DSpace at VNU: Vectored DSL: Potential, Implementation Issues and Challenges

This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION Vectored DSL: Potential, Implementation Issues and Challenges Christopher Leung, Sean Huberman, Khuong Ho-Van, and Tho Le-Ngoc Abstract—This paper investigates specific techniques suitable for Vectored DSL, their performance, complexity and practical implementation More specifically, various Vectored DSL techniques for both upstream and downstream transmission are discussed, including the Tomlinson-Harashima Pre-coder (THP), Diagonalizing Pre-coder (DP), Zero-Forcing (ZF) canceller, and Decision-Feedback (DF) canceller A thorough discussion on some of the practical implementation aspects of Vectored DSL is provided In particular, various implementation challenges are discussed, including computational load, memory storage, line management, partial crosstalk cancellation, and the effect of imperfect channel knowledge As well, the potential gains and challenges of combining Phantom DSL and Vectored DSL are also discussed Illustrative examples are provided based on both measured data and channel models to compare the various Vectored DSL techniques and their practical implementation challenges Index Terms—Digital Subscriber Line (DSL), Vectored DSL, pre-coding, interference cancellation I I NTRODUCTION D IGITAL Subscriber Line (DSL) service providers are in fierce competition with cable companies to provide services such as multicast/unicast video, HDTV, and 3D TV The demand for data-intensive services is on the rise In order to support more sophisticated multimedia services and compete with cable companies, DSL is pushing for higher data-rates One solution for achieving higher data-rates involves running optical fiber wire directly from the Central Office (CO) to every Customers Premise (CP), known as Fiber-To-The-Home (FTTH) Deploying FTTH can require costly investments especially in buried-cable areas As such, service providers, who have already heavily invested in DSL technology and in their copper-wire network, wish to make use of hybrid optical fiber and copper wire networks to meet the data-rate demands at a lower cost The family of hybrid optical fiber and copper wire networks are referred to as FTTx networks The type of FTTx network Manuscript received May 15, 2012; revised October 4, 2012 This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and Bell Canada through the Industrial Research Chair program Moreover, some of the authors were funded by the Fonds qu´ebecois de la recherche sur la nature et les technologies C.Leung, S Huberman and T Le-Ngoc are with the Department of Electrical and Computer Engineering, McGill University, 3480 University Street, Montreal, Quebec, Canada, H3A 2A7 (e-mails: christopher.leung@mail.mcgill.ca, sean.huberman@mail.mcgill.ca, tho.lengoc@mcgill.ca) K Ho-Van is with the Department of Telecommunications Engineering, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Viet Nam (e-mail: khuong.hovan@yahoo.ca) Digital Object Identifier 10.1109/SURV.2013.011413.00098 used depends on the range of copper line lengths in the system For example, Fiber-To-The-Node (FTTN) uses optical fiber wire to transmit information from the CO to a node and then uses copper wire to transmit from the node to every CP in its distribution area In North America, FTTN loops can contain loop lengths up to 1.5 km, but FTTN loop lengths of up to 500 m are more common Similarly, Fiber-To-The-Curb (FTTC) uses optical fiber wire to transmit information from the CO to a small DSL Access Multiplexer (DSLAM) which typically contains loop lengths of up to 500 m [1] Furthermore, FiberTo-The-Building (FTTB) uses optical fiber wire to transmit information from the CO to a building DSL systems transmit data to and from various CPs over bundles of copper wire encapsulated within a cable binder The interference between neighbouring lines is known as crosstalk Crosstalk is the limiting factor in the achievable data-rates of DSL systems As such, to improve the achievable data-rates, the crosstalk interference must be reduced or removed entirely There are two types of crosstalk: Near-End-Crosstalk (NEXT) and Far-End-Crosstalk (FEXT) NEXT is the crosstalk seen by neighbouring lines at the transmitter side and FEXT is the crosstalk seen by neighbouring lines at the receiver side DSL uses Frequency-Division Duplexing (FDD) in order to remove the NEXT interference As such, the only significant form of system crosstalk is the FEXT interference Hence, higher data-rates can be achieved by minimizing or even removing the FEXT interference Spectrum Management (SM) techniques can be employed to achieve this goal The most basic form of SM is known as Static SM (SSM) SSM implements static spectral masks based on a worst-case scenario assumption for all users This leads to an inefficient use of the frequency spectrum whenever the scenario is not the worst-case and consequently leads to highly sub-optimal performance Dynamic SM (DSM) is a wide field which looks to adaptively apply different spectral masks for each user with the intent of maximizing the throughput of the overall system DSM allows for a far more efficient use of the spectrum than SSM does There are three levels of DSM [2]; DSM level performs spectrum balancing independently from line to line to mitigate crosstalk, DSM Level performs spectrum balancing jointly across multiple lines to mitigate crosstalk, and DSM Level performs signal-level coordination to remove crosstalk A detailed survey of DSM Levels and is provided in [3] DSM Level applies Vectored DSL to effectively remove crosstalk Vectored DSL makes use of pre-coding in downstream transmission and makes use of Multi-User Detection (MUD) interference cancellation in upstream transmission 1553-877X/13/$31.00 c 2013 IEEE This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION DSM Level can also incorporate DSM Levels and in order to mitigate any crosstalk which is not removed (e.g., due to imperfect channel knowledge or to crosstalk from nonvectored lines) In the early 21st century, a method using phantom circuitry was proposed to transmit up to three channels worth of data over two physical twisted-pair wires [4] The phantom circuit can significantly increase the capacity of the system; however, it also significantly increases the crosstalk in the system which makes it more difficult to achieve the capacity Due to the increased crosstalk, the phantom circuit (applied to DSL) was abandoned, until the recent advances in Vectored DSL technology [4] Applying the phantom circuit to DSL technology is known as Phantom DSL By combining Phantom DSL with the crosstalk mitigation of Vectored DSL, the capacity gains of Phantom DSL can be achieved without the increased crosstalk (i.e., Vectored DSL can remove the original crosstalk, as well as the additional crosstalk generated by the phantom process) [5] While Phantom DSL promises increased capacity, it also provides some challenges from an implementation perspective More specifically, Phantom DSL requires more sophisticated modems and chipsets, which are capable of combining/recovering the three-channels worth of data over two physical channels As well, the multiple-line requirement for Phantom DSL may require infrastructure changes in locations where consumers are only provided a single DSL line; however, it is common for two twisted-pair copper lines to service a single dwelling, allowing for a third “virtual” pair Finally, thus far, Phantom DSL results have only been obtained within a lab-setting The rest of this paper is organized as follows Section II discusses the xDSL environment Section III presents some downstream and upstream vectored transmission techniques Section IV provides some numerical results to demonstrate the performance gains of Vectored DSL Section V presents some issues and solutions in implementing Vectored DSL Section VI investigates the use of partial cancellation techniques, in order to reduce the computational complexity of Vectored DSL Section VII shows the effect of channel estimation error on the performance of Vectored DSL Section VIII gives an overview of Phantom DSL and summarizes some preliminary in-lab test results Finally, Section IX provides some concluding remarks Notation: In this paper, non-bold variables denote scalars (e.g., a), lower-case bold variables denote vectors (e.g., a), and upper-case bold variables denote matrices (e.g., A) [A](n,m) refers to the (n, m)-th element of matrix A Similarly, [A](n, ) refers to the vector whose elements are given by the n-th row of matrix A A† refers to the conjugate transpose of matrix A diag(A) refers to the matrix of all-zeros except with diagonal elements identical to A II V ECTORED DSL AND THE X DSL E NVIRONMENT xDSL is a family of technologies which make use of twisted-pair copper telephone wires to transmit digital data [6] [7] xDSL operates on the same physical twisted-pair copper wiring as Plain Old Telephone Service (POTS) by using the higher frequency bands, while POTS is restricted to the lower frequency band (less than kHz) Different frequency bands are used for different DSL technologies For example, in Asymmetric Digital Subscriber Line (ADSL) the maximum frequency used is 1.1 MHz, in ADSL2plus the maximum frequency used is 12 MHz, and in Very high bit-rate DSL (VDSL) the maximum frequency used is 30 MHz There are dedicated frequency bands for upstream and downstream transmission For most DSL technologies, the frequency bandwidth is allocated asymmetrically where a larger portion is allocated for downstream transmission than for upstream transmission xDSL technology uses Discrete Multi-Tone (DMT) transmission, a scheme which is similar to Orthogonal FrequencyDivision Multiplexing (OFDM) DMT is a transmission technique which divides the available frequency spectrum into many sub-channels or frequency tones The main difference between DMT and OFDM transmission is that DMT is also capable of optimizing the bit and energy distribution over the sub-channels (e.g., channel partitioning or bit-loading) [6] The