August 2010, 17(4): 13–17 www.sciencedirect.com/science/journal/10058885 http://www.jcupt.com

The Journal of China Universities of Posts and Telecommunications

Research on the low complexity adaptive power allocation algorithm in cooperative systems

WANG Liang1,2 ( ), XIE Wei-hao1,CHEN Hui-min1, WU Zhuo1

1. Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200072, China

2. China Mobile Communication Group Shanghai Co., Ltd, Shanghai 200060, China

Abstract

Cooperative diversity is a new technology to improve bit error rate (BER) performance in wireless communications. A new power allocation algorithm to improve BER performance in cellular uplink has been proposed in this paper. Some existing power allocation schemes were proposed for the purpose of maximizing the channel capacity or minimizing the outage probability. Different from these schemes, the proposed algorithm aims at minimizing the BER of the systems under the constraint of total transmission power. Besides this characteristic, the proposed algorithm can realize a low complexity real-time power allocation according to the fluctuation of channels. Simulation results show that the proposed algorithm can decrease the BER performance of the systems effectively.

Keywords cooperative communication, power allocation, BER

1 Introduction

Multiple-input multiple-output (MIMO) has been acknow- ledged as one of the key technologies in future wireless communication systems [1]. However, it is not easy to be implemented in wireless cellular system due to the size limitation of handsets. In order to solve this problem, cooperative systems were introduced in Refs. [2–3] in recent years. The performance of such systems can be improved without increasing extra antennas in mobile terminals by using cooperative users to relay the information to the destination. The power of mobile terminals is limited more strictly than that in base station (BS), so it is more essential for the uplink to apply cooperative communication to keep the reliability of transmission in cellular systems.

An effective power allocation algorithm can make use of the limited transmission power to achieve better performance. For example, the channel capacity can be maximized using the power control schemes proposed in Refs. [4–5]. A power allocation algorithm was proposed in Ref. [6] to minimize the

Received date: 11-05-2009 Corresponding author: WANG Liang, E-mail: wonderligh@shu.edu.cn DOI: 10.1016/S1005-8885(09)60481-7

outage probability. Though a few power allocation schemes were proposed to improve the BER performance [7–8], they have some disadvantages. The scheme in Ref. [7] did not include any theoretic basis, and the objective function in Ref. [8] does not match the BER curve well. Moreover, the fatal flaw of them is that power allocation will not be adjusted with the fluctuation of channels.

In this paper, a new power allocation algorithm to optimize the BER performance under the constraint of total transmission power has been proposed. Different from the schemes in Refs. [4–8], the objective function in the proposed algorithm is the signal noise ratio (SNR) at the receiver. The optimal power allocation is derived by maximizing the SNR. Besides this difference, the proposed algorithm can realize a low complexity real-time power allocation according to the fluctuation of channels.

The rest of this paper is organized as follows. In Sect. 2, the cooperative system model of uplink in cellular network is depicted. In Sect. 3, a new power allocation algorithm is proposed to improve the BER performance. In Sect. 4, numerical results are presented. Finally, some conclusions are drawn in Sect. 5.

14 The Journal of China Universities of Posts and Telecommunications 2010

2 System model

Because it is more essential to apply cooperative communication in uplink, the power allocation algorithm on the uplink is focused in this paper. The cooperative communication system model of a uplink cellular system is illustrated in Fig. 1. It is composed of the source user (S), the relay user (R) and the destination (D), which is called as the BS in cellular uplink. For simplicity, the source user and the relay user are assumed to be in a single cell. Amplify- and-forward (AF) protocol is applied in the system.

Fig. 1 Diagram of cooperative communication model in cellular network

The procedure of cooperative communication can be divided into two phases. In both phases, we assume that the users transmit their information through orthogonal channels such as time division multiplexing fashion (TDM) [2]. The information in called as x. The scenario in which there is only one cooperative user is paid attention in this paper.

In phase 1, the source user broadcasts its information to both BS and relay user. The received signals SRr and SDr at

the relay user and the BS can be expressed as follows:

SR SR SRsr P h x n= + (1)

SD SD SDsr P h x n= + (2)

where sP is the transmission power allocated to source, SDn and SRn denote the noise at BS and the relay user respectively.

