A multi-user power control algorithm for digital subscriber lines ...
IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 3, MARCH 2005
193
A Multi-User Power Control Algorithm for Digital Subscriber Lines Jungwon Lee, Student Member, IEEE, Ranjan V. Sonalkar, Senior Member, IEEE, and John M. Cioffi, Fellow, IEEE
Abstract— This paper investigates the power control problem in a frequency-selective interference channel. A centralized power control algorithm is developed with an objective of maximizing the achievable rate region given an average power constraint for each user. The proposed algorithm is based on the multi-user discrete bit-loading algorithm that considers the power allocation over frequency and users simultaneously. Simulation results for very high-speed digital subscriber line (VDSL) systems show that the proposed algorithm enlarges the rate region achieved by a power control algorithm based on the iterative waterfilling.
rate of long loops. The power control algorithm based on iterative waterfilling in [5] outperforms the algorithms in [7] but still shows a quite large performance gap from the optimal spectrum management algorithm in [6]. Although the optimal algorithm in [6] is less complex than the optimal algorithm based on the exhaustive search, it still has high computational complexity. This letter develops a power control algorithm with low complexity that can achieve significantly better performance than the algorithm based on iterative waterfilling.
Index Terms— Power control, dynamic spectrum management, discrete multi-tone, multicarrier systems, digital subscriber line.
I. I NTRODUCTION
R
ECENTLY, there has been growing interest in multiuser discrete multi-tone (DMT) systems [1]–[3]. Digital subscriber lines (DSL) with DMT are now viewed as a multi-user DMT system because of crosstalk, which is often dominant source of performance degradation. The crosstalk can be cancelled when the receivers or transmitters can be coordinated [4]. On the other hand, the effect of the crosstalk can be reduced by dynamic spectrum management when no coordination is allowed [5], [6]. Without the crosstalk cancellation or proper spectrum management, DSL systems suffer from a near-far problem: the user close to the central office limits the performance of the user far from the central office [7]. If all users employ equal power, the crosstalk from a short loop can severely degrade the performance of a long loop. Thus, a power control algorithm should be implemented to prevent a long loop from achieving unfairly small data rate. This power control algorithm should be able to change the power spectrum dynamically as well as the total power of each user so that the rate region is maximized. Many different algorithms have been proposed to maximize the rate region in DSL systems [5]–[7]. The algorithms in [7] are simple to implement. However, they tend to restrict the data rate of short loops in order to increase the data
Manuscript received March 31, 2004. The associate editor coordinating the review of this letter and approving it for publication was Prof. Ezio Biglieri. This letter was presented in part at IEEE GLOBECOM, November 17-21, 2002, Taipei, Taiwan. J. Lee is with Marvell Semiconductor, Inc., Sunnyvale, CA, USA (e-mail: [email protected]). R. V. Sonalkar is with MITRE Corp., Eatontown, NJ, USA (email:[email protected]). J. M. Cioffi is with the Department of Electrical Engineering, Stanford University, Stanford, CA, USA (e-mail: [email protected]). Digital Object Identifier 10.1109/LCOMM.2005.03004.
