to source is greater than the threshold power (Pth ). Otherwise the outage will occur if the relay fail to decode correctly and hence CRCs are not valid.

ECHO INTERENFERENCE

hRR R

In second time slot where relay followed with full duplex process i.e. relay receive from the user and transmit to the destination simultaneously. Here the echo interenference take place due to same frequency band between the present message and the previous message. At the same time user also transmit to the destination. The overall equation will be

YD = hSD xR + hRD xR +n YR = hSR xR + hRR xR + n The two condition arise

(1) Relay decode correctly when

Pr(PR > Pth )

hSR

hRD

(2) Relay fails when

Pr(PR < Pth)

hSD

S D

Fig.1 System model

The overall equation of the power received at the destination is

(1 – α)PSD + αPRD = PD

The overall equation of the power received at the relay is

PR =

αPSR =

|hSR|2

The outage has been occurred due to link failure or the relay fails

(1−α)PRR+1

|hRR|2 +1 (8)

to decode correctly. We assumed outage has been occurred when the instantaneous power at destination falls below the specified

Now we are solving equation (8). All channels are to be

distributed as Nakagami-m fading i.e. hij ~ Nakagami-m

2 2

threshold. Thus for the system the outage event can be defined

as

(mij, Ωij) and �hij � followed the Gamma distribution i.e. �hij � = ⎾

(kij, θij) where k measures the depth of the fading. So from these

Pout = Pr { P < P } = ∫Pth

f(p)dp

(5)

relation kij = mij and θij =

Ωij

mij

2

and therefore�hij �

= ⎾ �mij ,

Ωij �.

mij

Where P is the instantaneous received power and f (p) is the

In general Gamma distribution can be defined as

probability density function (p.d.f) of P, and Pth is the threshold power. For Nakagami - m distributed channels, instantaneous

fhij (p) =

pkij−1 exp� �

θij

kij

(9)

received power (P) has a Gamma distributed p.d.f, and therefore

θij

⎾�kij�

outage probability given in equation (5) can also be written as

And therefore |hSR |2 can be written as

P

out ∫0

1

⎾(m)

�m�m

P�

pm−1 exp �

−mp

P�

� dp (6)

|hSR

|2 =

pmSR−1 exp� �

ΩSR

mSR

(10)

Pout = 1 −

⎾�m�

mPth�

P�

(7)

� ΩSR �

mSR

⎾(mSR)

⎾(m)

Where P� represents the average value of received power and Pth

is the threshold power. ⎾(m) represents the gamma function

Now |hRR |2 + 1 can be solved as |hRR|2 + 1 → ⎾(URR, VRR ) where

URR and VRR can be defined as

mRR(ΩRR +mRR)2

which can be defined as⎾(m) = ∫ xm−1exp(−x) dx. ⎾(m, τ)

shows the upper incomplete gamma function which can be

defined as⎾(m, τ) = ∫ xm−1 exp(−x)dx.

and

URR =

(ΩRR

)2 (11)

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International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 156

ISSN 2229-5518

(ΩRR )2

Now we calculate the outage probability of corresponding cases

VRR =

RR

)2 (ΩRR

+mRR

(12)

)

of the relay

And therefore by using equations (11) and (12) |hRR|2 + 1 can be

written as

Pr(P > P ) = 1 − ∫Pth

f(pR) dp (21)

|hRR |2 + 1 =

pURR−1 exp� −p �

VRR

(13)

p�mSR−1�×⎾(mSR+URR)×� p

SR

−mSR−URR

+ 1 �

VRR

(VRR )URR ⎾(URR)

Finally equation (8) can be solved by using equations (10) and

(11), since |hSR |2 and |hRR |2 + 1 are two independent random

variables and these can be solved as

=1 − Pth

� ΩSR �

mSR

Pth

�mSR�

×⎾(mSR)×VRRURR ×⎾(URR)

dp (22)

f(z) = ∫∞ Yf (zy) ∗ f (Y)dy (14)

And hence

Pr(PR < Pth) = ∫0 f(pR) dp (23)

Or we can write as also

f|hSR|2 (x) =

xmSR−1 exp −x∗mSR�

ΩSR

mSR

(15)

p�mSR−1�×⎾(mSR+URR)×�

�

p

ΩSR

+ 1

� VRR

−mSR−URR

�

P __ __ dp

(24)

� ΩSR �

⎾(mSR)

∫ th

mSR

mSR

0 ΩSR mSR

�msr �

×⎾(mSR)×VRR

URR

×⎾(URR)

Similarly we can write this equation as

−zy∗mSR

Pr(PSD < Pth) =

⎾�mSD�

mSDPth�

P�

(25)

fx (zy) =

(zy)mSR−1 exp�

mSR

�

ΩSR

(16)

⎾(mSD)

� ΩSR �

mSR

⎾(mSR)

respectively. Here P� is the average power, f(pR) are the p.d.f of

the PSR and PR is the instaneous received power over source to

And now this is the again new random variable and we can

solve this as

relay.

Substituting (22), (24), (25) in equation (20) to get the complete

YURR−1 exp� −p �

VRR

expression of outage probability and we calculate this result

f|hRR|2+1 (Y) = (V

)URR ⎾(URR

(17)

)

numerically in Matlab.

Now the put the value of equations (16) and (17) in equation (14) and integrate the equation (14) from 0 to infinity and we get the final equation

Z�mSR−1�×⎾(mSR+URR)×� z

−mSR−URR

+ 1 �

f(z) =

ΩSR mSR

� ΩSR � VRR

mSR

URR

(18)

�msr�

×⎾(mSR)×VRR

×⎾(URR)

Now put the value of equation (18) in equation (8) and we get the value of p.d.f of received power at relay

Z�mSR−1�×⎾(mSR+URR)×� z

� ΩSR

−mSR−URR

+ 1 �

VRR

PR =

mSR�

( ΩSR )mSR ×⎾(mSR)×VRRURR ×⎾(URR)

SR

(19)

Fig. 2 outage probability vs. average power for different values of m

The overall outage probability can written as

Pout = Pr(PR < Pth) × Pr(PSD < Pth ) + Pr(PR > Pth) × Pr(PSD + (1 − α)PRD ) < Pth)

(20)

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International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 157

ISSN 2229-5518

Fig,3 outage probability vs. Threshold power

We derive the numerical result of the outage probability and also give the expression of the power received on the relay. For this we assumed all the channels are distributed as Nakagami-m distribution. Fig.2 shows the plot of outage probability with respect to the average power under the different values of Nakagami parameter m. It shows if we increase the value of m the outage probability is decreasing and hence the performance of the system will increase. Fig.3 shows the outage probability with respect to the threshold.

We analyse the outage behaviour of a coded cooperative communication system with one full duplex relay. The full duplex relay listens to source and transmits to the destination simultaneously. The expression for the outage probability is derived, and the effect of loop interference (that exists between the transmitting and receiving antennas of the relays) over the outage performance is investigated.

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