Power Allocation for OFDM-DF Cooperative Communication

Chen Yueyun1, 2, Hu Xining2, Tan Zhenhui1

1 State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China 2University of Science and Technology Beijing (USTB), Beijing, China

Email: chenyy2@sina.com

Abstract—A minimized power allocation scheme in a cooperative communication manner is studied to low power consumption and extent service life for transmission nodes. The model of the minimizing transmission power allocation for each sub-carrier of source node and relay node is not a convex problem, so it is difficult to find the global optimal solution. A new scheme of Decode-and-Forward Power Allocation (OFDM-DF-PA) is proposed. First, the power is allocated between source and relay node after sub-carrier is allocated under a given transmission power for each sub-carrier. Second, the power of each sub-carrier is allocated individually in source and relay node. Then, three different schemes of Non-cooperative Power Allcation (NPA), Equal Power Allocation (EPA) and OFDM-DF Power Allocation are compared. Simulation results show that OFDM-DF-PA consumes less power than the EPA and the NPA under the same BER performance in cooperative OFDM system with Frequency Reuse Factor of 1.

Keywords—OFDM; power allocation; cooperative communica-tion; interference

I. INTRODUCTION With the development of mobile communication, multi-

service and high rate data communications are required over wireless channel. Communication rate and spectrum efficiency are increased by Multi-antenna in the same bandwidth. A Vitual multi-Antenna Array (VAA) is composed of different users in cooperative communication. VAA is used to improve communication link performance and transmission rate in cooperative communication. OFDM technology can overcome frequency selective fading and improve the spectrum efficiency, which has been used in the next generation mobile communication network and other wireless networks.

Because of the requirement of different services, the power allocation methods have been proposed for different performance parameters. The authors in [1] analyze the selection of the amplification factor to minimize the outage probability in cooperative communication. The authors derive an optimum power allocation that minimizes the pairwise error probability for an Amplify-and-Forward protocol (AF) using linear dispersion space-time codes in [2]. The optimal power allocation for cooperative communication in a fading channel with knowledge of mean channel gains is still an open problem.

There is also reported research that focuses particularly in cooperative OFDM system. The authors consider a single relay in [3]. Then, a fixed power allocation is given at the source or relay. Water-filling among subchannels is proved to be optimal power allocation at the relay or source. The authors

in [4] propose suboptimal schemes with considerably less overhead and study the conditions under which they perform close to the optimal allocation scheme in multi-relay OFDM system. In order to reduce co-channel interference from neighboring cells, several methods have been proposed to avoid interference in 3GPP LTE. One of the most studied methods is differential frequency partitioning [5] [6]. It sets a Frequency Reuse Factor greater than 1 for the users located at the border of the cells, while setting a Frequency Reuse Factor of 1 for the users in the cells. Cooperative communication in the cellular area can reduce co-channel interference and increase the spectrum efficiency. In this paper, the power allocation problem of source node and relay node is studied in the interference environment for OFDM system. Because of the power limitation of the mobile terminal, the power allocation problem is to minimize the system transmission power under the conditions of meeting the system performance.

The paper is organized as follows. Section II describes the cooperative scheme. Section III describes the power allocation methods between the source node and the relay node. Section IV gives some numerical simulation results. Section V concludes the paper.

II. SYSTEM MODEL There are I neighboring cells in cellular area with Reuse

Factor 1. The number of sub-carriers M is allocated on the source node and relay node. It is considered that a two-hop cooperative communication system is shown in Figure 1. The node R is the nearest point from the node S.

(a) (b)

Figure 1. The transmission model of cooperative communication

The source node transmits signal to the Base Station D with the help of the relay node R. One transmission period is divided into two time slots. In the first time slot, S transmits the signal mx to R and D, where mx is the sending signal of

2011 Third International Conference on Communications and Mobile Computing

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DOI 10.1109/CMC.2011.33

319

the mth sub-carrier. Relay node R and Base Station D receive the signal sr

my and sdmy from the source node in the mth sub-

carrier, the signal srmy and sd

my are given in [7]:

(1)2

,( )

ssd sd dmm m m msd s

sd m m

Py h x nl Iσ

= ++

(1)

2,( )

ssr sr rmm m m msr r

sr m m

Py h x nl Iσ

= ++

(2)

In the second time slot, R decodes the information mx from the source node, and then R recodes and transmits the information '

'm

x to D. The Base Station D receive signal 'rdm

y is written as

' '' (2)'

' '2, ' '( )

rrd rd dm

m mrd rm mrd m m

Py h x nl Iσ

= ++

(3)

The Base Station D combines the directly received signal sdmy from the source node and the relayed signal '

rdm

y from the relay node by the Maximal Ratio Combining (MRC) method.

