Contract No U-BROAD D3.1 Characterization of the generic framework for coding and vectoring

Transcription

1 U-BROAD Deliverable No. D3.1 Contract No U-BROAD D3.1 Characterization of the generic framework for coding and vectoring Prepared by: Amir Leshem and Li Youming - Bar Ilan University Eyal Barnea and Rafi Ravid - Metalink Broadband Nikos Sidiropolous and Eleftherios Karipidis - Technical University of Crete Jerome Louveaux and Alle-Jan van der Veen - Delft University of Technology Abstract: In this report we lay down the foundation for the U-BROAD research related to advanced coding, spectral coordination and vectoring. We describe the general problems. Then we define some mathematical models relevant for various network configurations and spectral management restrictions. We continue with describing the applicable methods for each of the techniques involved: Advanced coding, spectral coordination, interference cancellation and multichannel transmission. Keyword list: Advanced coding, LDPC, spectral coordination, multichannel transmission, interference mitigation. Page 1-31

2 U-BROAD Deliverable No. D3.1 1 Executive Summary (or statement of result) This reports describes the basic approaches needed in order to achieve the ultra high bit rates envisioned over single and multiple pairs. The report describes analysis of the basic strategies to increase the available bandwidth for transmission over public telephone access network wires. As described and shown through capacity analysis the research should concentrate on the following topics: 1. Advanced coding techniques. Here we have shown that advanced coding together with proper band plans will enable the target of 100 Mbps DS transmission over 300m using a single pair, as well asymmetric 75 Mbps. Furthermore we have shown that symmetric 50 Mbps can be delivered to reach of 500m which implies 100 Mbps symmetric rate using two pairs. This is a natural continuation of the two pairs SHDSL in a business oriented environment. 2. We have discussed the topic of spectral coordination and shown how proper coordination can lead to better network exploitation. The cooperation can be achieved either by agreement or by setting a set of operating rules that are enforced by network management entity. Future research will concentrate on axiomatization of these rules. 3. We have demonstrated how fully coordinated transmission can enhance overall network capacity as well as the bandwidth available to each user. Research will focus on computationally efficient architectures and novel methods for interference cancellation, as well as on issues of channel estimation and synchronization. Also theoretical performance analysis is necessary in order to be able to evaluate the performance of the proposed methods. 4. A related topics that will be dealt in future research are the relevance of space-time coding techniques. Finally it should be emphasized that there is a need to test the algorithms proposed in this framework on data provided by OTE and FTRD. 2 Full description of deliverable content Page 2-31

3 U-BROAD DELIVERABLE D3.1 3 Contents I Introduction 4 II Signal model for single pair transmission 6 III Signal model for NEXT limited systems 6 III-A Signal model III-B The distribution of the received noise covariance matrix IV Signal model for precoded FDD systems 8 V Advanced coding for single and multi-channel transmission 10 V-A Structure of LDPC code V-B Decoding algorithm V-C Performance of LDPC code VI Coordinated transmission 14 VI-A Dynamic spectrum allocation algorithm VI-B Simulation results: Dynamic FDM for RT-VDSL and CO-ADSL VI-C Conclusions regarding spectral coordination VII Interference cancellation and precoding in multichannel DSL 18 VII-A Vectored-DMT VII-B Zero-forcing cancellation VII-C Additional developments VII-D Linear equalization VII-E NEXT suppression VII-F Channel estimation VII-G Transmit beamforming VIII Conclusions 28 References 28

4 U-BROAD DELIVERABLE D3.1 4 I. INTRODUCTION Copper based transmission equipment is divided into two families: Private networks equipment and public networks equipment. These two families of equipment have quite different operating environment and are subject to different regulations as well as very different physical channels and noise environments Base-T equipment [4] capable of delivering 1Gbps over special (Category 5) wiring or fiber optics, typical for private networks and fiber based networks, but non-existing in public access networks due to costs of installation Base-T [4] capable of delivering 100 Mbps over voice grade copper up to 100m. This equipment is widely deployed in private networks, however it falls short of meeting the public networks requirements in two substantial manners: a) The 100m reach is well below the length of typical public network loops, even when secondary networks with optical network units (ONU) is deployed deep into the access network. b) This equipment is spectrally incompatible with much of the legacy equipment already deployed such as ADSL and VDSL. This severely limits the possibility of using the equipment in the regulated public networks. Furthermore the deployment of such equipment in the access network would contradict the unbundling policy of the European Union. The spectrally compatible alternative for transmission over the public network is the DSL technology. Current state of the art transmission of data packets over access network loops provides up to 52 Mbps downstream and 26 Mbps upstream. Moreover, these high rates are currently limited to 300m wires and in practice translate to an actual throughput of less then 30Mbps in realistic deployment scenarios. Indeed both European and American VDSL standards [2], [3], [6] define rates up to 26 Mbps. While the reach is sufficient in the case of fiber to the basement architecture (FTTB), there is a need to increase the rates. The way to increase rate in DSL technology over a single pair is twofold: Using improved coding and enhancing the overall interference environment using spectral coordination. In the future we envision that a complete remote terminal will be coordinated and transmission will be joint. This leads to a second transmission model where the interference can be accurately estimated and removed. This is the second approach taken in this project. Crosstalk is the main impairment in DSL systems. There are two types of crosstalk, namely FEXT (Far-end crosstalk) and NEXT (Near-end crosstalk). They are represented in figure 1. NEXT is usually stronger since it comes from sources close to the receiver. However proper duplexing schemes such as frequency division duplexing (FDD) or time division duplexing (TDD) completely eliminates NEXT. If all the lines are coordinated 1, NEXT can easily be removed on that side since all the signals sent to the other lines, and which create NEXT, are known. Inversely, when the lines are not coordinated (as it is usually the case at the CPE), such a suppression is not possible. So, if NEXT is present, other techniques are needed. Several methods are described below. FEXT is usually weaker however it is the dominant impairment in FDD DSL systems, especially ones operating above 1MHz where echo cancelled transmission is typically not used (except for Ethernet in 1 connected to one single operating unit, usually the CO (central office), see figure 1