basic idea is to transmit the data in parallel over each frequency tone (note that some frequency tones might transmit no data, while others can transmit a lot of data) More information on DMT transmission and the xDSL environment can be found in [3] A System Model Consider a DSL network with a set of users (modems) N = {1, , N } and frequency tones (sub-carriers) K = {1, , K} Using synchronous DMT modulation, there is no Inter-Carrier Interference (ICI) and transmissions can be modeled independently on each tone k as follows: yk = Hk xk + zk (1) The vector xk [x1k , , xnk ]T contains the transmitted signals for all users on frequency tone k, where xnk is the transmitted signal by user n on frequency tone k Similarly, yk [yk1 , , ykN ]T and zk [zk1 , , zkN ]T where ykn is the received signal for user n on frequency tone k Likewise, zkn is the additive noise for user n on frequency tone k which contains thermal noise, alien crosstalk and radio frequency interference Hk is an N × N matrix such that [Hk ](n,m) is the channel gain from transmitter m to receiver n on frequency tone k, and is defined as hn,m The transmit PSD of user n k on frequency tone k is defined as snk E{|xnk |2 }/Δf , where E{·} denotes expected value, and Δf denotes the frequency tone spacing When the number of users is large enough, the interference is well approximated by a Gaussian distributed random variable, and hence the achievable bit-rate of user n on frequency tone k is defined as: bnk log2 + Γ n |hn,n k | sk , n,m m | sk + σkn m=n |hk where Γ is the Signal to Noise Ratio (SNR) gap which is a function of the desired Bit Error Rate (BER), coding gain, and noise margin [7], and σkn E{|zkn |2 }/Δf is the noise This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES power density of user n on frequency tone k The achievable data-rate for user n is therefore Rn = fs k bnk , where fs is the DMT symbol rate There are two types of physical power constraints imposed on the transmitted signals for each user The first constraint is a total power constraint (over all frequency tones for a single user), denoted by P n for user n The second constraint is a per-frequency tone maximum power constraint, referred to as a spectral mask The spectral mask constraint for user n on frequency tone k is denoted by sn,mask The power constraints k can be summarized as follows: snk ≤ P n for all n, Δf k for all n, k ≤ snk ≤ sn,mask k (2) B xDSL Network Configurations Fig shows a typical xDSL network As shown in Fig 1, the twisted-pair copper wire is run through binders There are sections of the network where all the lines belong to a particular CO or DSLAM There are also sections where the binder is shared between the CO and a DSLAM Optical fiber wire is run to a CO and/or to DSLAMs Twisted-pair copper wire is run from the CO and/or the DSLAMs to various Junction Wire Interfaces (JWIs) Twisted-pair copper wire is then run from the JWIs to the CPs and/or office buildings For this particular network (e.g., binder type B), due to the long length of the CO relative to the DSLAM, the DSLAM lines can cause severe crosstalk to the CO users (this is known as the near-far problem) Note that type B binders can also correspond to binders shared by lines from two DSLAMs It is worthwhile to note that loops where the CO directly connects to a JWI and/or CPs (i.e., binder type A) are becoming less and less common This is due to the fact that channel attenuation increases with line length, especially at higher frequencies As such, it is far more difficult to achieve higher data-rates for longer lines Lines corresponding to binder type A are often very long in length (e.g., on the order of kilometers) As such, network topologies similar to binder type C (i.e., FTTx) are becoming increasingly popular since they are capable of achieving higher data-rates The two types of network configurations corresponding to binders B and C, as shown in Fig 1, will be discussed in more details in Sections II-B1 and II-B2, respectively 1) Binders With Multiple Disturbing Loops: The first binder configuration type is where there are multiple loops sharing a binder Binder B in Fig is an example of this type of binder configuration Binder B is shared between the loop from the CO to the JWI and CPs at the top right of the diagram and the loop between a DSLAM and the JWI and CPs in the middle of the diagram One of the challenges of managing networks involving binders with multiple disturbing loops is known as the nearfar problem The near-far problem is caused by the fact that for twisted-copper pair wires, the attenuation increases with length Hence, when the receivers from one bundle of lines is in close proximity to the transmitters of another bundle, they receive large amounts of crosstalk More specifically, for binder B in Fig 1, for downstream transmission, the DSLAM lines will cause strong crosstalk to the CO lines Another challenge of binders with multiple disturbing loops is that from a network operator point-of-view, it is far more challenging to apply coordinated vectored spectrum management since the lines are not all co-located For such scenarios, vectored spectrum management can be applied to each disturbing loop separately treating the crosstalk from other loops as background noise While such binder configurations are still quite common in practice, in recent years, the focus has been on binders with co-located lines Co-located binder configurations will be discussed in Section II-B2 2) Binders With Co-located Lines: The second binder configuration type is where all the lines are co-located at either the transmitter or the receiver This corresponds to binder C in Fig For this network binder configuration, optical fiber wire is run to a node (e.g., DSLAM) and then twisted-pair copper wire is run to a JWI and the CPs Note that while Fig shows binder C servicing a building, this binder type can also service various CPs within a neighborhood There are several benefits of binders with co-located lines from a network operator point-of-view One of the main advantages is that such networks not suffer as drastically from the near-far problem described in Section II-B1; however, it can still cause significant performance degradation if the crosstalk is not properly managed Another benefit of binders with co-located lines is that such networks are well-suited for vectored spectrum management since all lines are colocated at either the transmitter or receiver, making joint signal processing simpler The emergence of FTTx networks has molded the binder topologies of DSL systems In particular, as optical fiber runs closer to each CP, there is less of a requirement for DSLAMs located at geographically separate locations to share a binder Moreover, for FTTN, FTTC and FTTB networks, it is far more common to deploy a single DSLAM (the size of which may vary) to service the customers in its distribution area rather than to have multiple DSLAMs sharing a binder Hence, in recent years, much interest in binders corresponding to binder C has developed, since they are becoming increasingly more popular from a practical perspective C Channel Knowledge Availability DSL systems consist of twisted-pair copper wires in static cable binders and typically, not move; hence, the DSL channel is considered very slow time-varying As such, the DSL channel is assumed to be time-invariant if new measurements are taken often enough Hence, Vectored DSL assumes full channel knowledge Full channel knowledge can be gained through the use of loop testing There are two types of DSL loop tests: Single Ended Loop Test (SELT) and Double Ended Loop Test (DELT) SELT measurements are initiated by the DSLAM without using the CP Equipment (CPE) More specifically, SELT measurements provide loop qualifications, such as the wire gauge and the length of the loop Since SELT measurements not require a CPE, they are often used to preemptively measure This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION Central Office A B DSLAM Fiber Links JWI: Junction Wire Interface DSLAM: Digital Subscriber Line Access Multiplexer DSLAM C Fiber Links Fig Example of a typical xDSL Network the loop characteristics prior to installing the CPE SELT measurements can also provide the direct channel attenuation and the background noise present on the line DELT measurements are initiated by the DSLAM but require coordination with the CPE As such, DELT measurements can provide more detailed on-the-fly measurements of the loop characteristics; however, they require compatible CPEs DELT measurements can provide full channel knowledge, as well as the background noise for all lines in both the upstream and downstream directions SELT and DELT measurements can be combined to provide the best results for service providers [8] SELT is more useful than DELT during the pre-installation phase, while DELT is more useful once the CPE is connected [8] Once the CPE is connected, SELT measurements can still be useful when locating line faults in situations where the line conditions are too poor for DELT D MIMO Transmission: Downstream vs Upstream Vectored DSL transmission makes use of concepts originally developed for Multiple Input Multiple Output (MIMO) systems [9] A wireless MIMO system consists of NT transmit antennas and NR receive antennas, where NT and NR are not necessarily equal As well, for a wireless MIMO system, all the NT transmit antenna are co-located and all the NR received antennas are co-located Hence, for a wireless MIMO system, pre-coding and/or interference cancellation (using MUD) can be performed MIMO DSL transmission differs from wireless MIMO systems in the following ways First, NT = NR since each “antenna” corresponds to the end of a twisted-pair copper wire Second, MIMO DSL systems are typically not co-located at both ends Typically, MIMO DSL systems are co-located at one end or can be grouped into clusters of lines which are each co-located at one end (e.g., corresponding to a multi-user MIMO wireless system) ADSL and VDSL transmission makes use of FDD, where there are separate bandwidths for upstream and