2007 International Symposium on Information Technology Convergence
Computer Simulation Performance of Iterative Water-filling Algorithm for ADSL2+ and VDSL Mixed System Jian Xu and Jong-Soo Seo Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea E-mail: {jianxu, jsseo}@yonsei.ac.kr
Lu Xue and Sang Seob Song Department of Electronic Engineering, Chonbuk National University, JeonJu, Korea E-mail:
[email protected]
Abstract
lines so that the second band of ADSL2+ cannot be used. The previous research in [3] has not investigated this scenario. In that case the effects of crosstalk must be mitigated through spectrum management. With spectrum management the transmit spectra of the modems within a network are limited in some way to minimize the negative effects of crosstalk. Static spectrum management is the traditional approach. In SSM, spectral masks are employed which are identical for all modems. To ensure widespread deployment, these masks are based on the worst-case scenarios [4]. As a result they can be overly restrictive and lead to poor performance. Another promising method developed in ANSI is called dynamic spectrum management (DSM) [3], which overcomes this problem by designing the spectra of each modem to match the specific topology of the network. These spectra are adapted based on the direct and crosstalk channels seen by different modems. This paper is to show that the problem of spectrum compatibility for ONU-based VDSL and ADSL2+ in the same binder, fixed margin iterative water-filling, as a DSM algorithm, can be used to realize much of the gain. The remainder of this paper is organized as follows. Section 2 reviews the DSL environment system model. Section 3 describes the fixed margin iterative water-filling algorithm. In section 4, the simulation results are given. And conclusions are made in section 5.
Crosstalk is a major issue in modern ADSL and VDSL systems. Static spectrum management (SSM), the traditional way to guarantee spectrum compatibility, employs spectral masks which can be overly restrictive and result in poor performance. In this paper, fixed margin iterative water-filling algorithm is applied in downstream VDSL and ADSL2+ scenario when they are in the same binder. The algorithm can minimize the transmission power and at the same time the overall high-quality service is guaranteed for all the users of the same binder. The simulation results show that ADSL2+ can realize performance gains by up to 80% compared with SSM techniques or ADSL.1
1. Introduction Crosstalk is a major issue in modern digital subscriber line (DSL) systems. Typically 10-20 dB larger than the background noise, crosstalk is the dominant noise source of performance degradation. As the demand for higher data rates increases, veryhigh bit-rate digital subscriber line (VDSL) based on optical network units (ONU) has evolved toward higher frequency bands. For example, the 998 plan [1] uses the 0.138-3.75 MHz band and 5.2-8.5 MHz band for downstream transmission. However, the other nice method for satisfying the demand for higher data rates, ADSL2+ [2], reached consent recently at the ITU and joined the ADSL2 standards family as G.992.5. The ADSL2+ recommendation doubles the downstream bandwidth, thereby increasing the downstream data rate on the lines shorter than about 5000 feet. Thus VDSL and ADSL2+ will share the higher frequency band where the crosstalk problem is more pronounced. When they are bundled together, ONU-based VDSL can potentially emit strong crosstalk into ADSL2+ 1
2. The DSL environment and system model DSL modems use frequencies above the traditional voice band to carry high-speed data. The telephone channels are severely frequency selective. One way to combat intersymbol interference (ISI) is to use discrete multitone (DMT) modulation, which divides the frequency band into a large number of ISI-free subchannels and lets each subchannel carry a separate
This work was supported by the Brain Korea 21 Project.
0-7695-3045-1/07 $25.00 © 2007 IEEE DOI 10.1109/ISITC.2007.38
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data stream. This paper considers DMT modulation scheme as standardized for ADSL and VDSL. Because a great number of subscriber lines are bundled together in a DSL binder, the lines create electromagnetic interference into each other, thus causing crosstalk noise. Near-end crosstalk (NEXT) refers to crosstalk created by transmitters located on the same side as the receiver. Far-end crosstalk (FEXT) refers to crosstalk created by transmitters located on the opposite end of the line. NEXT is usually much stronger than FEXT. Usually in DSL transmission systems frequency division duplexing (FDD) is used to avoid NEXT. Thus FEXT is the main crosstalk. The DSL environment consists of multiple transmitters and multiple receivers interfering into each other as shown in Fig. 1. This model is usually referred to as an interference channel (IC). Although the unresolved problems about the capacity of IC, the aim here is to focus only on the problem of power allocation for each user. Suppose that the entire system has N frequency tones, the signal-to-interference-plus-noise ratio (SINR) of user i in subchannel n is expressed as SINRi (n ) =
H i2,i (n )Pi (n ) ∑ j ≠i H i2, j Pj (n ) +N i (n )
X1
H 21 H12
X2
N2
Y1 Y2
HM2 H 22
HM1
NM
XM
YM
Fig.1. Multiuser channel and crosstalk transfer functions.