5 U-BROAD DELIVERABLE D3.1 5 Figure 1. DSL crosstalk environment. Copied from [25]. private installations). Once again, the situation is different at the CO and at the CPE. Hence, FEXT is treated differently in downstream and upstream. In downstream, the transmitters of the different lines are coordinated, which enables some kind of pretreatment of the signals to avoid FEXT. At the receiver, only the signal from the line of interest is available. Thus the possibility of using crosstalk cancellation techniques is limited in downstream. It is the opposite situation in upstream: The receivers are coordinated but the transmitters are not. In that case, the possibility of pre-compensation is limited, but some joint processing at the receiver can cancel crosstalk. Different methods of pre-compensation or cancellation are presented below. Finally, it should be noted, that in some cases, multiple lines can be hired by a single customer. In that case, several lines can be coordinated at the CPE side and more advanced crosstalk suppression techniques can be used. The structure of this document is as follows. We begin with an overview of relevant system and channel models sections II-IV. Then, we present state of the art and some new research results related to the various topics contained in this work package. We concentrate on the following topics: 1. Advanced coding (section V). For single and multiple channel transmission. This includes Low density parity check codes and Turbo codes. However as both can be interpreted in a similar way we concentrate on LDPC. 2. Multichannel spectral coordination and dynamic spectral management (DSM) (section VI). This includes all levels from uncoordinated iterative waterfilling, partial coordination such as dynamic FDM and full coordination. 3. Multichannel transmission (section VII). This includes transmit precoding and beamforming, receiver interference cancellation and space-time coding. We also survey the recent results within the project and define the framework for future work in this work package. The main techniques that we identified as having potential are advanced coding and more specifically low density parity check codes, FEXT pre-compensation and cancellation and spectral coordination techniques. We do not specifically consider one possible modulation technique since past experience proved that both single carrier and multicarrier modulations have merits for DSL transmission [46]. However when appropriate we chose the modulation that simplifies the presentation or the hardware implementation involved.

6 U-BROAD DELIVERABLE D3.1 6 II. SIGNAL MODEL FOR SINGLE PAIR TRANSMISSION In this section we describe the fundamentals of single pair transmission as it is used today. Our focus is on capacity analysis using gap approximation which enables us to estimate performance of transmission systems in a reasonable complexity. Consider a received signal x i (t) given by x i (t) =h i;i Λ s i (t)+ P l6=i hfext i;l Λ s l (t) + P l6=i hnext i;l Λ I l (t) +ν i (t) (1) where h i;i is the i th pair channel impulse response, h fext i;l,h next i;l are the FEXT and NEXT transfer functions from pair l to pair i respectively, ν k (t) is zero mean circularly symmetric additive white Gaussian noise with covariance matrix E (νν Λ )) = ff 2 (typically the AWGN power is assumed to have a PSD of -140 dbm/hz in DSL applications). Translating to the frequency domain we obtain that P P x i (f )=h i;i (f )s i (f )+ l6=i hfext i;l (f )s l (f )+ l6=i hnext i;l (f )I l (f )+ν i (f ) (2) The achievable rate on the i 0 th channel under no coordination is now given by [20] 0 Z C i = log 2 1+ P i (f ) jh ii (f )j 2 f P fi l6=i P fi fi fi fext l (f ) fih fext il (f ) fi P fi 2 + l6=i P l next (f ) fi fi h next il (f ) 1 fi 2 C A 2 + jn i (f )j df (3) where P i(f ) is the desired signal PSD, P fext l (f ),Pl next (f ) are the FEXT and NEXT PSD respectively and is the gap to capacity which for coded QAM with BER 10 7 is 9:8 c g + m g where c g is the coding gain and m g is the margin. For estimating capacity the gap should be 0 db ( =1). III. SIGNAL MODEL FOR NEXT LIMITED SYSTEMS In this section we describe the signals and the noise models that appear in multichannel DSL transmission when echo cancelled systems are co-located and operating in the same frequency band as the analyzed system. We use the model of [31], adapted to various types of binders. We then generalize it to a multidimensional statistical model that enables us to estimate the capacity of the multidimensional system capacity. Finally, we incorporate physical properties of the binder to obtain a model that is valid for large number of pairs. III-A. Signal model Assume that we have a binder consisting of P twisted pairs. typical binders include 25,28, 50 or 100 pairs. Assume that a system coordinating the transmission of p pairs numbered i 1 ;:::;i p out of the P pairs is operating in the binder. Assume that simultaneously L other pairs n 1 ;:::;n l are used by alien systems not coordinated with the system under consideration. We further assume that all systems operate using the same frequency allocation which is overlapping between upstream and downstream. Therefore the dominating impairment is the near end cross-talk (NEXT) generated by the transmitters co-located with the receiver [59]. The received signal at pairs i 1 ;:::;i p can be written as x i (t) =h i Λ s i (t) + P k6=i h ik Λ s k (t) P p k=1 g i;i k Λ r ik (t)+ P L l=1 g i;n l Λ r nl (t) +ν i (t) (4)