downstream transmission and, hence, the two transmission cases can be dealt with independently Fig 2(a) shows how upstream vectored transmission applies to DSL networks Since all the receivers are co-located and full channel knowledge is assumed, the crosstalk can be mitigated by MUD interference cancelling Similarly, Fig 2(b) shows how downstream vectored transmission applies to DSL networks Since all the transmitters are co-located and full channel knowledge is assumed, the signals can be pre-distorted using pre-coding so that they arrive at each CP crosstalk-free E Multi-Segment Problems There are several multi-segment issues with regards to Vectored DSL, including vector clusters, the differences between inter-crosstalk and intra-crosstalk, and alien-crosstalk generated from mixed xDSL networks (e.g., some ADSL lines and some VDSL2 lines) The multi-segment issues listed above will be discussed in what follows Vector clusters refers to implementing vectoring over a subset of the lines (or several subsets of lines) For example, if a DSLAM is servicing 192 customers, rather than applying vectoring across all 192 lines, it might be more computationally efficient to cluster the customers into four groups of 48 lines and apply vectoring to each cluster separately As such, the intra-crosstalk refers to crosstalk within the particular cluster and inter-crosstalk refers to the crosstalk from one cluster to another Inter-crosstalk and intra-crosstalk also arise whenever binders have multiple disturbing loops as discussed in Section II-B1 and shown in binder B of Fig In particular, the CO and DSLAM represent two vector clusters Also note that it is possible that both the CO and DSLAM could apply vector clustering on their respective lines resulting in additional vector clusters The effects of intra-crosstalk can be removed using vectoring; however, the effects of inter-crosstalk cannot be removed by vectoring, instead, the inter-crosstalk must be mitigated using spectrum management techniques (i.e., DSM levels and 2) A survey of spectrum management techniques is given in [3] Note that inter-crosstalk refers to crosstalk from This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES (a) Upstream (b) Downstream Fig Vectored DSL transmission lines that the network operator has control of and can apply spectrum management to Similar to inter-crosstalk, is crosstalk generated from scenarios where there are mixed xDSL networks (e.g., some ADSL and some VDSL2 lines) Such scenarios typically arise when different service providers are sharing a binder and as such neither one has control over the other’s lines For such scenarios, the crosstalk generated is referred to as aliencrosstalk and it is treated as background noise III V ECTORED T RANSMISSION Vectored transmission for DSL can be grouped into three main methods: downstream transmission, upstream transmission, and joint transmitter-receiver transmission In the joint transmitter-receiver transmission, pre-coding and cancellation can be performed at the transmitter and receiver sides This transmission style is only practical in cases where both the transmitter and receiver are co-located On the other hand, as discussed in Section II-D, customers are not usually colocated In this case, pre-coding at the transmitter is appropriate for downstream transmission and cancellation at the receiver is appropriate for upstream transmission A Downstream Transmission The network configuration in downstream DSL transmission makes it often impossible for interference cancellation to occur at the receiver side However, since the signals are transmitted from the same location, pre-coding can still be applied to pre-distort so that the signals arriving at the CPEs are crosstalk-free This section presents the two main methods for applying vectoring in downstream transmission: the ZeroForcing (ZF) pre-coder [10], and the Tomlinson-Harashima Pre-coder (THP) [11] 1) Zero-Forcing: Unlike the THP, the ZF method is a rather simplistic linear pre-coder that uses the channel inverse for pre-coding Under this method, the resulting received signal is given by ˜ k ) + zk yk = Hk (H−1 (3) k x It is evident that the ZF method has the potential to predistort the signal such that the signal is interference free when it arrives at the receiver end However, there is the possibility that applying the inverse as the pre-coder can lead to large transmit power increases and can violate the transmit power or spectral mask constraints, especially if the channel matrix is ill-conditioned Yet, [12] showed that in cases where the transmitters are co-located, the channel matrix is row-wise diagonal dominant which leads to a near-optimal ZF method This Row-Wise Diagonal Dominance (RWDD) stems from the fact that the crosstalk signal transmitted from one line to another to propagate through the full length of the disturber’s line just like the direct signal Thus, both the direct and crosstalk signals travel the same distance but the crosstalk signals are being additionally attenuated by the insulation between cables Hence, the diagonal element, [Hk ](n,n) , dominates the other elements on the same row, [Hk ](n,m) We established previously that the ZF method can increase the total transmit power In a similar manner, the ZF method can also increase the PSD However, there exists an upper bound on the allowable PSD known as the PSD mask In order to guarantee that the PSD mask remains intact, [12] proposed to use a scaling factor on the pre-coding matrix The scaling factor, βk , ensures that any PSD-mask-compliant input to the pre-coder will remain compliant once pre-coded The scaling factor for each user is obtained by satisfying the following constraint: sn,mask > E |xnk |2 k =E = βkn = n βk [H−1 ˜nk k ](n, ) x βkn [H−1 xnk |2 k ](n,m) E |˜ m∈N [H−1 ˜n,mask k k ](n,m) s m∈N −1 Therefore, = m∈N |[Hk ](n,m) | However, since the scaling factor must be identical for each user, the final scaling βkn This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION The second step of the THP is to find the values of x˜nk corresponding to crosstalk-free transmission for all users Hence, it is required that the following equality be satisfied: factor is selected as the largest among all users: βk max βkn n −1 The resulting pre-coder is H−1 k βk and the effective received signal vector is: ˜ k + zk yk = x (4) βk The effective channel gain in (4) is the same for all users and depends on the worse βkn Hence, [12] further proposed the Diagonalizing Pre-coder (DP) The DP has the form: −1 yk = Hk H diag(Hk )˜ xk + zk βk k The corresponding scaling factor for the DP is given by: n ⎢ ⎣ rk1,1 ⎡ ⎤ rk1,1 x ˜1k ⎢ 1,2 ⎥⎢ ⎥ ⎢ rk ⎦⎣ ⎦=⎢ ⎣ N,N x ˜N rk k rk1,N ⎤⎡ = log2 n |hn,n ˜k k | s 1+ n diag σ Γ(βk ) k n−1 xˆnk = modsn,mask k (5) 2) Tomlinson-Harashima pre-coder: The THP method for vectoring is based on its original application for channel equalization developed independently by Tomlinson [13] and Harashima [14] At the transmitter, it is a two-step non-linear ˜ k , is converted into an pre-coder The input of the THP, x intermediate variable defined as (xk )int , which is used to generate the true transmitted signal, xk The first step begins by taking the QR decomposing of the complex channel such that: H†k = Qk Rk , where Qk is a unitary matrix and Rk is an upper triangular matrix By setting the pre-coder matrix to Qk , the received signal can be modeled as yk = Hk (Qk (xk )int ) + zk = (Qk Rk )† Qk (xk )int + zk = R†k (xk )int + zk ⎤ ⎡ int ⎤ ⎥ (xk ) ⎥⎢ ⎥ ⎥⎣ ⎦ ⎦ N int (xk ) N,N 0 rk2,N · · · rk (xnk )int = modsn,mask x ˜nk − The effective bit-rate using the DP is given by: ··· ··· rkm,n m int , (x ) rn,n k m=1 k √ √ M /2 where modM [a] a − M a+√M The process can be easily transformed for the complex constellation case Similarly, at the receiver, a second modulo operation is applied to estimate the transmitted symbol as follows: m∈N The effective received signal vector is therefore given by: xk + zk yk = diag diag(Hk )˜ βk bnk rk2,2 In order to ensure the spectral mask constraint is satisfied after pre-coding, (xnk )int should be set as [11] when using real-valued constellations: k m,m |[H−1 | k ](n,m) hk βkdiag = max ⎡ (6) The first step of the THP method effectively transforms the transmission channel into the lower triangular matrix R† in int (7) It can be easily seen that ykn = nm=1 [R†k ](n,m) (xm + k ) n zk Hence, user n = transmits crosstalk-free and every other user n = 2, , N experiences crosstalk from users 1, , n− 1, respectively The second step of the THP takes advantage of the fact that with the transmitted signal of user n = known, the crosstalk induced from that user to other users is also known and the transmitted signals of users 2, , N can be recursively pre-distorted Once the recursive process is completed, each user experiences crosstalk-free transmission ⎡ 1,1 ⎤ rk ··· ⎢ r1,2 r2,2 · · · ⎥ k ⎢ k ⎥ † Rk = ⎢ (7) ⎥ ⎣ ⎦ rk1,N rk2,N · · · rkN,N ykn zkn ˜nk + n,n n,n = x rk rk Based on the RWDD discussed in Section III-A1, |hn,n k | for m = n which implies that Hk is almost diagonal and hence in the QR decomposition, Qk is almost equal to the identity matrix Thus, |rkn,n | ≈ |hn,n k | due to RWDD The bit-rate of user n on frequency tone k can be written as: |hn,m | k bnk = log2 + |rkn,n |2 snk Γσkn ≈ log2 + n |hn,n k | sk n Γσk It is apparent that the ordering in the THP method will affect the performance This is studied in [15] where it is shown that there are O(N !)K possible combinations of ordering to determine the optimal ordering However, in a similar manner to the zero-forcing method, the RWDD characteristic of the downstream DSL channel implies that the channel is almost diagonal and hence, in the QR decomposition, Qk is almost equal to identity Thus the diagonal elements of Rk are similar to those of Hk and the benefits of finding the optimal ordering are far outweighed by its complexity B Upstream Transmission The network configuration in upstream DSL transmission makes it often impossible for pre-coding to occur at the transmitter side; however, since the signals are all received at the