Adaptive Optimal Transmit Power Allocation for Two-hop Non-regenerative Wireless Relaying System Zhang Jingmei, Zhang Qi, Shao Chunju, Wang Ying, Zhang Ping
Zhang Zhang
Wireless Technologies Innovation Labs, Beijing University of Posts and Telecommunications P.O. Box 92, BUPT, Beijing 100876, P.R.China E-mail:
[email protected]
Ericsson Research (Bei jing) Encsson (China) Co. Ltd.
[email protected]
order to combat fading in wireless networks and increase the capacity of a system, cooperation is allowed among the terminals in the network. The adaptive optimal power allocation (PA) scheme based. on certain system performance is an important issue for the relaying routing and the network operation. This paper analyzes the twnhop nun-regenerative (NR) relaying channel with and without diversity, and investigates the optimal PA scheme between the source terminal (TX) and the relaying terminal (RS) under power constraint. Since i n the real relaying environments, the transmitter usually knows the instantaneous channel state information (ICSI) of the 1st hop and the statistical channel state information (SCSI) of the 2nd hop, the proposed PA schemes are based on two-hop lCSl and two-hop mixed channel state information (MCSI) respectively. With the adaptive scheme, the system performance nut only outperforms that of the direct transmission system, but also obtains the maximum channel capacity or SNR of the relaying system.
an adaptive optimal power allocation (PA) scheme based on certain system performance is an important issue for the relaying routing and the network operation. Some papers analyze the wireless relaying channel and allocate equal power at each relaying node [4][5]. Others give the adaptive PA scheme based on the bit error rate (BER) [6], while it is dependent on the modulation scheme employed. An optimal coherent combining in the cooperative relaying network is analyzed in [7]. However, these schemes do not consider whether the receiver knows the instantaneous or statistical channel state information.
Abstract-In
Keywords- cooperative rehying, Optimal power allocation, Channel capmi$, Non-regenerative
1.
INTRODUCTION
Digital cooperative relaying is a technique that uses certain mobile terminals to act as the relaying nodes for those who do not have reliable communication links [1][2]. The advantage of the cooperative relaying system consists in its combating fading and exploiting spatial diversity [3]. The most important thing is that with the same transmit power it substantially improves the network specifications, such as signal to noise ratio (SNR) and channel capacity. Repeater is a simple cooperative relaying scheme with low complexity [4][5]. There exist at least two cooperative diversity schemes to realize the repeater [6]. One is the non-regenerative relaying which amplifies and forwards what it received, and the other is regenerative relaying which decodes and forwards what it received. In the research about the repeater, the optimal allocation of the radio resources (the transmit power and the bandwidth) between the transmitter and the relaying nodes is still an open issue.
This paper analyzes the two-hop non-regenerative (NR) relaying transmission with and without diversity, and investigates the optimal PA scheme between the TX and the RS under power constraint. In the real relaying environments, the instantaneous channel state information (ICSI) of the 1st hop can be easily got, while the transmitter only knows the statistical channel state information (SCSI) of the 2nd hop. So the proposed PA schemes are based on the two-hop ICs1 and two-hop mixed channel state information (MCSI) separately, and with these adaptive schemes, the system can obtain the maximum channel capacity or SNR. The two-hop wireless communication system model is provided in Section II. In Section 111, the optimal PA schemes are analyzed. Numerical results are presented in Section lV, and conclusions are drawn in Section V. 11. TRANSMISSION MODEL
The two-hop wireless communication system model is composed of a source terminal TX, a receiving terminal RX, and a relaying terminal RS (see Fig.1). The whole transmit process includes two timeslots. The TX transmit signal at the 1st timeslot, and the RS relayed the signal at the 2nd timeslot.
The efficient power allocation is an effective way to save the transmit power and improve the coverage and capacity of the system. Besides, it can provide some guidance to the relayng selection algorithm (mobile RSs) or the site selection algorithm for the RSs (fixed RSs) in the real networks. Thus This work is fmanced by Ericsson company.