7 U-BROAD DELIVERABLE D3.1 7 where h i is the i th pair channel impulse response, g i;k are the NEXT transfer functions from pair k to pair i, ν k (t) is zero mean circularly symmetric additive white Gaussian noise with covariance matrix E (νν Λ )) = ff 2 (typically the AWGN power is assumed to be -140 dbm/hz in DSL applications). Since the p pairs are coordinated we can assume that self NEXT is cancelled by applying echo-cancellation techniques using the transmitted signals and thus the middle term in (4) disappears. This reduces (4) to x i (t) =h i Λ s i (t) + P k6=i h ik Λ s k (t) + P L l=1 g i;n l Λ r nl (t) +ν i (t) (5) translating to the frequency domain we obtain that x i (f )=h i (f )s i (f )+ P L l=1 g i;n l (f )r nl (f )+ν i (f ) (6) In vector form we can represent the received signal by where x(f )=H(f )s(f )+G(f )r(f )+ν(f ) (7) H(f )= h 11 (f ) h 1p (f ). h p1 (f ) h pp (f ) is the channel and FEXT frequency responses matrix, s(f )=[s 1 (f );:::;s p (f )], r(f )=[r 1 (f );:::;r L (f )] are the frequency domain representations of the signals transmitted by the system and the alien NEXT signals, and 2 3 g i1;n 1 (f ) g i1;n L (f ) G(f. )= g ip;n 1 (f ) g ip;n L (f ) is a p L matrix of the crosstalk coupling response towards the pairs of the system. Also denote the l th column of G(f ) by g l (f ). In some cases where NEXT is dominant we would like to ignore FEXT (which would consist of off-diagonal elements) obtaining a diagonal matrix H(f )= h 11 (f ) h pp (f ) III-B. The distribution of the received noise covariance matrix We now analyze the distribution of the noise covariance matrix in a multipair system. To describe the statistical properties of the pair to pair NEXT coupling we follow the analysis of [31]. This analysis is based on large amount of experimental data and is consistent with other important empirical characterization e.g., [43], [44]. A more detailed analysis can be found in [42], [54], [55] where the validity of the statistical models is tested as well as capacity distributions. The power distribution of the NEXT coupling function, g ik;n l (f ), is modeled by a log-normal distribution with frequency dependent mean : E (10 log 10 jg ik;n l (f )j) =μ p (f )= 165: log(f ) dbm/hz (8) 7 5

8 U-BROAD DELIVERABLE D3.1 8 and constant variance ν 2 =9:2 db, where f is measured in Hz. Therefore the amplitude is log-normal distributed with mean μ a (f )= 82:7 +7:5 log(f ) (9) and ν 2 = 4:6 db. Furthermore we can assume that the phase is uniform in [ ß; ß) Similarly for real signals we can take the phase to be ±1. We now generalize the log-normal model to the multidimensional case. Since the NEXT can be modeled as Gaussian we need only characterize the statistical distribution of the crosstalk channel in order to characterize the distribution of the capacity. The situation is similar to fading channels where the channel response exhibits statistical behavior. However in our case the channel is stationary during the entire transmission. Once crosstalk coupling realization has been chosen it is fixed. A second difference is that the variation is of the noise response rather than of the channel itself. The attenuation of copper lines is very stable and is very similar for various pairs in the same binder. However the crosstalk channels between various pairs are quite random due to twisting density of the various pairs and to location of the given pairs. In this situation we will show that correlation of the coupling functions actually increases capacity, since it enables better estimation of the noise process. To summarize the above discussion the noise covariance matrix R nn (f )=Pnext (f )G(f )GΛ (f )) + ff 2 I = LX l=1 g l (f )g Λ l (f )+ff2 I (10) where Pnext (f ) is the power spectral density of the NEXT disturbers. The components of each g l (f ) are (correlated) log-normal random variables with mean and variance defined in (9). Therefore fi 10 log figi;l fi 10 (f ) fi ο N (μa (f );ν 2 ) (11) Furthermore we have [8] μg l (f )=E(j(g l (f )) i j 2 )=K next f 3=2 : (12) IV. SIGNAL MODEL FOR PRECODED FDD SYSTEMS Next we describe the signal model of a multichannel precoded system that will be used for analysing precoding techniques for downstream transmission. We concentrate on discrete multitone (DMT) systems where the transmission is done independently over many narrow sub-bands. Assume that we have a binder consisting of p twisted pairs, typical binders include 25,28, 50 or 100 pairs. A system coordinating the transmission of all p pairs numbered 1;:::;pis operating in the binder. We further assume that the systems under consideration operate in a frequency division duplexing mode (FDD), where upstream and downstream transmissions are performed at separate frequency bands, similar to VDSL. Hence near end crosstalk (NEXT) is eliminated. The received signal at pair i, 1;» i» p can be written as P x i (t) =h i;i Λ s i (t)+ l6=i h i;l Λ s l (t) +ν i (t) (13) where h i;i is the i th pair channel impulse response, h i;l are the FEXT transfer functions from pair l to pair i, ν k (t) is zero mean circularly symmetric additive white Gaussian noise with covariance matrix

