Band-Preference Dynamic Spectrum Managementin a DSL EnvironmentWooyul Lee, Youngjae Kim, Mark H. Brady and John M. CioffiDepartment of Electrical EngineeringStanford University, Stanford, CA 94305Email: {wylee, youngjae, mhbrady, cioffi}@stanford.eduAbstract— This paper introduces an algorithm for spectrummanagement for digital subscriber line (DSL) systems based onband preference. The proposed method influences the usage ofspectrum through band preference factors that subtly modifythe loading algorithm of DSL modems. Ad-hoc algorithms forcomputing such band preference factors are discussed. Simu-lation results in a practical ADSL environment show that theperformance of the proposed method is better than that ofIterative Water-filling (IWF) [1] and is close to that of OptimalSpectrum Balancing (OSB) [2], even with a small number ofcontrol parameters.I. INTRODUCTIONWhile DSL systems are widespread in today’s data accessnetworks, there still exist several barriers to achieving higherdata rates. Chief among these barriers is Far-End Crosstalk(FEXT), which is the electro-magnetic interference from othersame-direction users in the binder. In order to mitigate FEXT,current ADSL systems rely on a Static Spectrum Manage-ment (SSM) scheme to set power spectral density masks(PSDMASKs) for all the modems [3]. PSDMASKs limiteach modem’s transmitted power so that its FEXT into otherusers can be guaranteed to be lower than an acceptable level.However, this form of static spectrum management must bedesigned conservatively, and thus its overall performance ismuch lower than what can be achieved by Dynamic SpectrumManagement (DSM).Techniques for DSM may be stratified into levels of coor-dination [4]. In Level 0 DSM such as Iterative Water-filling(IWF), each user views other users’ signals as noise and seeksto maximize its data rate in a fully distributed manner. In Level1 DSM, a Spectrum Management Center (SMC) is able tosend limited control commands to each modem such as rateor power back-off. In Level 2 DSM, an SMC coordinates thespectra of all modems centrally. In Level 3 DSM, completecoordination, or ‘vectoring’ occurs as all modems terminate atthe same multiplexor, resulting in a MIMO channel [5].This paper considers Level 2 DSM, for which much workhas been undertaken. The “optimal spectrum balancing” (OSB)algorithm attempts to maximize the weighted sum rate of allusers [2]. Several methods for reducing OSB’s exponentialcomplexity have been reported in [6], [7], and [8]. However,these methods require central controllers with significant con-trol overheads that may be limiting when system parameterschange rapidly.Band Preference Spectrum Management (BPSM) avoidsthese problems by instead relying on the inherent adaptivecapability of each of the DSL modems. A central controllerinfrequently communicates to each modem which frequencybands are preferable (and conversely undesirable) for loading.Cognizant of these “band preferences”, each DSL modem thenautonomously adapts to any subsequent channel variations.Thus, BPSM significantly reduces control overhead whileallowing a largely distributed implementation.Other techniques for mitigating the control and overheadproblem have been studied in [9]. [10] discusses a differentform of BPSM based on setting PSDMASKs.The novel approach of the proposed BPSM algorithm is toemploy power scaling factors instead of a PSDMASK [10]or “reference line” [9]. These scaling factors are, heuristicallyspeaking, penalties that are given to tones. During the bit-loading process, a modem usually finds the tone that requiresminimum energy to load a new bit. Under the proposedalgorithm, the modem instead finds the tone that requiresminimum penalized energy. If a central controller determinesthat it is desirable for some bands to load a smaller numberof bits (e.g. to protect other users from FEXT), large scalingfactors may be given to those bands. In this way, spectrumcan be managed without direct control of each modem.The remainder of the paper is organized as follows: SectionII introduces the system model of multi-user DSL systemsand formulates the problem. Section III details the proposedband-preference algorithm and provides the simulation results.Section IV concludes the paper.II. SYSTEM MODEL AND PROBLEM DEFINITIONThis paper considers a multi-user Discrete Multi-Tone based(DMT) DSL system of L users, which models a copper-wirebinder group. For each tone, the channel can be expressed asa linear system as follows:yu,n=LXi=1H(u,i)nxi,n+ nu,n(u = 1, · · · L, n = 1, · · · , N),(1)where H(u,i)nis the (u, i)thentry of the channel matrix thatrepresents crosstalk from the transmitter i to the receiver u,yu,nis the output of user u, xi,nis the input of user i, nu,nis the noise of user u at tone n, and N is the total number ofused tones.In this model, no signal coordination is assumed betweenlines and the signals from other users are treated as noise; sucha multi-user channel is often called an “interference channel”.Under this assumption, the rate of user u is proportional to:b(u)n= log2Ã1 +1Γn|H(u,u)n|2p(u)nσ2n+Pj6=u|H(u,j)n|2p(j)n!= log2µ1 +1Γn· g(u)n· p(u)n¶(bit/dim)Ru=NXn=1b(u)n, (2)where g(u)n= |H(u,u)n|2/³σ2n+Pj6=u|H(u,j)n|2p(j)n´is thenormalized channel gain, p(u)nis the transmit power user u attone n, and Γnis the implementation gap on tone n.III. BAND-PREFERENCE ALGORITHMA. Power Scaling Factors, αnThe case of a single DSL modem is first considered. A goodDMT modem, in the absence of PSD masks, loads bits toapproximate the following “water-filling” condition in a toneset E = {1, . . . , N}pW Fn=µK1−Γngn¶+, n ∈ E,NXn=1pW Fn= P, (3)where K1∈ R is a nonnegative constant, P is a total powerconstraint, and (x)+, max(x, 0). We will say that water-filling is the process by which pW Fnand K1satisfying (3) arefound (for given Γ, gnand P). Scaling factors that modify(3) are introduced as follows.Definition 1: The scaled water-filling condition is said tohold when the following conditions are satisfiedpn=µK2αn−Γngn¶+, n ∈ E,NXn=1pn= P , K2≥ 0 (4)Accordingly, the process of finding pW Fnand K2that satisfy(4) (for givenΓ,g, αandP) is termed scaled water-filling.Note that for α = 1, scaled water-filling is equivalent to water-filling.In (4), the factors α may be interpreted as a tone-dependantpenalty that is useful for controlling the modem’s power onthat tone. For all n such that αn= ∞, observe that