0 - 7 8 0 3 - 8 2 5 5 - W ~ . 0 0OuM4 IEEE.
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Figure I . Syslem model for two-hop relaying channel
Each terminal receives a signal given by
Y.:(t)=hi(t)~~j(f)tZ,(t)
(1)
where X,( t ) is the transmitted signal at time I , and Y.(I) is is the power of the received signal corresponding to X,( I ) , the transmitted signal. For the NR relaying, A',(/) may contain some noise received by the RS. hi ( i= 0,1,2) captures the effects of the attenuation and the multipath fading between the transmitter and the receiver. The multipath fading is Rayleigh distributed. Shadowing effects are not considered here. Z j ( t ) captures the effects of the additive noise and other forms of interference, which is a zero-mean complex Gaussian white noise process. The variance of Z i ( t ) is uj*. The TX transmits the original symbol sequences. In case that the direct path suffers from a deep fading, i.e. h, is too low to provide a satisfactory quality, the symbol will be relayed to the destination terminal RX via the intermediate terminal RS. The RX may only receive the relayed signal (relaying without diversity) or combine the signals from both the TX and the RS (relaying with diversity).
B. Optimal PA based on the huo-hop ICSI When TX knows the ICSI of the 1st hop and the 2nd hop, the channel capacity based on Shannon theorem is taken as the cost function. The channel capacity of the NR relaying with diversity is expressed as:
c = log, (I+ r D ) Where
(6)
r D is the SNR at the RX with diversity [SI: (7)
For the two-hop ICSI, the maximization of the channel capacity is equivalent to the maximization of SNR, so the optimal PA issue can be presented as
s. f. P, = P7\.+P,,
Then some notations can be written as
(8)
Applying Lagrange Multiplier, the optimal transmit power P, and PRs can be obtained.
where
Equation (9) holds when and only a l a , +a,a, - - , a , >Oand a l a 2 P , - a , a , P o - a , > O .
Consider the power constraint at the transmitter, PTx + PRs = Po, and Po denotes the reference power.
when
For the relaying without diversity, the optimal PA is the case of a , = 0 in (9), which can be written as
111. OPTIMAL POWER ALLOCATION
A. Acqiiisition of Channel Information
In terms of the different feedback capabilities, the acquisition of the channel information can be classified into 3 categories: the TX and the RS know the lCSl of the 1st hop and the 2nd hop; the TX and the RS know the SCSl of both hops; the TX and the RS know the ICs1 of the 1st hop and the SCSl of the 2nd hop, which is called two-hop MCSI. These three conditions reflect the differences of the feedback capabilities and correspond to distinct optimization strategies. In the real systems, SCSI is not very practical since the TX and the RS can easily get the ICs1 of the 1st hop. So the optimal PA schemes are analyzed based on the two-hop ICs1 and two-hop MCSI.
C. Optimal PA based on the hvo-hop MCSI If the 1st hop ICSl and 2nd hop SCSl are known to the TX, it tums to the MCSI condition, and the average SNR is taken as the cost function. The optimal PA issue is the same as (X),
but it should be noted that now r2 is an exponentially distributed random variable because the channel is Rayleigh fading [ 5 ] . So the optimal solution can not be got directly by (8) . , as the case of ICSI. and the ootimization is according to the average SNR at the RX,
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-
r D.
-
The PDF of
r,
Then the optimal PA can be derived from the following equation:
is 1
--Yi
fr2(Yz)=,e
,Y, > O
*I
1 4 1 r ?'
where R, is the expected value of the random variable
-
Ihpm and C& =-=a,P,, U,,
- , which depends on the -
attenuation and fading, Ih2
1'
r, ,
-
For the relaying without diversity, the optimal PA is the case of a, = 0 in ( I X), which can be written as
r Dis
141' d
r,
and using (2) and (3), the power constraint can be written as
-
a, (P,a*y-l) -
-x=
a,'y
01
(15)
+a*y
Then (13) can be expressed as
~e-" - x r D=ro+ I--;-.e".('~U'du=r,+x.(I-ye'. J-dfr) ,U v U -
-
= r,,+ a1 (Poa,J'-l) . ( I - ye' +a,y
,
1-
,.