9 U-BROAD DELIVERABLE D3.1 9 E (νν Λ )) = ff 2 I (typically the AWGN power is assumed to have a PSD of -140 dbm/hz in DSL applications). Translating to the frequency domain we obtain that x i (f )=h i;i (f )s i (f )+ P l6=i h i;l(f )s l (f )+ν i (f ) (14) In vector form we can represent the received signal by where H(f k )= x(f k )=H(f k )s(f k )+ν(f k ) (15) h 1;1 (f k ) h 1;p (f k )..... h p;1 (f k ) h p;p (f k ) is the channel frequency response, s(f k )=[s 1 (f k );:::;s p (f k )] are the frequency domain representations of the signals transmitted by the system. Since we assume a discrete multitone transmission we shall assume that f k correspond to the frequency bins of the specific DMT system at hand, and the signals at each frequency are typically QAM modulated signals with modulation level determined by the SNR at the receiver at the given frequency. The modulation level varies from 2-QAM up to 2 15 QAM when the signal to noise ratio is sufficiently good. When the specific frequency processed is not relevant for the discussion we shall suppress the explicit dependence on f k and use the following notation x = Hs + ν (16) A ZF linear precoder pre-multiplies s by H 1 D where D is the diagonal matrix The received signal now becomes D = h h pp (17) x = Ds + ν (18) and therefore we obtain FEXT free channel. Furthermore since H is diagonally dominated no substantial power is added since the precoder is a almost identity matrix. The achievable rate on the i 0 th channel under no coordination is now given by Z 0 1 C i = log P i (f ) jh ii (f )j 2 1+ f P A df (19) l6=i P l(f ) jh il (f )j 2 + jν i (f )j 2 where is the gap to capacity which for coded QAM with BER 10 7 is 9:8 c g + m g where c g is the coding gain and m g is the margin. For estimating capacity the gap should be 0 db ( =1). Assuming linear ZF precoding the capacity is now given by Z ψ! C P i(f ) jh ii (f )j 2 i = log 2 1+ df (20) f jν i (f )j 2 As can be seen in [41] in typical cases this leads to substantial increase in rate.

10 U-BROAD DELIVERABLE D V. ADVANCED CODING FOR SINGLE AND MULTI-CHANNEL TRANSMISSION Existing DSL technology utilizes two coding techniques: Trellis coded modulation [56], [57] at the rates of 1-10 Mbps (SHDSL and ADSL) and Reed Solomon coding for ADSL and VDSL. These codes (when concatenated together) provide about 6 db of coding gain. This means that the Shannon gap for SHDSL and ADSL is about 4 db and for VDSL is about 6 db. Closing this gap is possible using advanced turbo coding [10] or low-density parity check codes [26]. However the computational requirements are very high and a need for efficient architectures for both encoders and decoders are necessary in order to enable the incorporation of these codes. While we can predict that in next generation SHDSL current state of the art strong coding techniques might be incorporated due to the lower data rates, it is still much more complicated to use these codes at the 100 Mbps rates. To do that we would need to develop new parallel decoding algorithms that would meet the fast computational requirements. Currently LDPC codes seem more amenable to parallel implementation than using turbo decoding and therefore we focus on LDPC codes. We will now describe the basics of LDPC decoding and provide simulation results regarding the gain in utilizing these codes. In his classical 1962 paper [26] Gallager defined low density Parity Check (LDPC) codes and iterative coding. Since then those codes were rediscovered several time during the past 40 years e.g., [62],[50]. In 1995 Mackay and Neal [45] rediscovered LPC codes once again, and set forth a substantial research effort. This effort was also motivated by the discovery of the turbo principle [10]. V-A. Structure of LDPC code A LDPC code is linear block code, with a spare parity-check matrix H. Like all other iterative codes (Block Turbo codes, Expander codes, Product codes) LDPC code can also be represented by a bipartite graph. A bipartite graph is a graph in which the nodes are decomposed into two disjoin sets, such that no two nodes within the same set are connected. We can look at the graph as composed of left-side nodes and of right-side nodes, where each edge will connect a node in the left-side to a node in the right-side. For the LDPC code the left side nodes will be called variable nodes, and the right side nodes will be called the check nodes. The variable nodes represent the codeword bits, while the check nodes represent the parity check constrain of the code. Each check node represent a parity check constrain. A check node is connected by an edge to all variable node that are part of the constrain. For a linear block code with a block length n, and k information bit, the bipartite graph will have n variable nodes and m = n k check nodes. Figure 2 shows a bipartite graph of such a code. In this example the codeword isof length 13 (i.e 13 variable nodes) and eight constrains (parity check equations). A regular (d v ;d c ) LPCD code is defined by a spare parity-check matrix H which has a exactly d v 1 s in each column and d c 1 s in each row, where d v, d c are small numbers (in compared to the matrix dimensions). The bipartite graph of a regular (d v ;d c ) LDPC code will be such that it will have exactly d v edges for each variable node (i.e. the variable node degree), and d c edges for each check node. We

11 U-BROAD DELIVERABLE D define the code rate for regular LDPC code by: R m d =1 n =1 v (21) d c Figure 2 illustrate a regular (3,4) LDPC code. Figure 2. A regular (3,4) LDPC code. An irregular (d v ;d c ) LDPC code is defined by a sparse parity-check matrix H and a bipartite graph in which the degree of variable nodes and check nodes can vary. Defining by i the fraction of edges connected to a degree i variable node, and by ρ the fraction of edges connected to a degree i check node, we can define the following: ψ! X 1 i d v = (22) i i ψ! X 1 ρ i d v = (23) i and similarly (x) = ρ(x) = For irregular coded the code rate is defined by: R 1 d v d c =1 i X i X P i ρ i i i Pi i i i x i 1 (24) ρ i x i 1 (25) =1 R 1 0 ρ(x)dx R 1 0 (x)dx (26)