same location at the CO or DSLAM, interference cancellation can be used to remove the crosstalk from each user’s signal This section discusses two methods for vectored upstream transmission: the Decision-Feedback Canceller (DFC) and the ZF canceller The former is a non-linear canceller that decodes one user at a time and uses the estimate to decode the next user The latter is similar to the downstream ZF method discussed in Section III-A1, where the channel inverse is used This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES 1) Decision-Feedback Canceller: The optimal solution in upstream vectoring in the Minimum Mean-Squared Error (MMSE)-sense lies in the use of Integer Least Square (ILS) programming The least square arises from using MMSE estimation of the transmitted signal while the integer stems from the transmitted symbols being selected from a discrete set as in the following optimization problem for each frequency tone k: |ˆ xnk − xnk |2 , n n {ˆ xk ∈Ak }n∈N n∈N where Akn is the constellation of the n-th user on the k-th frequency tone However, the ILS problem is NP-hard and relies on searching for the optimal solution Based on the VDSL2 standard, this would require decoding 1000 symbols per second per sub-carrier per user Hence, an ILS-based solution is not feasible Instead, the DFC provides a suitable approximation to the optimal solution Mathematically, upstream transmission on frequency tone k can be written as: ˜ k = Qk yk = Qk Hk xk + zk , y (8) where Qk is the interference cancellation matrix The DFC makes use of QR decomposition of a matrix, similarly to the THP in Section III-A2 The DFC selects Qk from the QR decomposition of Hk = QR as Qk = Q† As such, DFC transmission can be expressed as [11]: ˜ k = Q†k Qk Rk xk + zk = Rk xk + Q†k zk , y (9) where (9) follows from the fact that Qk is a unitary matrix Moreover, since Qk is a unitary, the noise, Q†k zk , remains Gaussian The DFC essentially transforms the transmission channel into an upper-triangular matrix, Rk , shown in (9) Since the components of Q†k zk are uncorrelated, the input, xk , can be recovered using the decoding procedure that follows First, N † note that y˜kn = m=n rkn,m xm ˜kN is k + [Qk ](n, ) zk Hence, y received crosstalk-free (with some additive noise) and thus xN ˜kN −1 contains only crosstalk k can be decoded Next, y N information from xk , which is now known and therefore it can be decoded By recursively decoding the received signal (ordered from user N to user one), the full transmitted signal can be recovered Mathematically, the estimate for the n-th transmitted signal, x ˆnk , can be expressed as: x ˆnk = Decode y˜kn rkn,n N rkn,m m − xˆ rn,n k m=n+1 k , n = N, N −1, , The crosstalk will be completely cancelled if each transmitted signal is correctly decoded Since the receivers are co-located, the crosstalk signal transmitted from one line (disturber) to another line (victim) must propagate through the full length of the disturber’s line [10] As well, since the insulation between lines n (disturber) and m (victim) increases the attenuation, |hn,n |hm,n | for n = m k | k This can be described as Column-Wise Diagonal Dominance (CWDD) [10] in Hk Due to CWDD, |hn,n |hm,n | for k | k n = m which implies that Hk is almost diagonal and hence in the QR decomposition, Qk is almost equal to the identity matrix Thus, |rkn,n | ≈ |hn,n k | The bit-rate of user n on frequency tone k can be written as: |rn,n |2 sn |hn,n |2 sn bnk = log2 + k n k ≈ log2 + k n k Γσk Γσk Like with the THP covered in Section III-A2, the DFC also depends on the decoding order However, unlike the THP, the benefits of ordering can be substantial [15] Another similar DFC method can be derived based on the MMSE criteria with a similar decoding procedure [16] However, the MMSE-based DFC does not preserve the Gaussian properties of the noise and the difference in performance with the ZF-based method (Section III-B2) becomes minimal at large SNR 2) Zero-Forcing Canceller: The ZF canceller sets Qk = H−1 k Hence, the ZF transmission can be expressed as follows: ˜ k = H−1 y k yk = xk + H−1 k zk (10) Therefore, ideally the crosstalk is removed entirely Note that (10) can be re-written as: y˜kn = xnk + [H−1 k ](n, ) zk |hm,n | for n = m, Hk is Based on CWDD, |hn,n k | k n,n −2 approximately diagonal and hence, ||[H−1 k ](n, ) || ≈ |hk | As such, the modified noise PSD for user n on frequency tone k, σ ˜kn , can be written as [10]: σ ˜kn E = ≈ [H−1 k ](n, ) zk Δf , n ||[H−1 k ](n, ) || σk , n σk n,n |hk | Since |hn,n k | < 1, the modified noise PSD is larger than the original noise PSD Hence, ZF can entirely remove the crosstalk at the expense of increasing the noise and the bitloading of user n on frequency tone k can be written as: snk n Γ ||[H−1 k ](n, ) || σk n,n n |hk | sk 1+ Γ σkn bnk = log2 + ≈ log2 (11) C Joint Transmitter-Receiver Processing In scenarios where both the transmitter and receiver are colocated, Vectored DSL can apply both pre-coding at the transmitter and interference cancellation at the receiver Singular Value Decomposition (SVD) can be used to obtain the precoding and the interference cancellation matrices [17] Under this scheme, Vectored DSL does not increase the total transmit power and each channel has a gain equal to the corresponding eigenvalue of the channel matrix However, this scheme can only be applied when all transmitters and receivers are colocated, in order for joint signal processing to take place Although such scenarios are rare, using SVD can be practical in scenarios where data is transmitted over a bundle of twisted copper pair linking the source and the destination and hence, allows for processing to be performed at both the transmitter and receiver This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION The SVD method decomposes the channel matrix as follows: Hk = Uk Λk Vk† , = U†k (Hk xk + zk ) = = U†k Hk xk + U†k zk ˜ k + U†k zk U†k Hk Vk x ˜ k + U†k zk Λk x The effective channel through the SVD decomposition method is Λk and hence, is crosstalk free Since U†k is unitary, the new noise vector U†k zk remains white The resulting bit-rate under the SVD decomposition method is given by: bnk = log2 + −40 −60 −80 −100 −120 ˜ k = U†k yk y = −20 Gain (dB) where Uk and Vk are unitary matrices, and Λk is a diagonal matrix with non-negative real numbers The goal is to have Λk be the effective channel Hence, Vk is used for pre-coding and Uk for cancellation ˜k The pre-coding matrix pre-multiplies the data vector x with Vk Similarly, the cancellation matrix post-multiplies the received signal vector yk with U†k This results in the following received signal vector after cancellation: ANSI direct gain ANSI crosstalk gain |[Λk ](n,n) |2 snk Γ σkn D Downstream and Upstream Zero-Forcing The row-wise and colomn-wise diagonal dominance of the DSL channel in downstream and upstream transmission results in ZF being near-optimal [10], [12] The bounds on the nearoptimality were further investigated in [18] and a tight rate approximation was produced in [19] In cases where the noise at each user is correlated (e.g., the non-cancelled crosstalk from ADSL users), the upstream ZF will amplify the noise at the receiver In these cases, the use of the non-linear DFC may be more appropriate Yet, the linear and the near-optimal properties make zero-forcing a good and simple algorithm for many vectoring cases Moreover, it lends itself to partial crosstalk cancellation (covered in Section VI) IV V ECTORED DSL DATA -R ATE The data-rate increase of Vectored DSL is apparent using either measured channel data and channel models On one hand, measured channel data confirms the ability for Vectored DSL to meet higher data-rate demands and shows how well the channel model can predict true data-rates On the other hand, the use of channel models allow for simple evaluation of the potential throughput gains of Vectored DSL in various scenarios The channel model used is the American National Standards Institute (ANSI) model which is an empirical model for generating the direct and crosstalk channel gains based on the 99% worst-case That is, 99% of the time, the direct and crosstalk gains will be better than the ones generated using the model Although this model remains pessimistic, it is suitable for generating custom test cases Unless mentioned otherwise, a 26-AWG gauge wire is assumed when using this model −140 10 Frequency (MHz) 12 14 16 18 Fig Channel gains from the ANSI model and from measured data for 25 500-m users sampled at every 100 frequency tone Three types of illustrative examples are provided in this section The first involves measured data and focuses on the case where all lines are 500 m and all use the ZF diagonalizing precoder bit-rate (5) to calculate the downstream performance and the ZF precoder bit-rate (11) for upstream performance While the lengths of lines within a DSL network can vary, FTTN networks typically consist of lines up to 500 m Hence, the 500-m measured data case provides a realistic assessment of a typical FTTN network The second illustrative example makes use of channel models in order to evaluate the performance of scenarios involving equal length users, at varied line lengths Finally, the third illustrative example focuses on the most common case of unequal line lengths, using channel models The measured data was taken by Morawski, Ho-Van, and Zhao, in the Broadband Communications Research Laboratory at McGill University The setup consisted of 25 500-m long 26-AWG twisted copper pairs bundled together The channel gains (i.e., direct and crosstalk) and the background noise were measured for each line The comparison between the ANSI model and the measured data can be observed in Fig for the direct and crosstalk channel gains Fig shows the measured background noise for both upstream and downstream transmission directions A 500-m Performance Using Measured Data For the 25-user 500-m measured data, the achievable rate is calculated using a flat transmit PSD scheme for both nonvectored and vectored transmission A total transmit power of 11.5 dBm per user is used for upstream and downstream