(16)
dtr) 11
Take the derivative with respect to y , and set it to 0,
d - d a,(P a -rD =--[T, + ""-l)
dv
dv
a , +a,y
me-"
.(1 -ye" . 1.
(19)
C = a l +a,y
Assuming
x+l -+-=Po
-- 1
B = ,,Poy
Then the average SNR at the RX with diversity is calculated as:
x
(18)
A=a,P,,+I
average
(12)
=
a,A(a, + a , ) + B C a ,
a,e'.[(l+y)BC+~Ay]
Where
y s0
"1
=
11
, ofthe 2nd hop.
Then the cumulative distribution function (CDF) of
01
-
*e-"
(11)
l
1
=
a,A+BC
e'[(l+y)BC+yAy]
(20)
Although it is quite difficult to get the closed-form solutions to (19) and (20), the numerical solutions are possible through computation.
Iv. NUMERICAL RESULTS Some numerical results are given in this section. Monte Carlo method is used to evaluate the performance. Pass loss is given by L = d - P , where d is the distance between the transmitter and the receiver, which is normalized with respect to the distance between the TX and the RX. Path loss exponent p is 3. The multi-path fading is complex Gaussian distributed with zero mean and 0.5 variance per complex dimension. Thus the envelope follows a normalized Rayleigh distribution. Shadowing effects are not considered. For simplicity, the variance oj2of additive white Gaussian noise random variables at each receiver is assumed equal and unified, i.e. 0: = 6' = I . The transmit power constraint Po is unified as 1. To comparing the system performance with optimal PA scheme and that with the direct transmission and the uniform PA scheme, a square area is studied, where the TX and RX are located at (0,O) and ( I ,0) respectively, and the RS ranges from 0 to 1 along the x-axis and -0.5 to 0.5 along the y-axis (Fig.2 and Fig.3) or ranges at the x-axis (Fig.4 and Fig.5). For the MCSI, the channel capacity is averaged. Fig.2 shows the channel capacity with diversity under the proposed PA based on ICSI, and the horizontal plane represents the capacity of the direct transmission. Fig.3 gives the case of MCSI. From Fig.2 and Fig.3, it can be seen that the NR relaying with diversity can always bring the capacity gains over the direct transmission in the simulated area. Besides, the point with the best performance is closer to the RX and the distribution of the performance is asymmetric. It indicates that the capacity gain is fairly sensitive to the relative position of RS, which can be used to make routing.
du)]= 0 ( 17)
U
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Capactty Comparison (NR Without Diversity)
Average Capacity of Optimal PA Based on ICSI, NR with Diversity 1051
,
I
Figure 2. Channel capacity with optimal PA based 00 iCSl
Capacity Comparison [NR Wfih Diversity)
Average CapacityofOptimal PA Based on MCSI, NRwith Diversity 16
-
0.81 0.09
'
0.19
0.X
0.39
0.49
0.59
0.6g
0.19
0.0
I
0.S
d l (from the source terminal) Figure 3. Channel capacity with optimal PA based an MCSI
Figure 5. Capacity comparison among differentPA with diversity
For the channel capacity without diversity, its shape is similar to that in Fig.2 and Fig.3, but the performance is worse than that with diversity, which is expectable.
For the system without diversity, the capacity with the optimal PA based on MCSI is always higher than that with the uniform PA despite of the RS's position, while for the system with diversity, the capacity with the optimal PA scheme based on MCSI becomes higher than that with uniform PA when the distance between TX and RS increases. This is because that in some circumstances, the optimal PA does not exist according to the adopted PA algorithm, and the direct transmission is taken in place.