II. S YSTEM M ODEL A DSL channel with multiple users can be viewed as an interference channel, a broadcast channel, or a multiple access channel depending on the coordination allowed at the transmitter or receiver side. When the transmitters can generate a signal cooperatively, a DSL channel can be modeled as a broadcast channel. On the other hand, when the receivers can process the received signal cooperatively, it becomes a multiple access channel. For these broadcast and multiple access channels, a vectored DMT technique can be used to cancel the crosstalk among users [4]. However, in current loop topology of DSL systems, the coordination at the signal level is often impossible. In this case, a DSL channel should be viewed as an interference channel. When the DMT technique is used with synchronized receivers, a DSL channel can be modeled as N independent frequency non-selective subchannels, each of which is an interference channel of M users. Without crosstalk cancellation, the signal-to-interference-plus-noise ratio (SINR) of user i in subchannel n is expressed as Si (n) =
2 (n)Pi (n) Hi,i , M 2 (n)P (n) Ni (n) + j=1,j=i Hi,j j
(1)
where Pi (n) and Ni (n) are the signal power and the background noise power of user i in subchannel n, respectively. The channel coefficient Hi,i (n) represents the direct channel gain of user i in subchannel n, while Hi,j (n) represents the crosstalk channel gain from user j to user i. Assuming that the crosstalk and the background noise are Gaussian [8], the data rate of user i in subchannel n is approximated by Si (n) bi (n) = log2 1 + , (2) Γ where Γ is the SINR gap to capacity that depends on the probability of symbol error, the noise margin, and the coding gain [1]. Here, it is assumed that common single-user codes
c 2005 IEEE 1089-7798/05$20.00
194
IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 3, MARCH 2005
14
for the AWGN channel are used instead of complex coding schemes specifically designed for a multi-user interference channel. The data rate of user i is then =
N
bi (n),
(3)
n=1
in bits per symbol. A rate region is defined as the union of all the rate sets (R1 , · · · , RN ) that can be achieved while satisfying the following power constraint: Pi ≤ Pmax,i for i = 1, · · · , M, where Pi =
N
(4)
Data rate of a 3000 ft loop (Mbps)
Ri
12
10
8
6
4
2
Pi (n),
(5)
n=1
and Pmax,i is a maximum power for user i. The main problem of interest is to develop a power control algorithm that maximizes the achievable rate region for the best trade-off of data rates among near and far users. In this letter, it is assumed that a centralized spectrum management center has the channel information and regulates the power spectrum and data rate of each user. The degree of coordination necessary for the spectrum management is much less than the vectored DMT scheme that requires signal-level coordination. Thus, a spectrum management center can be deployed with a minimal change in current DSL systems. III. P OWER C ONTROL A simple approach to the power control for DSL systems was proposed in [5]. The power control algorithm in [5] assigns a power budget to each user and allocates the power to subchannels with iterative waterfilling. If the resulting rate set is not satisfactory, a new power budget is assigned, and the power is allocated to subchannels again. The assignment of a power budget and the power allocation process are repeated until a desirable rate set is achieved. In this power control algorithm, the power control process is separated from the power allocation. This separation of the power control from the power allocation makes the algorithm simple, but it can cause performance loss. The total power used by each user should be determined as a result of the power allocation. Here is an example that illustrates this point. Consider two users, one far from a central office and the other near the central office. To increase the rate of the far user, the power control algorithm in [5] reduces the power of the near user. Then with a given power budget, the iterative waterfilling algorithm will allocate the power to subchannels. This power allocation will result in a certain data rate for the near user and the far user. In many cases, for DSL channels, the far user will occupy only the low frequency band. Thus, if the remaining power of the near user is poured into the high frequency band that are not used by the far user, the data rate of the near user can be increased without affecting the far user. This example shows how the power control algorithm in [5] can be improved in a simple manner. The power of each user should be used in full if there are subchannels that are not shared with other users. In general, the power control should be done in conjunction with the power allocation to maximize the performance.
0 0
Fig. 1.
Iterative waterfilling Proposed algorithm Vectored DMT 5
10
15 20 25 Data rate of a 2000 ft loop (Mbps)
30
35
40
Rate region of a 3000 ft loop and a 2000 ft loop.