transmission For vectored transmission, the ZF method is used with an effective flat PSD Fig shows the achievable rate in the upstream direction for each of the 25 users Similarly, Fig shows the achievable rate for each user in the downstream direction In both transmission directions, the Vectored DSL gain is clear and shows that vectoring increases the data-rate for each user by around 50% This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES 120 −120 −140 dBm background noise Noise profile upstream Noise profile downstream 100 80 −130 Rate (Mbps) Noise PSD (dBm/Hz) −125 −135 60 −140 40 −145 20 −150 10 Frequency (MHz) 12 14 16 18 Flat PSD Vectored Flat PSD Non−Vectored 10 15 20 25 User # Fig Background noise PSD of -140 dBm/Hz compared to the measured background noise PSD in the 25 500-m users setup sampled at every 100 frequency tone Fig Achievable downstream rate for each user using the 25 500-m user measured data 35 100 30 Flat PSD Vectored Flat PSD Non−Vectored 90 80 25 15 Flat PSD Vectored Flat PSD Non−Vectored 10 Rate (Mbps) Rate (Mbps) 70 20 60 50 40 30 20 10 0 10 15 20 25 User # 0 500 1000 1500 Distance (m) Fig Achievable upstream rate for each user using the 25 500-m user measured data Fig Achievable upstream rate per user in a 25-user setup over different lengths B Performance Using Channel Model While using measured data provides realistic assessments of the performance, it is far more difficult to obtain measured data for generalized scenarios (i.e., varied line lengths) As such, in order to investigate the performance of scenarios for various line lengths, ANSI channel models are used When using the ANSI channel models, the channels become symmetrical and identical for all users with identical line lengths Thus, the resulting data-rates will be identical for each user if the same parameters are used Hence, instead of showing the data-rate for each user at a given distance, we show the achievable data-rate per user at various line lengths Fig shows the achievable rate in the upstream direction for various lengths of a bundle of 25-users Similarly, Fig shows the achievable rate in the downstream direction The vectored gain is quite remarkable when the length is within 500 m This coincides with the measured data performance gains discovered in Section IV-A At long distances, the direct and crosstalk channel gains are so low that removing crosstalk does not have any substantial benefit This can be particularly observed in the upstream transmission at lengths above 1000 m This further reinforces the benefits of DSL with respect to length and further justifies the adoption of the FTTx type network topologies Comparing the results from the measured case to the channel model, we see that the measured non-vectored rates are slightly better than predicted by the rate-reach results This is due to the rate-reach results using the more pessimistic 99% worst-case model On the other hand, the vectored rates are slightly worse than predicted by the rate-reach model This is because as crosstalk is cancelled, the background noise becomes main interferer, and because the measured background noise is greater than that used by the empirical model in the better low-frequency downstream and much greater in the upstream bands, as shown in Fig This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination 10 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION 60 250 Flat PSD Vectored Flat PSD Non−Vectored Flat PSD Vectored Flat PSD Non−Vectored 50 200 Rate (Mbps) Rate (Mbps) 40 150 100 30 20 50 10 500 1000 1500 10 Fig Achievable downstream rate per user in a 25-user setup over different lengths V V ECTORED DSL I MPLEMENTATION This section discusses practical implementation issues regarding Vectored DSL and discusses some potential solutions A Vectoring Types A DSLAM services up to 192 or 384 or more customers depending on the size of the shelf [1] Within each DSLAM are line-cards, each consisting of 24, 48 or more lines (or pairs) [1] Vectored DSL can be performed in one of two vectoring modes: DSLAM level or line-card level vectoring [1] (also referred to as NodeScale or LineCard vectoring by [20]) DSLAM level vectoring performs joint vectoring across all line-cards in a particular DSLAM, while line-card vectoring applies vectoring separately for each line-card and treats the crosstalk generated by other line-cards as noise Intra-line-card 20 25 Fig Achievable upstream rate for each user in the 25-user near-far scenario The line length for each user increases from user #1 towards user #25 120 C Near-Far Case Flat PSD Vectored Flat PSD Non−Vectored 100 80 Rate (Mbps) The previous two Vectored DSL performance assessments only give an insight on its gains when every user has the same line lengths However, scenarios like binder C in Fig are very common, where a near-far effect can be observed Fig and Fig 10 show the gain of vectoring over one implementation of binder C for upstream and downstream transmissions, respectively In this implementation, there are 25 users with uniformly distributed lengths between 500 and 1000 m One can observe that the most important gain is on the far users (with longer line lengths) in the upstream direction This is because the far users no longer receive large crosstalk from the near users; without vectoring, the far users would receive large amount of crosstalk from the near users It is interesting to note that the performance gain increase per-line is dependent on each user’s own line length, regardless of whether or not all lines are of equal length This is due to the fact that once the crosstalk has been removed, it is as though each line is operating independently Hence, a performance increase of at least 50% should be expected for non-equal line lengths as well, depending on the amount of crosstalk present in the system prior to vectoring 15 User # Distance (m) 60 40 20 0 10 15 20 25 User # Fig 10 Achievable downstream rate for each user in the 25-user near-far scenario The line length for each user increases from user #1 towards user #25 crosstalk (i.e., within the same line-card) is typically 8-10 dB larger than the inter-line-cards crosstalk; however, the interline-card crosstalk still provides significant coupling DSLAM level vectoring mode has the potential to partially or fully cancel the crosstalk in the entire DSLAM, leading to significant rate improvements at a high computational cost Line-card level vectoring provides a small rate increase; however, its computational complexity is significantly reduced as compared to that of DSLAM level vectoring An alternative to full DSLAM level vectoring or line-card level vectoring is to applying vectoring across the dominant sources of crosstalk Typically, there are only a handful of dominant crosstalk sources limiting the system performance If the dominant crosstalk signals are suppressed using vectoring, then the only weaker crosstalk signals would remain Clearly, optimal performance is achieved by cancelling all the crosstalk signals [21]; however, often simply suppressing the the strongest crosstalk signals is sufficient to achieve close to optimal performance for both DSLAM level vectoring This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES 10 h1,1 k 2,1 k 3,1 hk 4,1 h k h5,1 k h6,1 k h −10 −20 dB −30 −40 −50 −60 −70 −80 −90 Fig 11 500 1000 1500 2000 2500 Tone index 3000 3500 4000 4500 Channel gains for 6-pair 600-ft 24-AWG cable bundle [22] and line-card level vectoring This approach is referred to as partial crosstalk cancellation and will be discussed in greater detail in Section VI An important factor for partial crosstalk cancellation is the feasibility of implementation In particular, it is crucial to intelligently determine which crosstalk signals should be cancelled fast enough to allow for it to be implemented while limiting the performance losses due to the presence of crosstalk B Computational Resources Vectored DSL provides significant data-rate improvements, at the expense of computational resources Two significant computational issues are memory constraints and computational complexity 1) Memory Constraints: The channel gain matrices, Hk , must be estimated/measured and stored for vectoring Assuming that each channel gain, hn,m , is represented by B k bytes, then the memory required to save all Hk matrices is N KB (bytes) Consequently, the DSLAM level vectoring requires C times memory size more than the line-card level vectoring where C is the number of line-cards per DSLAM For example, consider a VDSL2 system with a DSLAM consisting of 192 users, line-cards (each servicing 48 users), 4096 frequency tones and assuming that each channel gain is represented by bytes The memory size will be (4 × 48)2 × 4096 × ≈ 604 (MBytes) for DSLAM level vectoring and 482 × 4096 × ≈ 38 (MBytes) for each individual line-card level vectoring, respectively With a symbol rate of fs , the memory bandwidth required is N KBfs (bytes/s) Following with the previous example, with fs = 4000 (symbols/s), the memory bandwidth required would be 2.4 (TBytes/s) for DSLAM level vectoring and 148 (GBytes/s) for each line-card level vectoring, respectfully These memory bandwidth requirements are very significant and would likely factor into the feasibility of the vectoring approach taken Various interpolation and partial cancellation techniques can be applied to overcome the memory requirements [23] [24] [25] The interpolation techniques are based 11 on the fact that the channel gains, hn,m , vary relatively k slow with respect to frequency (see Fig 11) As a result, only storing the channel gain matrices corresponding to the frequency tones k = (v − 1)Kg + for v = 1, 2, , K/Kg can reduce the memory size and the memory bandwidth by a factor of (Kg − 1) The intermediate channel gain matrices can be interpolated The results of [24] illustrated that the interpolation technique can reduce the memory (or memory bandwidth) storage by 99.2%, while only experiencing a 4.4% decrease in the data-rate relative to the no interpolation case It is worthwhile to note that even though the data-rate is reduced due to