12 U-BROAD DELIVERABLE D V-B. Decoding algorithm There are two main decoding algorithm families for LDPC codes. Both are iterative algorithms, described by the bipartite representation of the code. Below is s a brief description of both. V-B.0.a. Bit Flipping Algorithm In the Bit flipping algorithm the check nodes are satisfied, if and only if, the sum of all adjacent variable nodes is zero. If the sum is not zero, then the check node is unsatisfied. Variable nodes flip their value if the number of unsatisfied adjacent check nodes is larger then the number of adjacent satisfied nodes. This method leads to linear time decodable asymptotically good codes, but with limited error correction capability. V-B.0.b. Message-Passing Algorithms The message passage algorithms [27] has larger complexity than the bit-flipping algorithm, but has also better error-correction capability. At each iteration, a message is being passed on each edge from the variable node to the check node, and then backs to the variable node. The message being passed from node n on edge e may take into account all the values received on edges connected to n other than edge e in the previous round. The belief-propagation algorithm is the most common between all message-passing algorithms. Some of its major advantages are: - It is a MAP decoder when the bipartite graph is cycle-free - Low decoding complexity (compared to other MAP and message-passing algorithms) - Allow parallel implementation - Allows analytical analysis of performance The belief-propagation algorithm is defined by the following: A variable node message is computed by: m l vc = ( mv l =0 m v + P c 0 2N (v) c ml 1 c 0 v l 1 Where m v is the LLR of the bit v, and N (v) is the set of adjacent check nodes of v. A check node message is computed by: tanh m l vc 2 = Y v 0 2N (c) v tanh m l v 0 c 2 N (c) is the set of adjacent check nodes of c. Bydefining a function ':» jxj '(x) = sign(x); log tanh 2 The check node message can be computed as a simple sum. (27) (28) (29) V-C. Performance of LDPC code In this section we evaluate the performance enhancement by using LDPC codes for U-Broad modem. We first have to discuss the scenario in use.

13 U-BROAD DELIVERABLE D Direction and band f 998 min f 998 max f 997 min f 997 max DS US DS US Table I. VDSL band plans. Direction and band f min f max DS US DS US DS US Table II. Symmetric extended 998 band plan. V-C.0.c. Usable frequencies and band plans In order to increase the overall capacity the U-Broad modem must use a wider bandwidth then any other DSL modem. The current state of the art VDSL standard [1] uses frequencies up to 12MHz, using 4 bands in and frequency division duplexing (FDD). There are two main band plans for VDSL. The first is knows as plan 998 and the second as plan 997 (Annex A and Annex B respectively of [1]. The band plan can be found in table V-C.0.c: We assume that the U-Broad modem will use frequencies up to 30 MHz, using 6 bands where the first four bands are overlapping the current VDSL band plan. V-C.0.d. Coding gain The current state of the art VDSL modems use Reed-Salomon code with either QAM or DMT as their modulation technique. The gap from the channel capacity for that modulation scheme is 9.8db and the RS coding gain is 3.8db. This lead to a 6db gap from the channel capacity.. In theory LDPC code can achieve a rate that is very close to the channel capacity. As we have to take into account also practical implementation issues, we can assume that using LDPC code we can have coding gain of about 7-8db. V-C.0.e. Simulation results In the first scenario we use the band plan of table II that targets symmetrical rates at a loop length of 300m. The noise included 4 self-fext disturbers and AWGN with PSD of 140dBm=Hz. The margin was 3 db and a maximum spectral efficiency of 15 bps/hz. Cable was 26 AWG (0.4 mm) and the transmit PSD level was -60 dbm/hz for all bands. An overhead of 10% was also assumed. We can clearly see that the achievable rate with a 7db gain LDPC is about 16Mbit/sec better than with RS (i.e. 23% rate improvement). When using a stronger code, with 8db coding gain, the difference for a 300m line is about 22Mbit/sec which is almost 27% increase in capacity. This shows the high potential of LDPC codes, and that using a strong LDPC code one can expect to get very close to 100Mbit/sec symmetrical DSL even in a scenario with cross-talks.

14 U-BROAD DELIVERABLE D Shannon Rate Reach plot 4 FEXTs DS 8 db Coding Gain US 8 db Coding Gain DS 7 db Coding Gain US 7 db Coding Gain DS RS US RS 100 Payload Rate [Mbps] Reach [Km] Figure 3. Performance with and without advanced coding for symmetric band plan. Direction and band f min f max DS US DS US DS US Table III. Asymmetric extended 998 band plan. We now consider a second band plan depicted in table III Using the same noise and assumptions as before we otain the results of figure 4. For 300m line using 7db coding gain we can achieve upstream and downstream rates of 102 and 70 Mbps respectively compared to 80 and 58 Mbps for the same bands with VDSL1 and Reed Solomon coding. For 500m line using 7db coding gain we can achieve rates of 90Mbps for downstream and 50 Mbps for downstream compared to rates 70, 40 Mbps respectively with Reed Solomon coding. VI. COORDINATED TRANSMISSION Dynamic spectral allocation is a very active research field. Spectral coordination is instrumental in improving overall network capacity. During recent years many contributions and papers devoted to uncoordinated transmission have appeared e.g., [17], [18], [39]. It has been also shown that simple algorithm imposed on modems can enhance the overall network performance [17], [39], [60], [32]. Very appealing interpretations of these uncoordinated strategies in terms of Nash equilibrium in non-

15 U-BROAD DELIVERABLE D Shannon Rate Reach plot 4 FEXTs DS 7 db Coding Gain US 7 db Coding Gain DS RS US RS 110 Payload Rate [Mbps] Reach [Km] Figure 4. Performance with and without advanced coding for asymmetric band plan. cooperative games have been demonstrated as well as the existence of such Nash equilibrium [16], [40]. It has been also demonstrated that even very simplified strategies that use pre-coordination outperforms the non-cooperative approaches to dynamic spectral allocation [39]. Extending these results into the cooperative framework will enable much better methodology for spectrum allocation, that will be improve the performance of both future and legacy systems. Game theoretic insights regarding the formation of coalitions in cooperative games can lead to better allocation of the available spectrum using several levels of coordination: 1. Non-coordinated transmission using fixed bandwidth. This is basically the common usage of spectrum in existing technology. 2. Pre coordinated spectral allocation. This is basically allocation by agreement a-priory to use certain strategies for using the spectrum. 3. Partially cooperative Real-time coordination through network management 4. Fully coordinated allocation. Each modem provides full data regarding its transmission and interference from other channels to a central entity that coordinates the spectral allocation. One typical example of the need for spectral coordination is demonstrated in figure 5. We can see that remotely deployed equipment generates interference into a legacy ADSL equipment. To ensure network integrity we must ensure that the remotely deployed equipment will not interfere with CO based legacy transmission. In this part of the work we will extend our previous approach to cope with partial and full coordination spectral allocation.