The data rate of user i is then
Ri =
1 Ts
N
∑ b (n ) i
(3)
n =1
where Ts is a symbol period. The objective of the system design is to maximize the set of rates (R1 , " , R M ) subject to the power constraints A rate region is defined as the union of all the rate sets (R1 , " , R M ) that can be achieved while satisfying the following power constraint:
(1)
Pi ≤ Pmax,i for i = 1," , M
where Pi (n ) and N i (n ) are the signal power and the background noise power of user i in subchannel n respectively. H i,i (n ) represents the direct channel gain
(4)
where Pi is transmit power of user i . N
Pi = ∑ Pi ( n )
of user i in subchannel n , while H i , j (n ) represents
(5)
n =1
the crosstalk channel gain from user j to user i . Assuming that all transmitted signals and background noises are Gaussian, the reliably transmittable bit rate with QAM modulation under a certain bit error rate (BER) and coding scheme is then expressed as:
1 H i2,i (n )Pi (n) bi (n ) = log 2 1 + ⋅ 2 Γ ∑ j ≠i H i, j Pj (n) +N i (n)
N1
H11
and Pmax,i is a maximum power for user i .
3. Rate and power control using IW fixed margin mode 3.1. Iterative water-filling
(2)
As we all know, water-filling is the optimal-power distribution algorithm for the single-user communication and provides the basis for the power and bit allocation schemes in most DMT based modems. Given the channel signal-to- noise ratio (SNR) information in the frequency domain, the optimal power allocation Pi ( n ) maximizing the data rate is obtained by allocating more power to frequency bands with higher channel SNR. The single user waterfilling procedure is given in [5].
where Γ is called SINR gap, which is the function of the target BER, noise margin and coding schemes [5]. For example, Γ = 9.8 + γ m − γ c where γ m is the margin, γ c is the coding gain of receiver and 9.8 is to ensure that BER is equal to 10-7.
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Iterative water-filling can be viewed as an extension of the water-filling process for a multi-user communication environment. This algorithm is based on formulating power allocation in the multi-user interference channel as a non-cooperative game, where each user adjusts its power allocation to maximize its own data rate, while regarding all other interference as noise. The conditions for existence and uniqueness of the Nash Equilibrium were given in [6], and also experimentally these conditions are satisfied for all the possible DSL channel environments that have been tested. Thus an iterative water-filling algorithm, where in every step each modem updates its PSD regarding all interference as noise, converges to the unique Nash equilibrium from any starting point. Simply, the iterative water-filling process for two users [7] is illustrated in Fig. 2. We can see that at each step each user’s power spectra move away from the tones region where strong interference exists. Thus better performance is realized step by step. The procedure of multi-user iterative water-filling could be found in [3].