the interpolation technique, there was still a 25.2% net improvement in the data-rate relative to the no vectoring case The partial cancellation technique (discussed in more detail in Section VI) adaptively employs vectoring on selected lines and frequencies By carefully and appropriately selecting the lines and frequencies used for vectoring, a significant reduction in the memory size (or memory bandwidth) can be achieved with a negligible performance degradation 2) Computational Complexity: Vectored DSL provides significant performance improvements but also requires significant computational power For example, the ZF precoder/canceller requires computing the inverse of the channel matrix for all frequency tones The computational complexity of computing the inverse of the channel matrix with many lines (e.g., a 192 × 192 matrix) for each frequency tone (e.g., 4096 tones) is very large Even though using the RWDD of the channel matrices to approximate the inverse of the channel matrix can dramatically reduce the number of computations required [26], the computational resources may not be sufficient to apply vectoring across all lines In order to reduce the size of the channel gain matrix and the number of tones involved in vectoring, various techniques for interpolation, partial cancellation, and priority settings (i.e., apply vectoring on lines with high priority) can be utilized C Training Process During the training process, channel gains are required for computing the coefficients of the pre-coder/canceller This can be done through channel estimation which can be implemented at the receiver which then feeds back the estimated channel gains to the transmitter (if necessary) via bandwidth-limited channels [25] With any practical system, channel estimation provides imperfect channel knowledge The effect of imperfect channel knowledge on Vectored DSL is investigated in Section VII While it is important to get somewhat accurate channel knowledge, there is an inherent trade-off between the computational time to acquire accurate channel knowledge In particular, it may be beneficial to apply a scheme that provides less accurate channel knowledge but requires significantly less computational time, while trying to minimize the performance loss As an example to demonstrate some issues and solutions with respect to the training process, the following considers the training process for a pre-coder In the G.993.5 standard [27], pre-coder training is achieved by the VDSL2 Transceiver Unit at the Operator side (VTU-O) transmitting a pilot sequence during its sync symbol, once every 257 DMT symbols The This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination 12 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION coefficients of the pre-coder are estimated and updated using a Least-Mean Squared (LMS) algorithm, based on errors between the pilot symbols and the signals at the output of the frequency-domain equalizer calculated by the VDSL2 Transceiver Unit at the Remote side (VTU-R) and fed back to the VTU-O Due to limited feedback channel bandwidth and the large number of frequency tones used in xDSL systems, each error on each frequency tone is quantized by a low number of bits (e.g., only 0.7 bits per error sample dimension [25]), leading to high quantization error and resulting in a low data-rate at convergence due the estimation errors Again, the interpolation technique is an efficient solution in which only the error on every k th tone is fed back Hence, the number of quantization bits increases as there are fewer error values to feedback, leading to an improved estimation of the channel and data-rate For example, with an interpolation factor of 8, the number of quantization bits is increased to bits per error dimension with only a minor performance degradation [25] Since the pilots are only transmitted every 257 DMT symbol, the convergence of training algorithms can be very slow (e.g., 10 seconds, exceeding an acceptable period of time) It is shown in [25], that at least 12 quantization bits per error sample dimension are required for converging to a high data-rate within 10 seconds while the limit is bits per error dimension when using the interpolation technique with a factor of In order to solve the problem of high quantization error and slow training convergence, scaling the error sample before quantization is essential [28] The error scaling takes advantage of the fact that the error magnitude decays rapidly as the algorithm converges That means the quantization range can be considerably reduced as the algorithm converges, ensuring a lower quantization error even when very few feedback bits are used Simulation results illustrated that with quantization bits per error sample dimension and the error scaling, the algorithm can converge within 10 seconds with minor data-rate reduction resulting from channel estimation errors D System Parameter Adjustments Before vectoring is applied, crosstalk is the dominant impairment degrading the system performance With perfect vectoring, all FEXT signals are eliminated and thus, the variable noise sources such as impulse noise or Radio Frequency Interference (RFI) can become dominant and cause transmission errors and re-initialization [29] because the interference will have greater relative variations (where the absolute variation remains and the interference reduces with FEXT) Hence, system parameters used for impulse noise protection must be correspondingly adjusted to cope with the remaining noises after vectoring There are many configuration tools available to mitigate the impact of these noise sources [1] Seamless Rate Adaption (SRA) can be used in a slow-changing noise environment to provide more stability while interference sources fluctuate by preventing a line from retraining Combinations of Impulsive Noise Protection (INP), Inter-leaver Delay and physical layer retransmission can be used to mitigate the effects of impulsive noise Save Out Showtime (SOS) can be used to prevent lines from retraining when crosstalk increases suddenly (e.g., impulsive noise) Other tools such as virtual noise and erasure decoding can provide additional line stability As vectoring is introduced, the parameters used in the configuration tools will become more important in order to provide a tradeoff between stability and vectoring performance E Managing Non-Vectored Lines and Legacy CPEs Occasionally, DSL binders may contain mixes of lines belonging to different xDSL technologies (e.g., VDSL and ADSL lines) Similarly, DSL binders may contain both vectored and non-vectored lines The crosstalk generated from non-vectored lines onto the vectored lines cannot be cancelled and may cause significant performance degradation to the vectored lines [1], [30] One method to solve this problem would involve the combination of DSM levels 1, and to cancel out crosstalk where possible and mitigate it using DSM levels or where it is not possible Another approach would involve upgrading the respective CPEs to vectoring-capable CPEs The legacy CPE issue arises in areas where outdated services are being provided (e.g., ADSL, VDSL, VDSL2) but it is desired to also deploy Vectored DSL to provide higher data-rates [1] The Vectored DSL system should be capable of providing the increased data-rates associated with Vectored DSL, while still providing the existing services to legacy customers without upgrading their CPEs In order to solve this problem, the ITU has developed a downloadable firmware known as “vectoring-friendly CPE” which can allow for existing CPEs to operate in a “vectoring-friendly” mode [1] This would allow legacy lines to operate as before, while allowing for the crosstalk generated by those lines to the vectoring lines to be cancelled F Managing Unbundled Lines Unbundled lines arise when competing service providers each have lines within the same binder (e.g., two Vectored DSLAMs from different service providers share a binder) [1], [31] The interference between clusters cannot be cancelled due to a lack of coordination between competing service providers Ideally, cooperation would allow for all the crosstalk to be cancelled (e.g., using a third-party coordination engine) When coordination is not possible, the combination of DSM levels 1, and can again be employed to mitigate any remaining crosstalk which could not be vectored Another issue is that of the physical location of lines within a binder The crosstalk between lines in close proximity is significantly larger than the crosstalk between lines that are far apart; hence, it would be ideal to place lines which will be jointly-vectored close to one another Unfortunately, the rewiring of lines within a binder is difficult, costly and not practical from an implementational perspective [1] VI PARTIAL C ANCELLATION Vectored transmission is an intensive process with a computational complexity that grows linearly with the number of frequency tones and quadratically with the number of users This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination For example, say 50 users and 2000 frequency tones, precoding requires at least million multiplications per symbol With a symbol rate of 4000 Hz, at least 20 billion multiplication and 20 billion addition operations are required every second Partial cancellation reduces the computational load by only removing the crosstalk between specific users on specific frequency tones The partial cancellation method uses the ZF method for both upstream and downstream transmissions It works by setting some values in the pre-coding matrix or the cancellation matrix to zero By doing so, the number of operations required for crosstalk cancellation can be approximately proportionally reduced with the number of elements set to zero Therefore, for upstream transmission, we want a cancellation matrix Pk such that: [Pk Hk ](n,m) = =1 if cn,m k n,m if ck = =1 if cn,m k n,m if ck = , with Hk Pk representing the effective channel A simple partial cancellation interpretation was developed in [32] for upstream transmission and in [33] for downstream transmission In upstream