This letter proposes a power control algorithm that employs the multi-user bit-loading algorithm in [9], which not only has low complexity but also performs almost as well as the optimal exhaustive search algorithm. The multi-user bitloading algorithm is a greedy algorithm that allocates power and bit to the user and subchannel pair with the least cost. The power allocation is repeated until any of the user cannot increase the data rate without violating the power constraint of any user. For the purpose of the power control, the cost function in [9] is modified to the weighted sum of incremental power: M wj ∆Pj,i (n), (6) J(n, i) = j=1
where ∆Pj,i (n) is the incremental power of user j to add one bit to user i, and wi is a nonnegative weight of user i. With this modified cost function in the multi-user bitloading algorithm, the power control algorithm can be described as follows: 1) Initialization: Let the weight wi = wi,initial for i = 1, · · · , M . 2) Power allocation: Allocate power to subchannels and users using the multi-user bit-loading algorithm with given power weights. 3) Test of rate requirement: If the desired rate set has been achieved, stop here. 4) Assignment of a new weight: a) If the data rate of user i needs to be increased, reduce wi by setting wi = wi /ζ. b) If the data rate of user i needs to be decreased, raise wi by setting wi = wi ζ. c) Go to the power allocation step. In the above, ζ should be chosen depending on how much the rate set (R1 , · · · , RM ) should be changed. In a typical DSL channel, ζ of 10 is a reasonable choice. The proposed power control algorithm varies the power assigned to each user indirectly by changing the weights. Here is how it works for two user case. If the weight of user 1 is smaller than the weight of user 2, the cost function is less
LEE et al.: A MULTI-USER POWER CONTROL ALGORITHM FOR DIGITAL SUBSCRIBER LINES
195
30
10
Proposed algorithm Iterative waterfilling 25
8
Average data rate of four short loops (Mbps)
Average data rate of four 3000 ft loops (Mbps)
9
7 6 5 4 3 2 1 0 0
Fig. 2.
Iterative waterfilling Proposed algorithm 2
4
6 8 10 12 14 16 Average data rate of four 2000 ft loops (Mbps)
20
15
10
5
0
18
20
Rate region of four 3000 ft loops and four 2000 ft loops.
influenced by the power increase of user 1. Thus, user 1 is favored over user 2, and the power of user 1 will be allocated faster than user 2. If user 2 can increase its data rate without disturbing user 1, user 2 can use all its power. However, if user 2 cannot find a way of increasing its data rate without affecting user 1, user 2 will not use all its power. Thus, the multi-user bit-loading algorithm may not allocate the maximum power Pmax,i for all users, and the amount of power assigned to each user is controlled by the weights in the cost function. IV. S IMULATION R ESULTS The proposed algorithm is applicable to any DSL system whose performance is limited by far-end crosstalk (FEXT) [1]. In this section, it is applied to the VDSL upstream transmission with the simulation parameters taken from [10]. Fig. 1 shows the rate region of a 3000 ft loop and a 2000 ft loop achieved by the proposed algorithm, the power control algorithm based on the iterative waterfilling [5], and the vectored DMT scheme [4]. As can be seen from the figure, the proposed algorithm outperforms the algorithm based on the iterative waterfilling, and the vectored DMT scheme outperforms the proposed algorithm. However, the vectored DMT scheme requires the coordination among receivers at the central office, whereas the proposed algorithm does not require any coordination in decoding process. Fig. 2 shows the achievable rate region of four 3000 ft loops and four 2000 ft loops. Since the data rates of same-length loops are approximately equal, the average data rates are taken so that the rate region can be drawn in two dimension. Compared to the two-loop case, the rate region is much smaller due to the crosstalk among same-length loops. However, the proposed algorithm still works better than the algorithm based on the iterative waterfilling. Although it is not shown in the figure, the rate region achieved by the vectored DMT is almost the same as the rate region for the two-loop case. Fig. 3 is a plot of the average data rate of four L ft loops, where L varies from 500 to 2500. The other four loops are 3000 ft long, and their data rates are fixed at 7.5 Mbps. It is shown that the proposed algorithm can increase the data rate
500
1000 1500 2000 Loop length of four short loops (ft)
2500
Fig. 3. Average data rate vs. loop length of four short loops: Four long loops are at 3000 ft and the average data rate of the long loops is fixed at 7.5 Mbps.