SDh and SRh stand for the channel coefficients from the

source to BS and the relay user respectively. In phase 2, the relay user amplifies the received signal and

then forwards it to BS. The signal received by BS at that moment is given by:

RD RD SR RDr h r nβ= + (3) where RDn denotes the noise at BS in this phase and RDh is the channel coefficient between the relay user and BS. β is the amplifier gain. The expression of β is revealed as follows:

r2

SR s 0

Ph P N

β =+

(4)

where rP is the power allocated to the relay user. In this paper, SDh , SRh and RDh are modeled as

independent zero-mean complex Gaussian random variables with variances 2

SDδ , 2SRδ and 2

RDδ , respectively. For

simplicity, channel state information (CSI) is assumed to have been known at the receiver and the transmitter doesn’t know the CSI. The channel is thought to not fluctuate dramatically in a transmission period. 0N is the variance of additive

white Gaussian noise (AWGN).

3 The low complexity adaptive power allocation algorithm in cooperative communication systems

As is well known to all, the SNR at the receiver affects the quality of communication greatly. The higher the SNR is, the more reliable the communication is. In other words, the higher SNR will bring lower BER. Based on this theorem, BER performance can be optimized by means of maximizing the SNR at the receiver. Therefore, the new power allocation algorithm to maximize the SNR has been proposed for the sake of better BER performance.

Because BS combines the received information by applying maximum-ratio combiner (MRC) [9], the output of MRC can be represented as follows:

SD SD RD RDr r rλ λ= + (5)

where *SD s SD 0P h Nλ = and (* * 2

RD RD SR 0 1sP h h Nλ β β⎡= + ⋅⎣

)2RDh ⎤

⎦ .

r can be written in term of x as follows:

( )

2 222*s SD s RD SRs SD

SD 220 0 0 RD1

P h P h hP hr x n x

N N N h

β

β= + + +

+

( ) ( )* *

s RD SRRD RD SR22

0 RD

1

P h hn h n

N h

ββ

β+

+ (6)

SDγ and RDγ denote the instantaneous SNR at BS in

phase 1 and that in phase 2, respectively. Based on Eq. (6), SDγ and RDγ can be obtained as following forms:

2

s SDSD

0

P hN

γ = (7)

( )

222s RD SR

RD 220 RD1

P h h

N h

βγ

β=

+ (8)

The instantaneous SNR at BS is denoted by γ . According to Ref. [10], γ can be expressed as

Issue 4 WANG Liang, et al. / Research on the low complexity adaptive power allocation algorithm in… 15

( )

2 222s SD s RD SR

SD RD 220 0 RD1

P h P h hN N h

βγ γ γ

β= + = +

+ (9)

If the amplifier gain β is replaced with Eq. (4), the objective function will be pointed out as follows:

2 2s r2SR RD

s SD 0 02 2s r0

SR RD0 0

arg max1

P Ph hP h N NP PN h hN N

⎧ ⎫⎪ ⎪⎪ ⎪+⎨ ⎬⎪ ⎪+ +⎪ ⎪⎩ ⎭

(10)

It is obvious that sP and rP have great impact on the

SNR at BS. The proposed power allocation scheme aims at optimizing Eq. (10) under the constraint of total transmission power.

sP and rP should be subjected to the constraints [4] as

follows: s r

s

r

00

P P PP PP P

+ = ⎫⎪< ⎬⎪< ⎭

≤

≤

(11)

where P is the total transmission power. sP and rP cannot exceed the total transmission power P and the sum of sP and

rP equals to P.

Based on Eqs. (10) and (11), Lagrange multiplier maximization method was applied to find the optimal solution for sP and rP . The modified objective function can be

written as Eq. (12). 2 2s r2

SR RDs SD 0 0

s r2 2s r0SR RD

0 0

( )1

P Ph hP h N N P P PP PN h hN N

ρ μ= + + + −+ +

(12)

2SD 0h N , 2

SR 0h N and 2RD 0h N reflect the qualities

of channels. They can be tracked easily and updated in a real-time way. If 2

SD 0h N , 2SR 0h N and 2

RD 0h N

are substituted by a , b and c respectively, Eq. (12) will be expressed as Eq. (13)

s rs s r

s r

( )1

cbPPaP P P PbP cP

ρ μ= + + + −+ +

(13)

The partial derivatives of sP and rP are taken. And then

Eq. (14) can be obtained by making them to equal to zero. 2

r s r s r2

s s r2

s s r s r2

r s r

s r

( 1) 0( 1)