transmission and in combination with the CWDD nature of upstream transmission in the DSL networks, it was determined that by letting: [Pk ](n,m) = n,m =1 [H−1 k ](n,m) if ck n,m if ck = , the SNR would be approximately: SNRnk ≈ σkn + 13 100 90 Full vectoring Partial cancellation No vectoring 80 70 20 40 60 80 Percent of total crosstalk tap allocated 100 Fig 12 Partial crosstalk cancellation sum rate with a varying number of cancellation taps where cn,m represents the cancellation tap on the crosstalk k generated from user m to n on frequency tone k Since Pk Hk is the effective channel after cancellation, the cancellation taps cn,m effectively removes the crosstalk generated from user k m to user n on frequency tone k Similarly, for downstream transmission, we want a pre-coding matrix Pk such that: [Hk Pk ](n,m) = Percent of full vectoring sum rate LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES n |hn,n k | sk n,m m | sk m:cn,m =0 |hk k Therefore, it was concluded that partial crosstalk cancellation using zero-forcing does not change the statistics of the noise nor does it amplify the non-cancelled crosstalk In [32], a joint tone-line selection algorithm was proposed where the cancellation taps cn,m are assigned based on the k greatest lost from no crosstalk to having a single crosstalk generator from sm k By using the joint tone-line selection on a 4×300-m and 4×1200-m user near-far scenario, Partial Crosstalk Cancellation (PCC) obtained 90% of the performance of full cancellation with only 29% of the cancellation taps active, and 80% of the full performance in downstream transmission with only 20% of the taps active The precoder for partial cancellation can also be obtained iteratively by using error signal feedback An analysis on the performance and convergence of the adaptive partial cancellation precoder is developed in [34] The results from applying an optimal PCC in the downstream direction to the 25-user 500-m measured case from Section IV using a flat PSD are shown in Fig 12 The sumrate over all 25 users shows that it is possible to achieve 90% of the full vectoring performance with only 40% of the cancellation taps Thus, with only 40% of the number of computations required by full vectoring, PCC can already increase the performance by 50% over the non-vectoring case The performance of PCC is also demonstrated in [35] where it is shown though simulations that cancelling around 50% of the crosstalk can achieve significant gain in a branched topology system with both vectored and non-vectored capable users A Partial Cancellation and Spectrum Management The combination of PCC and spectrum management was investigated in [36], [37] With spectrum management, the effect of crosstalk between users is reduced by allocating power to frequency tones generating less crosstalk Whereas, for PCC, frequency tones with large crosstalk values are targeted to remove the specific crosstalk Hence, if PCC and spectrum management were to run independently, the mutual benefit would not be exploited In the independent case, it is likely that the cancellation taps will be assigned to crosstalk links with high crosstalk channel gain as with the joint toneline selection algorithm However, it is also likely that a spectrum management algorithm would allocate little to no power to the interfering users on those crosstalk links This combination would result in an inefficient use of power since it would result in loading little power on tones where the crosstalk has been cancelled Therefore, there is a need of a joint-optimization for spectrum management and cancellation tap allocation By applying a binary-version of Optimal Spectrum Balancing (OSB) on the non-cancelled crosstalk, [37] showed that in a 2×600 m and 2×1200 m near-far topology, it is possible to achieve the same performance as full crosstalk cancellation by only using 30% of the crosstalk cancellation taps Moreover, with only 25% of the cancellation taps active, the performance remains nearly crosstalk free This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination 14 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION B Cross-layer Partial Cancellation A cross-layer approach where delay, rate, and cancellation taps were considered in [38] by using the following combined optimization problem n Q (t)R max cn,m ∀k,n,m=n k n (12) n∈N ˆ k = Hk + The estimated channel matrix can be written as H ˆ ΔHk The inverse of Hk can be written as [46]: ˆ −1 = (Hk + ΔHk )−1 H k −1 I + ΔHk H−1 = H−1 k − Hk k = I − (EUS )k xk + where C total represents the maximum number of cancellation taps and Qn (t) is the queue at user n and at time t Whereas Problem (12) is akin to the rate adaptive problem in [3], a cancellation tap reduction version of the problem was also investigated in [38] by modifying the objective function from Problem (12) to Qn (t)Rn − V C(t), ΔHk xk ˆ −1 zk , H k where (EUS )k is an N × N matrix representing the error in estimation associated with upstream transmission on frequency tone k Therefore, the upstream bit-rate for line n on frequency tone k can be expressed as: bnk = log2 SNRnk , Γ 1+ where n∈N where V is some cost factor and C(t) is the number of cancellation taps assigned at time t VII E FFECT OF C HANNEL E STIMATION E RROR ON V ECTORED DSL This paper has demonstrated the potential performance benefits associated with Vectored DSL; however, Vectored DSL requires knowledge of the channel in order to properly function In practice, channel knowledge is subject to inaccuracies As such, this section investigates the effect of channel estimation error on the performance of practical Vectored DSL systems DSL channel estimation is a well-researched subject In [39], crosstalk was estimated using a least-squares method by making use of an impartial third-party A maximumlikelihood channel estimation technique using a training-aided expectation-maximization algorithm was proposed in [40] and [41] A crosstalk channel estimation technique based on SNR measurements at the receiver was presented in [42] An optimal FEXT channel estimation technique in the leastsquares sense was proposed in [43] As well, a maximum likelihood channel estimator was derived in [43] and the effect of channel estimation error on the performance of nonvectored DSM systems was discussed in [44] Furthermore, the effect of generalized regression neural network-based channel estimation on Vectored DSL was investigated in [45] In this section, a ZF canceller is applied to upstream transmission and a DP is applied to the downstream transmission A Upstream Zero Forcing SNRnk − (EUS )k = m=n (EUS )k (n,m) (n,n) sm k snk ˆ −1 H k + (n, ) k (13) σkn It can be seen that as ΔHk approaches the all-zeros matrix, (EUS )k vanishes and bnk approaches that of ideal channel knowledge: bnk (Ideal) = log2 1+ snk Γ H−1 k (n, ) σkn B Downstream Diagonalizing Pre-coder Downstream vectored transmission with an estimated channel matrix is given by (15) ˆ 1,1 , , h ˆ N,N }xk + zk ˆ −1 diag{h y ˆk = Hk βk−1 H k k k (15) Similar to Section VII-A, substituting (14) into (15) gives: ˆ 1,1 , , h ˆ N,N }xk − y ˆk = zk + βk−1 diag{h k k βk−1 I + ΔHk H−1 k −1 ˆ 1,1 ˆ N,N } xk ΔHk H−1 k diag{hk , , hk (EDS )k = ˆ 1,1 , , h ˆ N,N } βk−1 diag{h k k − (EDS )k xk + zk , where (EDS )k is an N × N matrix representing the error in estimation associated with downstream transmission on frequency tone k Therefore, the downstream bit-rate for line n on frequency tone k can be expressed as: bnk = log2 1+ Γ βk−1 ˆhn,n − (EDS )k k m=n (EDS )k (n,m) (n,n) (˜ s)m k (˜ s)nk + Upstream vectored transmission with an estimated channel matrix is given by (13) k −1 (EU S )k n∈N m∈N k∈K ˆ −1 yk = H ˆ −1 (Hk xk + zk ) ˆk = H x k k ˆ −1 zk ˆ −1 Hk xk + H =H (14) Substituting (14) into (13) gives: cn,m ≤ C total , k max ΔHk H−1 k ˆ −1 zk − H−1 I + ΔHk H−1 ˆ k = xk + H x k k k such that cn,m ∀k,n,m=n k −1 σkn , where (˜ s)nk = E Qk (n, ) xk /Δf Similar to the upstream case, as ΔHk approaches the all-zeros matrix, (EDS )k vanishes and bnk approaches that of ideal channel knowledge: bnk (Ideal) = log2 1+ s)nk βk−2 |hn,n k | (˜ Γ σkn This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES 15 TABLE I E FFECT OF E STIMATION E RROR ON V ECTORED DSL FOR VARIED Δ Δ Upstream Sum Rate % of (Mbps) Δ=0 783 100.0 756 96.6 723 92.3 691 88.2 660 84.3 630 80.4 Avg % Diff 0.0 11.6 23.4 35.9 49.3 64.3 Downstream Sum Rate % of Avg % (Mbps) Δ=0 Diff 2596 100.0 0.0 2536 97.7 11.6 2423 93.3 23.4 2306 88.8 35.9 2194 84.5 49.4 2085 80.3 64.2 Fig 13 Phantom DSL conceptual drawing C Simulation Results In order to test the effects of channel estimation error on the performance of Vectored DSL, the values of the true channel measurements were uniformly modified by ±Δ [dB], for varying values of Δ, on the 500-m measured data test case Note the FEXT channel estimation error for the estimator derived in [43] was approximately uniformly distributed within [−3, 3] dB, corresponding to Δ = As such, the value of Δ = is assumed to be typical for practical networks [44] The value of Δ was varied from to 5, where Δ = corresponds to using the true measured values Table I shows the sum rate achieved, the corresponding percentage relative to perfect knowledge, and the average percent difference for each value of Δ As can be seen in Table I, imperfect channel knowledge (up to Δ = 5) results in over 80% of the perfect knowledge sum rate Moreover, with Δ selected according to what is typically seen in practice (Δ = 3) [43] [44], over 88% of the perfect knowledge sum rate was achieved As such, for practical deployment, it is reasonable to assume a 12% loss in throughput due to imperfect channel knowledge VIII V ECTORED DSL A PPLIED TO P HANTOM T ECHNOLOGY A Phantom DSL Technology: An Overview DSL Phantom mode technology [47] [48] is an innovative method for increasing DSL data-rates [49] Phantom technology transports three channels worth of data over two physical channels More specifically, Phantom technology makes use of coordination between the two physical channels to achieve the same data-rate that could be achieved using three independent physical