of the short loops by up to 60% compared to the algorithm based on the iterative waterfilling. V. C ONCLUSIONS This paper examined the power control problem in a frequency-selective interference channel and proposed a centralized power control algorithm utilizing the multi-user bitloading algorithm. It was shown by simulation that the proposed algorithm outperforms the power control algorithm based on the iterative waterfilling. R EFERENCES [1] T. Starr, M. Sorbara, J. M. Cioffi, and P. J. Silverman, DSL Advances, Upper Saddle River, NJ:Prentice Hall, 2003. [2] S. N. Diggavi, “Multiuser DMT: a multiple access modulation scheme,” in Proc. IEEE GLOBECOM, 1996, pp. 1566-1570. [3] J. R. Roche and A. D. Wyner, “Method and apparatus for transmitting signals in a multi-tone code division multiple access communication system,” U.S. Patent 5 410 538, 1995. [4] G. Ginis and J. M. Cioffi, “Vectored transmission for digital subscriber line systems,” IEEE J. Select. Areas Commun., vol. 20, pp. 1085-1104, June 2002. [5] W. Yu, G. Ginis, and J. M. Cioffi, “Distributed multiuser power control for digital subscriber lines,” IEEE J. Select. Areas Commun., vol. 20, pp. 1105-1115, June 2002. [6] R. Cendrillon, M. Moonen, J. Verliden, T. Bostoen, and W. Yu, “Optimal multi-user spectrum management for digital subscriber lines,” in Proc. IEEE ICC, 2004. [7] K. S. Jacobsen, “Methods of upstream power backoff on very high-speed digital subscriber lines”, IEEE Commun. Mag., vol. 39, pp. 210-216, Mar. 2001. [8] K. J. Kerpez, “Near-end crosstalk is almost Gaussian,” IEEE Trans. Comm., vol. 41, pp. 670-672, Jan. 1993. [9] J. Lee, R. V. Sonalkar, and J. M. Cioffi, “Multi-user discrete bit-loading for DMT-based DSL systems,” in Proc. IEEE GLOBECOM, 2002, pp. 1259-1263. [10] “Very-high-speed digital subscriber lines (VDSL) metallic interface, part 1: functional requirements and common specification,” T1E1.4 Contribution 2002-031R2, Editor: Q. Wang. Available: http://www.t1.org
193
A Multi-User Power Control Algorithm for Digital Subscriber Lines Jungwon Lee, Student Member, IEEE, Ranjan V. Sonalkar, Senior Member, IEEE, and John M. Cioffi, Fellow, IEEE
Abstract— This paper investigates the power control problem in a frequency-selective interference channel. A centralized power control algorithm is developed with an objective of maximizing the achievable rate region given an average power constraint for each user. The proposed algorithm is based on the multi-user discrete bit-loading algorithm that considers the power allocation over frequency and users simultaneously. Simulation results for very high-speed digital subscriber line (VDSL) systems show that the proposed algorithm enlarges the rate region achieved by a power control algorithm based on the iterative waterfilling.
rate of long loops. The power control algorithm based on iterative waterfilling in [5] outperforms the algorithms in [7] but still shows a quite large performance gap from the optimal spectrum management algorithm in [6]. Although the optimal algorithm in [6] is less complex than the optimal algorithm based on the exhaustive search, it still has high computational complexity. This letter develops a power control algorithm with low complexity that can achieve significantly better performance than the algorithm based on iterative waterfilling.
Index Terms— Power control, dynamic spectrum management, discrete multi-tone, multicarrier systems, digital subscriber line.