Fig.4 gives the capacity comparison of the NR relaying system among different PA schemes without diversity, and FigS gives the case with diversity. The x-axis is the distance from the TX to the RS, and the RS just ranges along the line between the TX and the RX. From Fig.4 and Fig.5, it can he seen that the system with the optimal PA scheme based on ICSI has the best performance. The reason is that the system with ICs1 can always track the channel fading in real-time, and the transmit power can be adjusted in an adaptive way.
0-7803-8255-2/w/$20.00 Oux)4 IEE.
The figures also show that the system with direct transmission has the lowest capacity when diversity is adopted. But for the case without diversity, the performance of the
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system with uniform PA is even worse in some areas. That is to say, the uniform PA scheme that does not take the channel information into account degrades the system performance in some areas, where the performance is even worse than that of the direct transmission. Comparing Fig.4 and Fig.5, it can be seen that the relaying system with diversity can get more capacity gains than that without diversity, and the capacity gain is quite dependent on the position of the RS.
[6] 1. Boyer. D. Falconer, and H. Yanikomeroglu. “A theoretical charactenration of multihop m,ircless communications channels.” Proc. of Canadian Workshop on Information Theory, 2001.
[7] Peter Larsson and Ericsson Research, “Large-Scale Cooperative Relaying Network with optimal Coherent Combining under Aggregate Relay Power Constraints,” FTC 2003. [8] T. Cover and A. El Gamal, “Capacity theorems for the relay channel: IEEE Trans. on Info. Th., vol. 25, pp. 572-84, 1979.
V. CONCLUSION This paper analyzes the two-hop NR relaying transmission with and without diversity, and investigates the optimal PA scheme between the TX and the RS under power constraint. Considering the different feedback Capabilities provided by the networks, the proposed PA schemes are based on the two-hop ICs1 and MCSI separately, which maximizes the channel capacity (with ICSI) or the average SNR (with MCSI) to get the better performance. The numerical results suggest that there are significant advantages to be gained by employing the relaying. Comparing with the uniform PA relaying and the direct transmission, the relaying with the optimal PA can get the better performance, except the case with diversity where there is no solution to the optimal PA based on the MCSI, and the direct transmission is taken in place. For the different feedback capabilities, the relaying based on ICSI has the better performance than that based on MCSI, because in ICs1 the transmitter can track the channel fading and adjust the transmit power in real-time. When diversity is included, the performance is improved. The analyses and the simulations in this paper give the direction to hrther study about the relaying techniques, for instance, the capacity gain corresponding to different RS positions can he used to assist in routing for the relaying network. ACKNOWLEDGMENT
The authors of this paper thank Hu Rong and Peter Larsson for their helpful discussions and suggestions. Their support is gratefully acknowledged. REFERENCES A. Sendonaris, E. Erkip, and B. Aazhang, “Increasing uplink capacity via user cooperation divmiiy,” in h o c . of IEEE Int. Symp. an h f u . Theoly, Cambridge, MA, Aug. 1998, p. 156. [2] J. N. Laneman and G.W.Womcll. ”Exploiting dismbuted spatial diversity in wireless networks.“ in Proc. of Allenon Conf. an Commun., Contr., and Computing, Urbana Champape, IL, Oct. 2000. [3] V. Emamian, and M. Kaveh, “Combating Shadowing Effects for Systems with Transmitter Diversity by Using Collaboration among Mobile Users”, Proceedings of the lntemational Symposium on Communications. Nov 13-16,2001, Taiwan. [4] J. Nicholas Laneman, “Cooperative Diversity in Wireless Nehuarks: Algorithms and Architectures.” M.I.T. Doctoral Dissertation, Sep. 2002. [5] J. N. Laneman, and G.W. Womell. “Energy-effcient antenna sharing and relaying for wireless networks,“ E E E Wireless Communications and Networking Conference. Vol. I , 2000. pp. 7 -12. [I]
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