channels The key concept is the use of a phantom (or virtual) channel Information desired to be sent over the phantom channel is split between the two physical channels and can be recovered at the receiver after processing While the amount of data transmitted within a given time frame increases, the process generates excess crosstalk Therefore, Vectored DSL can be applied in addition to Phantom technology to remove the crosstalk Phantom mode requires more sophisticated modems that are capable of supporting three-pair bonding More specifically, it requires a modem that can recover the three channels worth of data from the data received over the two physical channels As well, in order to combine Vectored DSL with Phantom mode technology, the DSL modem’s chip set must have enough processing power to vector the two physical channels and the phantom channel The concept of Phantom DSL can be generalized to more than two physical channels; that is, if C physical channels are used, there can be up to C − phantom channels Hence, for every C physical channels, 2C − channels worth of data can be transmitted Increasing the number of physical channels and phantom channels can significantly increase data-rates, at the expense of more complicated processing and hardware requirements In practice, it is common for a household to have two twisted-pair copper wire loops at their home (i.e., C = 2) In many cases, increasing the number of physical channels would require the re-wiring of lines in a binder which is often not practical A conceptual drawing of Phantom mode technology is shown in Fig 13 for the C = case As shown in Fig 13, the Phantom signal (denoted by ±c) is divided between the two physical channels At the receiver, the desired signals a, b and c can be recovered More technically, Phantom mode makes use of both differential signals and common mode signals [50] Differential signals are sent over the two physical twisted-pair channels, while a third signal which is in common mode with each of the physical twisted-pairs, but in differential mode between them is also sent Applying a differential amplifier to each of the physical channels filters out the common-mode signal so that the differential signals can be recovered [4] Similarly, amplifying the signal between the two pairs recovers the common-mode (phantom) signal [4] This can be seen in Fig 13, since the difference between the top twisted-pair is c + a − (c − a) = 2a and the difference between the bottom twisted-pair is −c+b−(−c−b) = 2b Similarly, the difference between the “virtual plus” (red) from the top twisted-pair and the “virtual minus” (blue) from the bottom twisted-pair gives c+a−(−c−b) = 2c+a+b, where a and b are known Hence, the signals a, b, and c can all be recovered at the receiver B Testing Results Phantom mode technology combined with Vectored DSL is seen as the future for wire-line communications As such, several companies have tested the performance of Phantom DSL in a lab-setting, including Alcatel-Lucent, Nokia Siemens Networks and Huawei Table II summarizes the downstream data-rates reported by the three companies using phantom mode and vectoring for various number of pairs and line lengths within a lab- This article has been accepted for inclusion in a future issue of this journal Content is final as presented, with the exception of pagination 16 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION TABLE II S UMMARY OF DOWNSTREAM P HANTOM AND V ECTORED DSL DATA - RATES BY COMPANY IN A LAB - SETTING Alcatel-Lucent Nokia Siemens Networks Huawei Number of Pairs Two Two Four Four Four Four Downstream Speeds (Mbps) 100 390 910 825 750 700 Line Lengths (m) 1000 400 400 400 500 400 setting1,2,3 Alcatel-Lucent showed that by combining Phantom mode with Vectored DSL, it could achieve downstream speeds of 390 Mbps over 400 m using two pairs or 910 Mbps over 400 m using four pairs Alcatel-Lucent also showed that it could achieve downstream speeds of 100 Mbps at km using two pairs Similarly, Nokia Siemens Networks showed that when combining Phantom mode and Vectored DSL, it could achieve 825 Mbps over 400 m using four pairs and that it could achieve 750 Mbps over 500 m using four pairs Huawei showed that by combining Phantom mode and Vectored DSL, they could achieve 700 Mbps at 400 m using four pairs The application of Phantom mode technology for DSL was also investigated in [4] It was shown in [4] using VDSL2 alone, an 800 m line could support 50 Mbps downstream, while using Phantom mode, a 1300 m line could support 50 Mbps downstream (an improvement of 62.5%) IX C ONCLUDING R EMARKS This paper presented an overview of Vectored DSL The main vectoring techniques for upstream and downstream transmission were presented It was shown that ZF is suitable for DSL given the CWDD and RWDD of the DSL channel Simulation results were provided to show the performance gains in terms of data-rates using Vectored DSL Many practical implementation issues regarding Vectored DSL were discussed and some potential solutions were provided The topic of partial crosstalk cancellation for reducing the computational complexity was also discussed Then, the effects of channel estimation error on the performance of Vectored DSL was investigated Finally, Phantom DSL was discussed as a potential future path for Vectored DSL Acknowledgements The authors would like to thank the reviewers for their helpful comments R EFERENCES [1] R Zidane, S Huberman, C Leung, and T Le-Ngoc, “Vectored DSL: Benefits and Challenges for Service Providers,” IEEE Commun Mag., Feb 2013 M Ricknă as, 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Lafata, P Jares, and J Vodrazka, “Increasing the transmission capacity of digital subscriber lines,” in 35th International Conference on Telecommunications and Signal Processing, Jul 2012, pp 292–296 [50] W Foubert, C Neux, L Van Biesen, and Y Rolain, “Exploiting the phantom-mode signal in dsl applications,” IEEE Trans Instrum Meas., vol 61, no 4, pp 896–902, Apr 2012 17 Christopher Leung received his M.Eng and B.Eng in Electrical Engineering in 2011 and 2009, respectively, from McGill University, Montr´eal, Qu´ebec, Canada Since 2012, he joined the M.Sc in Financial Engineering program at HEC Montr´eal Mr Leung was the recipient of the Alexander Graham Bell Canada Graduate Scholarship from the National Science and Engineering Research Council (NSERC) and the Bourses de maˆıtrises en recherche from the Fonds de recherche du Qu´ebec - Nature et technologies (FQRNT) in 2009; and the McGill Engineering Doctoral Award and of the Bourses de doctorat en recherche from FQRNT in 2011 Sean Huberman received his B.Sc in engineering (with first-degree honours) from Queen’s University, Kingston, Canada, in applied mathematics and engineering control and communications, in May 2008 He began his M.Eng in electrical engineering at McGill University, Montreal, Canada, in September 2008 In January 2010, he transferred into the PhD program in electrical engineering at McGill University His research interests include techniques of mathematical optimization, dynamic resource allocation, channel modeling and channel measurements Mr Huberman was the recipient of the Hydro Quebec Engineering Doctoral Award in 2009 In 2010, he was the recipient of the Vadasz Doctoral Fellowship in Engineering He was also the recipient of a three-year doctoral National Science and Engineering Research Council (NSERC) award and a three-year McGill Engineering Doctoral Award (MEDA) Khuong Ho-Van received the B.E (with the firstrank honor) and the M.S degrees in Electronics and Telecommunications Engineering from HoChiMinh City University of Technology, Vietnam, in 2001 and 2003, respectively, and the Ph.D degree in Electrical Engineering from University of Ulsan, Korea in 2006 During 2007-2011, he joined McGill University, Canada as a postdoctoral fellow Currently, he is an assistant professor at HoChiMinh City University of Technology His major research interests are modulation and coding techniques, diversity technique, digital signal processing, and cognitive radio Tho Le-Ngoc obtained his B.Eng (with Distinction) in Electrical Engineering in 1976, his M.Eng in 1978 from McGill University, Montreal, and his Ph.D in Digital Communications in 1983 from the University of Ottawa, Canada During 19771982, he was with Spar Aerospace Limited and involved in the development and design of satellite communications systems During 1982-1985, he was an Engineering Manager of the Radio Group in the Department of Development Engineering of SRTelecom Inc., where he developed the new point-tomultipoint DA-TDMA/TDM Subscriber Radio System SR500 During 19852000, he was a Professor at the Department of Electrical and Computer Engineering of Concordia University Since 2000, he has been with the Department of Electrical and Computer Engineering of McGill University His research interest is in the area of broadband digital communications He is a senior member of the Ordre des ing´enieurs du Qu´ebec and a fellow of the Institute of Electrical and Electronics Engineers (IEEE), the Engineering Institute of Canada (EIC), the Canadian Academy of Engineering (CAE) and the Royal Society of Canada (RSC) He is the recipient of the 2004 Canadian Award in Telecommunications Research, and recipient of the IEEE Canada Fessenden Award 2005 He holds a Canada Research Chair (Tier I) on Broadband Access Communications, and a Bell Canada/NSERC Industrial Research Chair on Performance & Resource Management in Broadband xDSL Access Networks  ... pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES (a) Upstream (b) Downstream Fig Vectored DSL transmission lines that the network operator has control of and. .. pagination 10 IEEE COMMUNICATIONS SURVEYS & TUTORIALS, ACCEPTED FOR PUBLICATION 60 250 Flat PSD Vectored Flat PSD Non? ?Vectored Flat PSD Vectored Flat PSD Non? ?Vectored 50 200 Rate (Mbps) Rate (Mbps)... pagination LEUNG et al.: VECTORED DSL: POTENTIAL, IMPLEMENTATION ISSUES AND CHALLENGES [29] M Mohseni, G Ginis, and J Cioffi, “Dynamic Spectrum Management for Mixtures of Vectored and Non-vectored