( 1) 0( 1)0

cbP bP cP cb PPaP bP cP

cbP bP cP bc PPP bP cP

P P P

ρ μ

ρ μ

⎫∂ + + −= + + = ⎪∂ + + ⎪⎪

∂ + + − ⎬= + = ⎪∂ + + ⎪⎪+ − = ⎭

(14)

Eq. (14) can be simplified as follows:

2 2 2 2 2 2s( 2 ) 2(ab abc ac b c bc P abcP ab ac P ac− + − + + + − − −

2 2 2 2 2s ) 2 0bc bc P P acP a ac P bc P bcP+ + + + + + = (15)

If Eq. (15) has only one root, it can be expressed as s1P . If Eq. (15) have two roots, the roots can be expressed as s1,2P ,

which denotes s1P and s2P .

The power allocation on the uplink of cellular networks in a single transmission period is depicted as follows.

Step 1 If the source needs to communicate with the BS, it will transmit a request signal which is a training sequence as well in the form of broadcast.

Step 2 One of the idle users who are around the source user can be determined as the relay user. The relay user informs BS its channel quality. Those who have not been chosen as the relay will wait the next transmission period.

Step 3 Because BS has known the CSI and the channels are assumed not to fluctuate dramatically, the parameters in Eq. (15), a, b and c can be calculated.

Step 4 Eq. (15) is solved to determine the power allocated to source and relay user.

1) Only one root of Eq. (15) is in the domain of sP . s1P is

supposed to the root. Then the power is allocated as follows: a) If 2 2 2 22 0ab abc ac b c bc− + − + = , Eq. (15) is a linear

equation. The power allocated to the source equals to s1P . 2 2 2 2

s1 2 2

s s1

r s

2 (0, ]2( )

acP a ac P bc P bcPP PabcP ab ac P ac bc bc P

P PP P P

⎫+ + + += − ∈ ⎪+ − − − + ⎪

⎬= ⎪⎪= − ⎭

(16)

b) If 2 2 2 22 0,ab abc ac b c bc− + − + ≠ Eq. (15) is a

quadratic equation with one unknown variable. Because only one root of Eq. (15) is in the domain of sP , the root in the domain of sP is the value of power allocated to the source.

2 2

s1,2 2 2 2 2

2 2 2

2 2 2 2

12 2 2 2 2

2 2 2 2 1

s

( )2

[( ) ( 2 )

(2 )] ( 2 )

abcP ab ac P ac bc bc PPab abc ac b c bc

abcP ab ac P ac bc bc Pab abc ac b c bc

acP a ac P bc P bcPab abc ac b c bc

P P

−

− + − − − += ±

− + − ++ − − − + −

− + − + ⋅

+ + + + ⋅

− + − += s1 s1 s2

s s2 s2 s1

r s

; (0, ] and (0, ]; (0, ] and (0, ]

P P P PP P P P P PP P P

⎫⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪∈ ∉ ⎪⎪= ∈ ∉⎪

= − ⎪⎭

(17)

2) If two roots of Eq. (15) are in the domain of sP , the values of γ caused by s1P and s2P should be compared. The root that makes the γ greater is identified as the value

16 The Journal of China Universities of Posts and Telecommunications 2010

of sP . Then the power is allocated as follows: 2 2

s1,2 2 2 2 2

2 2 2

2 2 2 2

12 2 2 2 2

2 2 2 2 1

s

( )2

[( ) ( 2 )

(2 )] ( 2 )

abcP ab ac P ac bc bc PPab abc ac b c bc

abcP ab ac P ac bc bc Pab abc ac b c bc

acP a ac P bc P bcPab abc ac b c bc

P P

−

− + − − − += ±

− + − ++ − − − + −

− + − + ⋅

+ + + + ⋅

− + − += s1 s1 s2

s s2 s2 s1

r s

; ;

P P

P PP PP P P

γ γγ γ

⎫⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪> ⎪⎪= >⎪

= − ⎪⎭

(18)

where s1Pγ denotes the value of γ when sP equals to s1P

and s 2Pγ denotes the value of γ when sP equals to s2P .

If neither of roots is in the domain of sP . Under this

circumstance, all the transmission power is allocated to the source. The result can be proved by analyzing the monotonicity of Eq. (9).

s

r 0P PP

= ⎫⎬= ⎭

(19)

Step 5 BS informs the source and the relay user the values of sP and rP .

Step 6 The source and the relay user transmit the information with the allocated power.