16 U-BROAD DELIVERABLE D Figure 5. Near far problem in multipair transmission with remote terminals VI-A. Dynamic spectrum allocation algorithm In this section we propose an a-priori coordinated rule for dynamic allocation of spectrum. We can show that the proposed dynamic co-ordination through co-operation yields enhanced results compared to unsupervised competitive power allocation. We also provide some insight to this result using combination of physical and game theoretic interpretation of the proposed scheme. The proposed spectral allocation algorithm consists of three steps: 1. Spectrum is used from the highest available frequency. 2. Spectral efficiency is optimized for the given rate (i.e., a narrower bandwidth with more efficient modulation is used). For that purpose either channel capacity with a gap or the well known Saltz s formula for DFE performance can be used. 3. Power back-off is performed if excess margin exists. Since this adjustment is minor, provided that first two steps have been performed we propose flat power back-off. The implementation details of the above algorithm for QAM VDSL modem are described in table VI-A. Similar implementation is possible for DMT modulation. The idea underlying the approach above is that CO based deployment typically uses the lower part of the spectrum, and therefore use of this part of the spectrum should be minimized in remote deployments. One extreme realization of this is the use of dynamic FDM between CO and RT. In this case the RT begins above a frequency determined either by the modem or by instruction of the network management / DSM center. In the following sections we demonstrate the rate region for the above algorithm in several typical cases. We also compare to previous DSM results using iterative water-filling.

17 U-BROAD DELIVERABLE D R =preassigned target rate for VDSL. 2. f min = minimal f such that the VDSL can achieve rate R using frequencies above f min. 3. Setup carrier frequencies f c1 ;f c2, symbol rates R symb1 ;R symb2 and constellation sizes 2 D1 ; 2 D 2 for the two DS bands, such that f min» f C1 R symb1 is maximal R = D 1 R symb1 + D 2 R symb2 and this transmission profile provides sufficient margin for operation. 4. Use the above transmission profile for steady state operation. Table IV. DFDM implementation for QAM based VDSL VI-B. Simulation results: Dynamic FDM for RT-VDSL and CO-ADSL In this section we analyze the rate region for RT based VDSL together with CO based ADSL. We compare the results of our proposed rule to the uncoordinated allocation through iterative water-filling (IW). We show that the rate region achieved is superior to that of the uncoordinated case relying on the game theoretic Nash equilibrium. We also compare the rate region to the rate region of remotely deployed ADSL using the same scheme as well as iterative water filling. We show that VDSL from the RT can co-exist with ADSL from CO even for very high downstream rates. This puts VDSL as the better choice for remote deployment, being more friendly to ADSL. The setup where we have VDSL lines originating from the RT fed by fiber, and ADSL lines originating from the CO sharing the same binder as the VDSL lines is depicted in figure 5. As we will show using a friendly mask does not cause any degredation to the ADSL from the CO without compromising the VDSL DS performance. All simulations used 26 AWG line. The first simulation presents the results when the RT was located at 3 kft from the CPE and the CO was located at 9, 10, 12, 14 and 16 kft. For each of these cases we have compared the rate region achieved by VDSL performing DS power back-off of the frequency band khz to a level of -110 dbm/hz, where is any frequency between 138 khz and 1.1 MHz. The results are presented in figure 6. We now compare these results to the results of iterative water-filling for unsupervised DSM [19] and presented in figure 8. We can see that the rate region for the iterative waterfilling algorithm is substantially less than that for the Dynamic FDM algorithm (DFDM). There are two main reasons: First reason is that [4] uses uncoded systems. This amounts to 4 db for VDSL and 5 db for ADSL. However there is also a second reason: The VDSL tends to put some of its energy in the ADSL DS band and therefore limits the ADSL performance more substantially than when it is forced out of this band. For better comparison with [6] we also provide the results for an uncoded system. Indeed we see that the maximal ADSL capacity is now reduced to 7.6 Mbps which is slightly more than with the IW, however the VDSL rates are also slightly higher for any given ADSL rate. To better understand the superiority of the pre-coordinated DFDM algorithm we now check the crosstalk environment for the 9 kft case. Figure 5 presents the signal and noise as received by the CPE of both ADSL and VDSL systems, as well as signal to noise ratio. We can see that the VDSL modem observes a very high SNR in the region below 1.1 MHz. Moreover no matter how much power the ADSL receiver will allocate in this band, it will not be able to keep the VDSL modem out of any part of this band. Therefore the FDM solution is not a stable Nash equilibrium point even though it is better for both players. This is much like the prisoners dilemma in game theory where the only stable equilibrium