I. I NTRODUCTION
R
ECENTLY, there has been growing interest in multiuser discrete multi-tone (DMT) systems [1]–[3]. Digital subscriber lines (DSL) with DMT are now viewed as a multi-user DMT system because of crosstalk, which is often dominant source of performance degradation. The crosstalk can be cancelled when the receivers or transmitters can be coordinated [4]. On the other hand, the effect of the crosstalk can be reduced by dynamic spectrum management when no coordination is allowed [5], [6]. Without the crosstalk cancellation or proper spectrum management, DSL systems suffer from a near-far problem: the user close to the central office limits the performance of the user far from the central office [7]. If all users employ equal power, the crosstalk from a short loop can severely degrade the performance of a long loop. Thus, a power control algorithm should be implemented to prevent a long loop from achieving unfairly small data rate. This power control algorithm should be able to change the power spectrum dynamically as well as the total power of each user so that the rate region is maximized. Many different algorithms have been proposed to maximize the rate region in DSL systems [5]–[7]. The algorithms in [7] are simple to implement. However, they tend to restrict the data rate of short loops in order to increase the data
Manuscript received March 31, 2004. The associate editor coordinating the review of this letter and approving it for publication was Prof. Ezio Biglieri. This letter was presented in part at IEEE GLOBECOM, November 17-21, 2002, Taipei, Taiwan. J. Lee is with Marvell Semiconductor, Inc., Sunnyvale, CA, USA (e-mail: [email protected]). R. V. Sonalkar is with MITRE Corp., Eatontown, NJ, USA (email:[email protected]). J. M. Cioffi is with the Department of Electrical Engineering, Stanford University, Stanford, CA, USA (e-mail: [email protected]). Digital Object Identifier 10.1109/LCOMM.2005.03004.
II. S YSTEM M ODEL A DSL channel with multiple users can be viewed as an interference channel, a broadcast channel, or a multiple access channel depending on the coordination allowed at the transmitter or receiver side. When the transmitters can generate a signal cooperatively, a DSL channel can be modeled as a broadcast channel. On the other hand, when the receivers can process the received signal cooperatively, it becomes a multiple access channel. For these broadcast and multiple access channels, a vectored DMT technique can be used to cancel the crosstalk among users [4]. However, in current loop topology of DSL systems, the coordination at the signal level is often impossible. In this case, a DSL channel should be viewed as an interference channel. When the DMT technique is used with synchronized receivers, a DSL channel can be modeled as N independent frequency non-selective subchannels, each of which is an interference channel of M users. Without crosstalk cancellation, the signal-to-interference-plus-noise ratio (SINR) of user i in subchannel n is expressed as Si (n) =
2 (n)Pi (n) Hi,i , M 2 (n)P (n) Ni (n) + j=1,j=i Hi,j j
(1)
where Pi (n) and Ni (n) are the signal power and the background noise power of user i in subchannel n, respectively. The channel coefficient Hi,i (n) represents the direct channel gain of user i in subchannel n, while Hi,j (n) represents the crosstalk channel gain from user j to user i. Assuming that the crosstalk and the background noise are Gaussian [8], the data rate of user i in subchannel n is approximated by Si (n) bi (n) = log2 1 + , (2) Γ where Γ is the SINR gap to capacity that depends on the probability of symbol error, the noise margin, and the coding gain [1]. Here, it is assumed that common single-user codes
c 2005 IEEE 1089-7798/05$20.00
194
IEEE COMMUNICATIONS LETTERS, VOL. 9, NO. 3, MARCH 2005
14
for the AWGN channel are used instead of complex coding schemes specifically designed for a multi-user interference channel. The data rate of user i is then =
N
bi (n),
(3)
n=1
in bits per symbol. A rate region is defined as the union of all the rate sets (R1 , · · · , RN ) that can be achieved while satisfying the following power constraint: Pi ≤ Pmax,i for i = 1, · · · , M, where Pi =
N
(4)
Data rate of a 3000 ft loop (Mbps)
Ri
12
10
8
6
4
2
Pi (n),
(5)
n=1
and Pmax,i is a maximum power for user i. The main problem of interest is to develop a power control algorithm that maximizes the achievable rate region for the best trade-off of data rates among near and far users. In this letter, it is assumed that a centralized spectrum management center has the channel information and regulates the power spectrum and data rate of each user. The degree of coordination necessary for the spectrum management is much less than the vectored DMT scheme that requires signal-level coordination. Thus, a spectrum management center can be deployed with a minimal change in current DSL systems. III. P OWER C ONTROL A simple approach to the power control for DSL systems was proposed in [5]. The power control algorithm in [5] assigns a power budget to each user and allocates the power to subchannels with iterative waterfilling. If the resulting rate set is not satisfactory, a new power budget is assigned, and the power is allocated to subchannels again. The assignment of a power budget and the power allocation process are repeated until a desirable rate set is achieved. In this power control algorithm, the power control process is separated from the power allocation. This separation of the power control from the power allocation makes the algorithm simple, but it can cause performance loss. The total power used by each user should be determined as a result of the power allocation. Here is an example that illustrates this point. Consider two users, one far from a central office and the other near the central office. To increase the rate of the far user, the power control algorithm in [5] reduces the power of the near user. Then with a given power budget, the iterative waterfilling algorithm will allocate the power to subchannels. This power allocation will result in a certain data rate for the near user and the far user. In many cases, for DSL channels, the far user will occupy only the low frequency band. Thus, if the remaining power of the near user is poured into the high frequency band that are not used by the far user, the data rate of the near user can be increased without affecting the far user. This example shows how the power control algorithm in [5] can be improved in a simple manner. The power of each user should be used in full if there are subchannels that are not shared with other users. In general, the power control should be done in conjunction with the power allocation to maximize the performance.