Power minimization of the fixed-margin DSL modem can be achieved theoretically by DSL power allocation Pi ( n ) at tone n that satisfies the equation Pi ( n ) +
Γ 2
(n) 2 ∑ j ≠i H i, j Pj ( n ) +Ni ( n ) H
2 i,i
(6)
=constant for all used tones
Actually (6) is the standard form of waterfilling in addition to the fixed margin. Thus for the principle of water-filling, the constant in (6) is determined by allocating non-negative power to the tones with higher ratio SINRs. And also equation (6) above is solved until the desired data rate of the DSL transmission system is equal to data rate computed by N SINRi ( n ) Ri = ∆f ⋅ ∑ log 2 1 + Γ n =1 N SINR ( n ) = ∆f ⋅ ∑ log 2 1 + 0.1⋅( 9.8i+γ m −γ c ) n =1 10
(7)
where ∆f is the frequency range for every tone. For the multi-user case, the power control algorithm proposed in [8] which is based on IW is applied here in order to obtain the minimized power for each user. The algorithm includes two stages. The inner stage is to make sure that each user optimizes its power in order to maximize the rate R i , in which a specific total power constraint Pi is given to each user and then water-filling is used to each user to maximize the total rate for the user under the given power constraint. This optimization for each user is performed iteratively until the power allocations of all the users converge to certain values. The outer stage finds the optimal total power constraint for each user based on the given target rate Ti . The outer procedure adjusts each user’s power based on the output rates of the inner stage. When the resulting total rate for a certain user is smaller than the target rate for the user, the total power budget for that user is increased and the inner stage is run again. Likewise, when the total rate for a certain user needs to be decreased, the total power budget is reduced and the inner stage is run again. The outer stage converges only when the set of target rates is within the IW rate region. Simply, the power control algorithm for two users is illustrated in Fig. 3. The outer loop of the power control algorithm essentially attempts to find the minimum amount of
Fig. 2. Iterative water-filling for two users.
3.2. Fixed margin mode Fixed Margin (FM) mode of iterative water-filling is the one that uses only power needed to guarantee best overall use of the binder and is finding increasing use with the service providers who are desired to ensure all services perform as best as possible. Because the use of FM mode allows other systems that have insufficient margin to improve and also coordination is unnecessary as long as the attempted data rates are in the achievable rate region of iterative water-filling. Any DSL modem that minimizes the transmit power necessary at a given fixed margin for a certain probability of BER to achieve the service-provider target data rate is said to operate with fixed-margin.
370
Fixed Margin Iterative Water-filling. For the channel topology of Fig.4, table 1 shows the obtained data rates and minimized power allocation for each set of lines based on the given target rates. The data rates for each set of 25 lines are the same, thus the data rates in table 1 represent the common data rates for the 25 short or long lines. Applying the power control algorithm described in section III, we can see that the target rates can be obtained approximately and accordingly the minimized power can also be obtained as long as the target rates are in the rate region
power that is needed to support the target data rate. And also fixed margin is used here to ensure the service quality for all the users in the same binder. The algorithm above can be alternatively thought of as each user doing “fixed-margin-adaptive” water-filling [6] against each other. And also as long as the set of target rates are in the rate region, the algorithm above can be easy to implement in practical modems distributively for the unnecessary centralized control.
4. Simulation results and analysis
5. Conclusions
The performance of the Fixed Margin IW algorithm is analyzed in this section. We investigate downstream transmission in ADSL2+ with 25 central office (CO) distributed 5000-ft lines and 25 ONU distributed 2000-ft VDSL lines. The ONU is located 4000-ft from the CO as depicted in Fig.4. A maximum transmit power of 20.4 dBm is applied to each CO-based ADSL2+ modem [9] and 11.5 dBm is the maximum transmit power for ONU-based VDSL modems [1]. The twisted pairs are assumed to be 26 AWG, and the crosstalk transfer functions are computed using the well-known FEXT models [10][11]. Fig.5 shows the rate regions corresponding to various spectrum management algorithms for CObased ADSL2+ and ONU-based VDSL downstream lines. Applying the SSM techniques, such as in the nominal situation of T1.417 using the 998-standardized spectrum for VDSL of –60 dBm/Hz and in the new proposed standard for ADSL2+ using the PSD maximum level [9], we can see from Fig.5 that the rates for CO-based ADSL2+ lines are even lower than the rates of CO-based ADSL lines which employ Fixed Margin IW algorithm. Thus the ADSL2+ original goal of increasing the rates cannot be realized if we just apply SSM technique; actually the extended second downstream band cannot be used in practice for the strong crosstalk from ONU-based VDSL lines. However, it makes a huge difference if we adopt the Fixed Margin IW algorithm for ADSL2+ and VDSL downstream lines. From Fig.5, we can see that the maximum rate can be improved by 80% compared with the common ADSL lines. The PSDs corresponding to 28 Mbps service on the ONU-based VDSL downstream 2000-ft lines are depicted in Fig.6 and Fig.7. Using Fixed Margin IW, the ADSL lines rate is 9.9 Mbps while the ADSL2+ lines can realize up to 17.6 Mbps. And furthermore, we can see from Fig.6 that the second band of ADSL2+ can be used successfully. Thus, the spectrum compatibility problem for the two high data rate service, ADSL2+ and VDSL, can be resolved applying
This paper examined the rate and power control problem in a downstream VDSL and ADSL2+ mixed scenario. Based on competitive optimality, the applied fixed margin iterative water-filling algorithm allows the lines to negotiate the best use of power and frequency with each other. The minimized power constraints for multi-user modems can be obtained in order to approximately satisfy the given target rate. Simulation showed that ADSL2+ can realize performance gains by up to 80% compared with existing SSM methods or ADSL.