18 U-BROAD DELIVERABLE D Figure 6. Rate region for 4 VDSL from RT and 4 ADSL from CO using the DFDM algorithm. Gap of VDSL is 12 db and of ADSL is 11 db. L=9 kft, L1=3 kft. is bad for both players. Hence the iterative water-filling algorithm which converges (if it converge) to the Nash equilibrium is highly suboptimal in this case. It clearly suggest that dynamic FDM, where the multiplexing point is chosen dynamically according to the DFDM algorithm is preferable. VI-C. Conclusions regarding spectral coordination In this section we have provided some initial analysis regarding partial coordination of lines. We have demonstrated that in some case partial coordination even with suboptimal algorithm yields superior results to the best competitive approach. This situation is similar to the prisoners dilemma where competitors will typically end in worst situation since they are unable to cooperate. VII. INTERFERENCE CANCELLATION AND PRECODING IN MULTICHANNEL DSL We investigate hereunder the different methods proposed in the literature. Usually, the authors provide algorithms for both the upstream and the downstream. All the methods rely on an estimate of the channel matrix. This issue is quickly discussed in the last section. VII-A. Vectored-DMT This method has been proposed by Ginis [25]. It is based on a QR decomposition of the channel matrix. It contains a decision-feedback section when used at the receiver and a Tomlinson-Harashima precoder when used at the transmitter. It achieves perfect crosstalk cancellation (assuming correct previous decisions). In upstream (receiver), it can be shown to be equivalent to the GDFE (generalized decision-feedback

19 U-BROAD DELIVERABLE D Figure 7. Rate region for 4 uncoded VDSL from RT and 4 uncoded ADSL from CO using the DFDM algorithm. Gap of VDSL is 16 db and of ADSL is 16 db. L=9 kft, L1=3 kft. equalizer). It is important to mention that, in order to keep consistency throughout this document, the notations used in this section are different from the ones used in the papers by Ginis. VII-A.0.f. Upstream transmission index is dropped for convenience) The channel matrix is decomposed as (subscript k denoting the tone H = Q R (30) where Q is a unitary matrix, and R is a lower triangular matrix. There is no coordination at the transmission so the symbols of the different users are not precoded: x = u. At the reception, the linear operation Q H is first applied (to invert the Q part of matrix H). The following vector is obtained z = Q H y = Ru + Q H n: (31) The noise is still white since Q is unitary. Now, since R is lower triangular, the transmitted symbols u may be recovered from z by a DF structure. First, u 1 is recovered from z 1, then its influence is removed from z 2 and u 2 can be computed, and so on. This set of operations may be written as ^u = R 1 d z (I R 1R)~u (32) where ^u is the estimation of the transmitted symbols, R d is the diagonal matrix with the diagonal of R, I is the identity matrix and ~u is the vector of decisions. The SNR for user i is given by d SNR i = ff2 u i j(r d ) i j 2 ff 2 n (33)

20 U-BROAD DELIVERABLE D Figure 8. Rate region for CO based ADSL and RT based VDSL, with unsupervised iterative water-filling (from [6]). L=9kft, L1=3kft. where ffu 2 i is the variance of the transmitted symbols of user i and ffn 2 is the noise variance (assumed the same on all the lines). To demonstrate the large gains in full crosstalk cancellation in upstream we have considered the following scenario. An ETSI loop (0.5 mm) is used for transmission. 13 VDSL modems are trnasmitting simultaneously so that without FEXT cancellation we have 12 self interferers. Also noise E disturbance is present. VDSL PSD was assumed to follow the 998 band plan with cabinet PSD M1 of -60 dbm/hz. Guard bands were assumed to be 175 khz following the ETSI VDSL1 standard, the maximal spectral efficiency we set to 15 bps/hz which is the limiting factor over very short loops. Two types of codes were tested: RS with 3.8 db coding gain. In this case also a conservative design with 6 db margin has been used. In the second scenario we assumed LDPC with coding gain of 7 db and lower margin of 4 db. and. The data rates as function of loop length are presented in figure 10. We present two types of cancellation: Only self FEXT cancellation where we assume that only interference from VDSL systems is cancelled and full cancellation where all interference is cancelled and the Gaussian noise is the limiting factor. In this case we only present the result for 3 db margin and 7 db coding gain. VII-A.0.g. Downstream transmission In downstream, there is coordination at the transmission, so a precoding among the users is possible. This time, the QR decomposition is applied on the transpose of the downstream channel H T = Q R; (34)

21 U-BROAD DELIVERABLE D Figure 9. Signals and noise at receivers. and R is an upper diagonal matrix. The precoding operations are divided in two parts. First, we have u 0 = R T R d u (35) and then, the samples are rotated by applying Q Λ before sending to the lines x = Q Λ u 0 (36) where superscript Λ denotes complex conjugation. With this precoder, it comes y = R d u + n (37) so that crosstalk-free transmission is achieved. However the first part of the precoder, given by (35), may create an energy increase, which is undesired at the transmission. The second part does not bring such a problem since Q is unitary. To solve that issue, Ginis proposed to use the concept of Tomlinson- Harashima precoding. The idea is to perform a modulo operation after (35) to avoid the energy increase. The modulo operation is however dependent on the symbol constellation used by each user. Thus, in order to ensure that the signal is recovered properly, the operation has to be performed with a feedback structure represented in figure 11. We denote by r ij the element (i; j) of matrix R. Writing (35) as r 11 0 ::: 0 r 12 r r 1L r 2L ::: r LL u 0 1 u 0 2. u 0 L = r 11 u 1 r 22 u ; (38) r LL u L