From the above process, we can find that only a quadratic equation with one unknown variable or a linear equation is needed to be solved, so the complexity is low.

4 Numerical results

In the simulations, the source user and the relay user are considered to be in the same cell. The source user is assumed to have one relay user. Binary phase-shift keying (BPSK) constellation is used at the transmitter. The uplink is assumed to be under ideally synchronization, and the channel state information is known at the receiver. The SNR at the relay user was assumed to be 20 dB.

Fig. 2 shows the BER performance in different power allocation algorithms. It is clear that the BER performance in the proposed power allocation algorithm is better than that in the equal power allocation (EPA) scheme and in suboptimal power allocation algorithm (SOPA) in Ref. [8].

The way to calculate the outage probability is revealed in Ref. [10]. The outage probability can be expressed as:

22 2 2out SR RD

AF 2 2 2SD SR RD

2 1( , ) ~2

R

P R δ δγδ δ δ γ

⎛ ⎞+ −⎜ ⎟⎝ ⎠

(20)

According to Eq. (20), the outage probability can be determined. In the simulations, the values of parameters in Eq. (20) are the same as that in Ref. [10]. Fig. 3 shows that the outage probability performance will be improved by the low complexity adaptive power allocation algorithm.

Fig. 2 BER comparison in different power allocation schemes

Fig. 3 Outage probability comparison in different power allocation schemes

5 Conclusions

A low complexity adaptive power allocation algorithm to improve the BER performance in cooperative systems has been proposed in this paper. Different from the existing power allocation schemes, the proposed algorithm can adjust the power of the source and the relay adaptively in a low complexity way. Compared with the existing power allocation schemes, the proposed algorithm improves the BER and outage probability performance effectively.

Therefore, the proposed power allocation algorithm to improve BER performance is significant to the uplink of cooperative cellular wireless systems.

Acknowledgements

This work was supported by the Shanghai Leading Academic Discipline Project and STCSM (S30108 and 08DZ2231100), the

Issue 4 WANG Liang, et al. / Research on the low complexity adaptive power allocation algorithm in… 17

Shanghai Pujiang Program (08PJ14057), and the Fund of Innovation for Graduate Student of Shanghai University (Shucx080151).

References

1. Berkmann J, Carbonelli C, Dietrich F, et al. On 3G LTE terminal implementation: standard, algorithms, complexities and challenges. Proceedings of the IEEE International Conference on Wireless Communications and Mobile Computing Conference (IWCMC’08), Aug 6−8, 2008, Crete Island, Greece. Piscataway, NJ, USA: IEEE, 2008: 970−975

2. Sendonaris A, Erkip E, Aazhang B. User cooperation diversity, Part I: system description. IEEE Transations on Communications, 2003, 51 (11): 1927−1938.

3. Laneman J N, Tse D N C, Wornell G W. Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Transactions on Information Theory, 2004, 50(12): 3062−3080

4. Zhang J M, Wang Y, Zhang P. Capacity analysis and power allocation for multi-antenna cooperative system. Journal of Beijing University of Posts and Telecommunications, 2005, 28(5): 11−15 (in Chinese)

5. Host-Madsen A, Zhang J. Capacity bounds and power allocation for

wireless relay channels. IEEE Transations on Information Theory, 2005, 51(6): 2020−2040

6. Hasna M O, Alouini M. Optimal power allocation for relayed transmissions over Rayleigh fading channels. IEEE Transations on Wireless Communications, 2004, 3(6): 1999−2004

7. Zheng Y Y, Hou X Y, Zheng T. A new power allocation scheme of cooperative diversity. Journal of Chongqing University of Posts and Telecommunications (Natural Science), 2007, 19(4): 465−467 (in Chinese)

8. Lin F, Li Q H, Luo T, et al. Impact of relay location according to SER for amplify-and-forward cooperative communications. Proceedings of the 2007 IEEE International Workshop on Anti-counterfeiting, Security, Identification (ASID’07), Apr 16−18, 2007, Xiamen, China. Piscataway, NJ, USA: IEEE, 2007: 324−327

9. Brennan D G. Linear diversity combining techniques. Proceedings of the IEEE, 2003, 91(2): 331−356

10. Seddik K G, Sadek A K, Su W F, et al. Outage analysis and optimal power allocation for multinode relay networks. IEEE Signal Processing Letters, 2007, 14(6): 377−380

(Editor: WANG Xu-ying)