0 0
Fig. 1.
Iterative waterfilling Proposed algorithm Vectored DMT 5
10
15 20 25 Data rate of a 2000 ft loop (Mbps)
30
35
40
Rate region of a 3000 ft loop and a 2000 ft loop.
This letter proposes a power control algorithm that employs the multi-user bit-loading algorithm in [9], which not only has low complexity but also performs almost as well as the optimal exhaustive search algorithm. The multi-user bitloading algorithm is a greedy algorithm that allocates power and bit to the user and subchannel pair with the least cost. The power allocation is repeated until any of the user cannot increase the data rate without violating the power constraint of any user. For the purpose of the power control, the cost function in [9] is modified to the weighted sum of incremental power: M wj ∆Pj,i (n), (6) J(n, i) = j=1
where ∆Pj,i (n) is the incremental power of user j to add one bit to user i, and wi is a nonnegative weight of user i. With this modified cost function in the multi-user bitloading algorithm, the power control algorithm can be described as follows: 1) Initialization: Let the weight wi = wi,initial for i = 1, · · · , M . 2) Power allocation: Allocate power to subchannels and users using the multi-user bit-loading algorithm with given power weights. 3) Test of rate requirement: If the desired rate set has been achieved, stop here. 4) Assignment of a new weight: a) If the data rate of user i needs to be increased, reduce wi by setting wi = wi /ζ. b) If the data rate of user i needs to be decreased, raise wi by setting wi = wi ζ. c) Go to the power allocation step. In the above, ζ should be chosen depending on how much the rate set (R1 , · · · , RM ) should be changed. In a typical DSL channel, ζ of 10 is a reasonable choice. The proposed power control algorithm varies the power assigned to each user indirectly by changing the weights. Here is how it works for two user case. If the weight of user 1 is smaller than the weight of user 2, the cost function is less
LEE et al.: A MULTI-USER POWER CONTROL ALGORITHM FOR DIGITAL SUBSCRIBER LINES
195
30
10
Proposed algorithm Iterative waterfilling 25
8
Average data rate of four short loops (Mbps)
Average data rate of four 3000 ft loops (Mbps)
9
7 6 5 4 3 2 1 0 0
Fig. 2.
Iterative waterfilling Proposed algorithm 2
4
6 8 10 12 14 16 Average data rate of four 2000 ft loops (Mbps)
20
15
10
5
0
18
20
Rate region of four 3000 ft loops and four 2000 ft loops.