22 U-BROAD DELIVERABLE D US Rate, ETSI Noise E, 0/12 FEXTs RS 12 FEXTs RS 0 FEXTs LDPC 12 FEXTs LDPC 0 FEXTs Full XT Cancellation, LDPC Rate [Mbps] Reach [Km] Figure 10. Upstream VDSL data rate. and adding the modulo operation, the first precoding operation can be written as 2 3 i 1 X u 0 i = M i 4 r ji ui u 5 0 j ; i =1; 2;:::;L (39) r ii j=1 where Mi denotes the modulo operation for the constellation size M i of user i. At the receivers, the symbols are recovered with ^u i = Mi [y i =r ii ]: (40) Using the linearity of the modulo operation, it is easy to show that it satisfies ^u i = Mi [u i + n i =r ii ] (41) which may be approximated by ^u = ur 1 d n: (42) The detection SNR for user i is SNR jr iij 2 ffu 2 i = i : (43) ffn 2 Note that the precoder, even with the modulo operation, still creates a slight energy increase. To show the gain in downstream FEXT precoding we have used the same set up as for upstream transmission. The downstream data rates achieved in this scenario are presented in figure 12. In this case we also present the signal and the noise PSD at the receiver (figure 13) VII-A.0.h. Additional comments Thanks to the diagonal dominance of the channel matrix, the QR decomposition always results in a Q matrix which is close to unity. As a consequence, the diagonal elements of R are close to the ones of H. Since the resulting transmission is given by (37), it appears that the proposed scheme almost performs as a perfect crosstalk removal. Another consequence is that the ordering of the user in the triangular matrix R is not so important.

23 U-BROAD DELIVERABLE D Figure 11. Precoder block. Copied from [25] DS Rate, ETSI Noise E, 0/12 FEXTs RS 12 FEXTs RS 0 FEXTs LDPC 12 FEXTs LDPC 0 FEXTs Full XT Cancellation, LDPC 70 Rate [Mbps] Reach [Km] Figure 12. Downstream VDSL data rate. 60 Signal and Noise RX PSD in DS1 at 300m PSD [dbm/hz] Freq [MHz Figure 13. PSD of signals and noise at the receiver.

24 U-BROAD DELIVERABLE D Usually,only a few crosstalk sources are dominant. Hence the channel matrix H and this can be used to reduce the complexity of the QR decomposition. The authors also investigate the influence of imperfect channel estimation. They show that an issue may arise when some of the diagonal elements are low (that is when one channel is poor). They conclude that it is better not to allocate power to those channels. Finally, the authors show how to allocate the energy to the different users and frequency so as to maximize the total bit rate. VII-B. Zero-forcing cancellation This method has been proposed by Cendrillon [14], [15]. In the framework of the UBROAD project some simplified versions are currently being studied. It is based on a simple linear zero-forcing operation. So it also ensures crosstalk-free transmission. This method is simpler because it does not require a feedback structure, or modulo operations. The authors show that, thanks to the diagonal dominance of the channel, the performance of zero-forcing cancellation approaches the optimal performance very closely (and thus is also very close to the previous method). VII-B.0.i. Upstream transmission For the upstream case, the receiver simply performs ^u = H 1 y: (44) This completely removes the crosstalk interference. Now the authors use the SVD of the channel matrix H = UΛV (45) where U and V are unitary matrices and where Λ is the diagonal matrix of singular values. Thanks to the CWDD property of H, the columns are almost diagonal, and thus V ß I. It results that matched filtering (H H = Λ H U H ) is equal to the inversion operation with except to some scaling factor for each user separately. Hence, the ZF operation causes almost no noise enhancement and achieves almost optimal performance. The authors provide a lower bound on the achieved data-rate. VII-B.0.j. Downstream transmission In downstream, the precoder attempts to diagonalize the channel: x = fih 1 H d u (46) where H d is the diagonal matrix extracted from H. The factor fi is added to ensure that there is no power increase at the transmitter on any line. Even with this constraint, the author show that, thanks to the RWDD property, fi ß 1 so that the individual channels of the users are not significantly affected. At the receiver, it comes y = fih d u + n: (47) The crosstalk is perfectly removed and the receivers do not need to be modified. The SNR of user i is SNR i = fi2 jh ii j 2 ff 2 u i ff 2 n (48)

25 U-BROAD DELIVERABLE D Zero forcing No cancellation First order Second order Third order 120 Data rate (Mbps) Line length (m) Figure 14. Data rates with different crosstalk precompensation techniques. Further simplifications of the zero forcing precoder that takes into account the special structure of copper line channels is done in the framework of the project. Figure 14 compares the optimal and some novel reduced complexity precoders using lines measured by FTRD [54]. VII-C. Additional developments In order to reduce complexity, a simplified scheme is proposed. It takes into account the fact that there are generally only a few dominant crosstalk source for each pair. It is thus not necessary to cancel the crosstalk coming from all the lines in the binder. It is sufficient to consider a matrix of reduced size, corresponding to the dominant crosstalk sources only. The matrix to invert is significantly reduced. In [13], algorithms are provided to select the lines to cancel for a given user. A further simplification is also possible by selecting a limited number of tones in which the crosstalk cancellation is performed. As argued in [13], low frequencies have a lower crosstalk amplitude, and high frequencies support only small bit-loading, even without crosstalk. So the gain of using crosstalk cancellation is reduced at those frequencies. Finally, an algorithm is presented to select jointly the tones and the lines where crosstalk cancellation is the most beneficial. The results obtained by these reduced complexity versions are given in figure 15. The simplified scheme (line and tone selection) has been presented for upstream only, that is for crosstalk cancellation. In downstream, since the precoding applied on each line affects many other lines through the matrix H, it is not clear whether the same simplification is also possible. VII-D. Linear equalization The use of linear equalizer has been proposed by Honig [29] for the suppression of crosstalk. In that paper, both FEXT and NEXT are considered, and both receiver and transmitters optimizations are analyzed. Depending on the configuration of interest, the general expressions in [29] can be particularized to the