', ,sd sr rdm m m

h h h denote the channel gains of the source-base channel, the source-relay channel and the relay-base channel in the mth and 'm th sub-carrier. It is assumed that they are independent, exponentially distributed random variables with 2 2 2, ,sd sr rdσ σ σ . s

mP (resp. 'r

mP ) is the transmission power

from the source node (resp. the relay node) in its mth (resp. 'm th) sub-carrier. s

mI (resp. 'rm

I ) is the interference from the neighboring cells in the mth sub-carrier allocated on its link with source node (resp. relay node). ,sd srl l and rdl denote the path loss (including shadowing effect) of source-base channel, the source-relay channel and the relay-base channel in the mth and 'm th sub-carrier. In the first and second time slot, the received SNR of source node S and relay node R are written as:

2

2,( )

sd sm m

sd sd ssd m m

h Pl I

γσ

=+ (4)

2

2,( )

sr sm m

sr sr rsr m m

h Pl I

γσ

=+ (5)

2

' '2

, ' '( )

rd rm m

rd rd rrd m m

h Pl I

γσ

=+ (6)

III. POWER ALLOCATION ALGHORTHM In this section the power allocation algorithm is introduced to minimize the system BER given a total power constraint for the source and the relay. It’s assumed that the channel h between any nodes is Raleigh fading channel, so 2h is an exponential distribution. The BER is given in [8]:

2( )1 expodl Ip

Pβ σ⎛ ⎞+= − −⎜ ⎟

⎝ ⎠ (7)

Where β satisfies the QOS requirement. In the first time slot, the BER in the mth sub-carrier of Base

Station D and relay node R is written as

2,

,

( )1 exp

sd ssd m me

sd m sm

l Ip

Pβ σ⎡ ⎤⎛ ⎞+

= − −⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ (8)

2,

,

( )1 exp

sr rsr m me

sr m sm

l Ip

Pβ σ⎡ ⎤⎛ ⎞+

= − −⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦ (9)

In the second time slot, the BER in the 'm th sub-carrier of Base Station D is written as

'

2, ' '

,'

( )1 exp

rd rrd m me

rrd mm

l Ip

Pβ σ⎡ ⎤⎛ ⎞+

= − −⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(10)

The Base Station D combines the signals sdmy and '

rdm

y by MRC, so the BER of Base Station D was given in [9]:

'

2 2, ,

,

2 2, ,

2, ' '

'

( ) ( )1 exp 1 exp

( ) ( )1 exp exp

( )1 exp

sd s sr rsd m m sr m me

s sm mm m

sd s sr rsd m m sr m m

s sm m

rd rrd m m

rm

l I l Ip

P P

l I l IP P

l IP

β σ β σ

β σ β σ

β σ

⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞+ += − − − −⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞+ +

+ − − −⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ ⎣ ⎦

⎛ +− −

⎝

⎡ ⎤⎞⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎠⎣ ⎦

(11)

A. Sub-carrers allocation The sub-carriers allocation aims to allocate the same

number of sub-carriers to source node and relay node. According to the channel conditions, the best sub-carrier is selected to minimize the received BER, so it is assumed that '

rm

P , smP is respectively 1. The formula (8), (9), (11)

respectively is:

2, ,1 exp ( )e sd s

sd m sd m mp l Iβ σ⎡ ⎤= − − +⎣ ⎦ (12)

320

2, ,1 exp ( )e sr r

sr m sr m mp l Iβ σ⎡ ⎤= − − +⎣ ⎦ (13)

{ }{ }{ }{ }{ }

' ',

2 2, ,

2 2, ,

2, ' '

( 1, 1)

1 exp ( ) 1 exp ( )

1 exp ( ) exp ( )

1 exp ( )

e s rmm m m

sd s sr rsd m m sr m m

sd s sr rsd m m sr m m

rd rrd m m

p p p

l I l I

l I l I

l I

β σ β σ

β σ β σ

β σ

= =

⎡ ⎤ ⎡ ⎤= − − + − − +⎣ ⎦ ⎣ ⎦

⎡ ⎤ ⎡ ⎤+ − − + − +⎣ ⎦ ⎣ ⎦

⎡ ⎤− − +⎣ ⎦

(14)

Sub-carriers allocation is consequently performed as follows: 1) Let 1 2{ , }sd sd sd sd sd

m Mh H h h h∈ = ，

1 2{ , }sr sr sr sr srm Mh H h h h∈ = , ' 1 2{ , }rd rd rd rd rd

Mmh H h h h∈ = ,

each of sdH , srH and rdH was arranged in descending order.

2) According to the formula , ,min( )e esd m sr mp p+ , source node

selects the mth sub-carrier. The mth sub-carrier is added to A, while sd

mh is removed from the set sdH and srmh is removed

from the set srH . 3) In the set rdH , it finds the 'm th sub-carrier to meet formula

',min e

rd mp , and the 'm th sub-carrier is added to B, while

'rdm

h is removed from the set rdH .

4) Repeat the steps 2) - 3), until the sets ( sdH , srH and rdH ) are empty.