influenced by the power increase of user 1. Thus, user 1 is favored over user 2, and the power of user 1 will be allocated faster than user 2. If user 2 can increase its data rate without disturbing user 1, user 2 can use all its power. However, if user 2 cannot find a way of increasing its data rate without affecting user 1, user 2 will not use all its power. Thus, the multi-user bit-loading algorithm may not allocate the maximum power Pmax,i for all users, and the amount of power assigned to each user is controlled by the weights in the cost function. IV. S IMULATION R ESULTS The proposed algorithm is applicable to any DSL system whose performance is limited by far-end crosstalk (FEXT) [1]. In this section, it is applied to the VDSL upstream transmission with the simulation parameters taken from [10]. Fig. 1 shows the rate region of a 3000 ft loop and a 2000 ft loop achieved by the proposed algorithm, the power control algorithm based on the iterative waterfilling [5], and the vectored DMT scheme [4]. As can be seen from the figure, the proposed algorithm outperforms the algorithm based on the iterative waterfilling, and the vectored DMT scheme outperforms the proposed algorithm. However, the vectored DMT scheme requires the coordination among receivers at the central office, whereas the proposed algorithm does not require any coordination in decoding process. Fig. 2 shows the achievable rate region of four 3000 ft loops and four 2000 ft loops. Since the data rates of same-length loops are approximately equal, the average data rates are taken so that the rate region can be drawn in two dimension. Compared to the two-loop case, the rate region is much smaller due to the crosstalk among same-length loops. However, the proposed algorithm still works better than the algorithm based on the iterative waterfilling. Although it is not shown in the figure, the rate region achieved by the vectored DMT is almost the same as the rate region for the two-loop case. Fig. 3 is a plot of the average data rate of four L ft loops, where L varies from 500 to 2500. The other four loops are 3000 ft long, and their data rates are fixed at 7.5 Mbps. It is shown that the proposed algorithm can increase the data rate
500
1000 1500 2000 Loop length of four short loops (ft)
2500
Fig. 3. Average data rate vs. loop length of four short loops: Four long loops are at 3000 ft and the average data rate of the long loops is fixed at 7.5 Mbps.
of the short loops by up to 60% compared to the algorithm based on the iterative waterfilling. V. C ONCLUSIONS This paper examined the power control problem in a frequency-selective interference channel and proposed a centralized power control algorithm utilizing the multi-user bitloading algorithm. It was shown by simulation that the proposed algorithm outperforms the power control algorithm based on the iterative waterfilling. R EFERENCES [1] T. Starr, M. Sorbara, J. M. Cioffi, and P. J. Silverman, DSL Advances, Upper Saddle River, NJ:Prentice Hall, 2003. [2] S. N. Diggavi, “Multiuser DMT: a multiple access modulation scheme,” in Proc. IEEE GLOBECOM, 1996, pp. 1566-1570. [3] J. R. Roche and A. D. Wyner, “Method and apparatus for transmitting signals in a multi-tone code division multiple access communication system,” U.S. Patent 5 410 538, 1995. [4] G. Ginis and J. M. Cioffi, “Vectored transmission for digital subscriber line systems,” IEEE J. Select. Areas Commun., vol. 20, pp. 1085-1104, June 2002. [5] W. Yu, G. Ginis, and J. M. Cioffi, “Distributed multiuser power control for digital subscriber lines,” IEEE J. Select. Areas Commun., vol. 20, pp. 1105-1115, June 2002. [6] R. Cendrillon, M. Moonen, J. Verliden, T. Bostoen, and W. Yu, “Optimal multi-user spectrum management for digital subscriber lines,” in Proc. IEEE ICC, 2004. [7] K. S. Jacobsen, “Methods of upstream power backoff on very high-speed digital subscriber lines”, IEEE Commun. Mag., vol. 39, pp. 210-216, Mar. 2001. [8] K. J. Kerpez, “Near-end crosstalk is almost Gaussian,” IEEE Trans. Comm., vol. 41, pp. 670-672, Jan. 1993. [9] J. Lee, R. V. Sonalkar, and J. M. Cioffi, “Multi-user discrete bit-loading for DMT-based DSL systems,” in Proc. IEEE GLOBECOM, 2002, pp. 1259-1263. [10] “Very-high-speed digital subscriber lines (VDSL) metallic interface, part 1: functional requirements and common specification,” T1E1.4 Contribution 2002-031R2, Editor: Q. Wang. Available: http://www.t1.org