References [1]
“Very-high bit-rate digital subscriber lines (VDSL): Metallic Interface” ANSI T1E1.4/2003-210R2. [2] “White paper: ADSL2 and ADSL2plus—The New ADSL Standards” DSL FORUM / March 25, 2003. [3] J. M. Cioffi, DSL Advances. Prentice Hall 2002, ch.11— Dynamic Spectrum Management. [4] Spectrum Management for Loop Transmission Systems, ANSI Std. T1.417, Issue 2, 2003. [5] T. Starr, J. M. Cioffi, P. J. Silverman, Understanding Digital Subscriber Line Technology, Prentice Hall, 1999. [6] W. Yu, G. Ginis, and J. M. Cioffi, “Distributed Multiuser Power Control for Digital Subscriber Line,” IEEE Journal on Selected Areas in Communications, vol. 20, no. 5 , pp. 11051115, Jun 2002. [7] K.B.Song, S.T.Chung, G.Ginis,and J.M.Cioffi “Dynamic Spectrum Management for Next-Generation DSL Systems,” IEEE Communications Magazine 2002. [8] W. Yu, G. Ginis, and J. M. Cioffi, “An Adaptive Multiuser Power Control Algorithm for VDSL,” IEEE GLOBECOM 2001 pp. 394 –398. [9] “Draft new Recommendation G.992.5 (G.adslplus)” ITU-T SG15/January 2003. [10] “Very-high bit-rate digital subscriber lines (VDSL): Part 1: Functional requirements and common specification. Part 3: Technical specification of a multi-carrier modulation transceiver,” ANSI T1E1.4/2002-031R1, 2001-013R2. [11] “Transmission and Multiplexing (TM); Access transmission systems on metallic access cables; VDSL; Functional Requirements”, ETSI Std. Ts 101 270-1, Rev. V.1.3.1, 2.3.
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Table 1. Obtained Data rates and minimized power allocation for each set of lines based on the given target rates for VDSL and ADSL2+ downstream deployment. Target Rate(Mbps)
Obtained Rate(Mbps) Minimized Power(dBm)
ADSL2+
VDSL
ADSL2+
17.5Mbps
20Mbps
17.68Mbps 20.54Mbps 20.4dBm
-21.5dBm
16.0Mbps
32Mbps
16.89Mbps 33.18Mbps 17.4dBm
-12.5dBm
14.0Mbps
42Mbps
14.64Mbps 42.83Mbps 16.4dBm
-3.5dBm
12.0Mbps
45Mbps
11.84Mbps 44.78Mbps 15.4dBm
2.5dBm
VDSL
ADSL2+
VDSL
Fig.5 Rate Regions in Downstream ADSL2+ and VDSL. P1
P2 Iterative
P1 = P1 − δ yes
P1 = P1 + δ
Water-filling
Water-filling
R1 ≥ T1 + ξ
R2 ≥ T2 + ξ
no
no
P2 = P2 − δ yes
P2 = P2 + δ
Fig.3 Power control based on iterative water-filling for two users. Fig.6 PSDs on 5000ft ADSL2+ and ADSL (2000ft VDSL Lines @ 28 Mbps).
CO
ADSL2+ 25
5000 feet
A2+
ONU V
4000 feet
CPE A2+
VDSL
25
2000 feet
V
CPE
Fig.4 CO-based ADSL2+ versus ONU-based VDSL.
Fig.7 PSDs on 2000ft VDSL (2000ft VDSL Lines @ 28 Mbps).
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