B. Power allocation

It’s assumed that ',m m

P is the power in the m th and 'm th

sub-carriers. Under the condition of a given power',m m

P , power allocation problem of source node and relay node can be described as

'

'

,

' ,

min em m

s rm m m m

p

subject to P P P+ = (15)

Let 2, ,( )sd s

sd m sd m ma l Iβ σ= + , 2, ,( )sr r

sr m sr m ma l Iβ σ= + , 2

, ' , ' '( )rd rrd m rd m ma l Iβ σ= + . For high SNR, the next formula

is exp( ) 1x x− = − . The formula (11) is written as

', , , , , '

,'

(1 )sd m sr m sd m sr m rd mes s s s rm m

m m m m m

a a a a ap

P P P P P= ⋅ + ⋅ − ⋅ (16)

By the Lagrange multiplier method, it is easy to get the relationship between source node power and total power, as

' ', ,s

m m m m mP Pα= , ' '' , ,

(1 )rm m m m m

P Pα= −

Where

'

2, , ' , ' , , '

,, ' ,

4 84 4

sr m rd m rd m sr m rd mm m

rd m sr m

a a a a aa a

α− + + +

=−

It puts' ', ,

sm m m m m

P Pα= , ' '' , ,

(1 )rm m m m m

P Pα= − into formula (16) as

' ' ' '3, , , ,m m m m m m m m

P Pϕ φ= + (17)

Where '

'

' ' '

, , , , ',2,

, , ,

(1 )

(1 )sd m sr m m sd m rd mm m

em mm m m m m m

a a a ap

α αϕ

α α− +

=−

,

'

' ' '

, , , '2,

, , ,( 1)

sd m sr m rd mem m

m m m m m m

a a ap

φα α

=−

It is easy to solve the formula (17) as

' ' '

' '

' ' '

1/32 3

, , ,

, ,

1/32 3

, , ,

9 81 12( )

18

9 81 12

18

m m m m m mem m m m

m m m m m m

P pφ φ ϕ

φ φ ϕ

⎛ ⎞+ −⎜ ⎟=⎜ ⎟⎝ ⎠

⎛ ⎞− −⎜ ⎟+⎜ ⎟⎝ ⎠

(18)

For the cooperative communication system with OFDM-QPSK modulation, the system bit error rate was given in [3]:

',

, 1

1 M

e m em m

p pM =

= ∑ (19)

In OFDM-DF system, power allocation of each sub-carrier can be described as

' ''

''

, ,, 1

*,

, 1

min ( )

1

Me

m m m mm m

Me

em mm m

P p

subject to p pM

=

=

≤

∑

∑ (20)

By Lagrange method, the formula (20) is converted to:

' ' '' '

*, , ,

, 1 , 1

1( ) ( )M M

e eem m m m m m

m m m m

G P p p pM

η= =

= + −∑ ∑ (21)

Let ',/ 0e

m mG p∂ ∂ = , so the value of

''

,( , 1, 2 )e

m mp m m M= is written as:

321

( )'

'

''

25

3, ,, 2

,2, *, ,

, 1

Msd j sr jm me e

j km mj m je sd m sr mk mj k

a ap p

Mp a a

αα

−

−

≠≠

=

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠

∑

(22)

According to formula (17), each sub-carrier can be allocated the power

''

,( , {1, 2,3...... })

m mp m m M∈ .

IV. SIMULATION RESULTS

In this section, consider a cooperative conmunication system with one source node, one relay node, and one destination node in the cellular network. The wireless link is assumed as Raleigh fading between nodes. This section provides numerical results to quantify the power consumption of OFDM-DF-PA, EPA and NPA.

System uses OFDM-QPSK modulation; the number of available sub-carriers M is 64; the transmission rate of system is M bits/symbol. The distance from source to relay, source to base, relay to base is respectively 0.4 km, 1.4 km, 1.1 km. The path loss model is Okumura-Hata: ( ) 133 38*log( )l d d= + in dB. The d is the distance from transmission node to receiving node.

Figure 2. Power consumption in different received SNR

Figure 2 and Figure 3 show the received SNR, interference and system total power. The power consumption of OFDM-DF-PA is about 10% (20%) less than EPA’s (NPA’s). When system demands high SNR, the power is raising rapidly with the interference increasing. OFDM-DF-PA is better than EPA in anti-interference ability.

Figure 3. Power consumption in different interference

For different power allocation algorithm, the system BER influencing on power is shown in Figure 4. Power

consumption of NPA is always greater than the EPA and the OFDM-DF-PA. EPA consumes more power than the OFDM-DF-PA with increasing BER. When the error rate is 10-4, the difference of them is about 0.5dBW. OFDM-DF-PA can consume about 8% less power than the EPA at the same performance.

Figure 4. System BER effect on power

V. CONCLUSION In this paper, a suboptimal power allocation algorithm is presented for relaying OFDM system. Because of the co-channel interference in the OFDM system (RF=1), power allocation aims to minimize transmission power under the constraint of the system BER. The power allocation is divided into two steps: sub-carriers allocation and power allocation. Simulation results show that the proposed algorithm can make the transmission node consume the least power among the algorithms of the OFDM-DF-PA, EPA and NPA under the same BER performance.

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