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Evaluation of receiver performance over VDSL noisy links Cherif, Mohamed Khaled 2000

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EVALUATION OF RECEIVER PERFORMANCE OVER VDSL NOISY LINKS by M O H A M E D K H A L E D C H E R I F Engineering Diploma, Ecole Polytechnique de Tunisie, 1997 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING We accept this thesis as conforming to the required standard T H E UNIVERSITY O F BRITISH C O L U M B I A April 2000 © Mohamed Khaled CHERIF, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. 1 further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of B(_ £C T £ \ cA-j 1 f j K K P ^ ^ ^ ^ The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract V D S L environment is hostile because of the severe propagation loss due to the difficulty to propagate a high frequency signal over unshielded twisted pairs. Important noise effects ranging from crosstalk to other environment-related additive noises such as Radio Frequency Interference and impulse noise can also be a serious harm. Several algorithms have been developed to mitigate the joint effect of channel distortion resulting in intersymbol interference, and additive noise. These algorithms try to recover the transmitted data sequence with a small number of errors suitable for data transmission. Converging these algorithms for V D S L channels is not feasible in many cases, especially when the start-up process has to be done blindly, without the help of a training sequence. Generally, in blind mode the equalizers need a special setup in order to (adaptively) compensate for the channel amplitude and phase distortions. As a consequence of the nature of the V D S L environment, the L M S algorithm was shown not to converge and the number of errors at the slicer output is very high after switching to the Decision-Directed (DD) mode. Among the attractive algorithms for V D S L applications there are the Reduced Constella-tion Algorithm (RCA) and the Constant Modulus Algorithm (CMA). Both have been tested for bandwidth-efficient CAP-modulated V D S L links in this thesis. A similar and improved algorithm is the Multi-Modulus Algorithm ( M M A ) [1], which is found to be more suitable for severe channels. A dual-algorithm receiver has been tested afterwards, it combines the M M A algorithm to initially converge the receiver and then it switches the L M S in the Decision Directed mode, to get a fine convergence. The maximum achievable V D S L data rates were reported for this receiver for V D S L ANSI standard test loops. ii Table of Contents Abstract i i List of Tables vii List of Figures viii Acknowledgment xi i Chapter 1 Introduction 1 1.1 Thesis objectives and organization 2 Chapter 2 D S L Technologies and Line Codes 4 2.1 DSL Technologies and applications 4 2.1.1 DSL Loops 6 2.1.2 ISDN - 7 2.1.3 HDSL 8 2.1.4 ADSL. . . . 9 2.1.5 Other ADSLs 10 2.1.6 V D S L : • 11 2.2 V D S L line Codes: DMT and Q A M / C A P 12 2.2.1 The D M T 13 2.2.2 Q A M / C A P Modulation 16 2.2.3 Comparison between DMT, Q A M and CAP 23 2.3 C A P - V D S L 23 Chapter 3 Channel and Noise Modeling 24 3.1 V D S L test loops , 24 3.2 PSD masks 27 iii iv 3.3 Noise sources 29 3.3.1 W G N 29 3.3.2 Impulse Noise 30 3.3.3 Radio Frequency Interference (RFI) 30 3.3.4 Crosstalk '. 30 3.3.5 N E X T 31 3.3.6 FEXT 33 3.3.7 Self-FEXT .35 3.3.7.1 Cyclostationary FEXT 35 3.3.7.1 Stationary FEXT 37 3.3.8 A D S L crosstalk 39 3.3.9 ISDN and HDSL crosstalk..........:. 40 3.4 Simulation Model : • 41 3.5 Channel capacity and Receiver Input SNR.^ 43 3.5.1 A W G N environment 43 3.5.2 Self-crosstalk environment 44 3.5.2.1 Case of a single interferer (Cyclostationary FEXT) 44 3.5.2.1 Case of multiple interferers (Stationary FEXT) 46 Chapter 4 Linear and D F E Equalization of V D S L Communication Links 49 4.1 DFE filtering :. 50 4.2 Conventional DFE 51 4.3 Linear Filtering 53 4.3.1 Fractionally Spaced Equalization 56 V 4.4 The Mean Square Error (MSE) algorithms 56 4.4.1 The L M S algorithm 57 4.4.2 The Four-CAP trained L M S 58 4.5 Blind Equalization 61 4.5.1 The Reduced Constellation Algorithm (RCA) 62 4.5.1.2 Short Loops 62 4.5.1.2 Medium Loops 65 4.5.1.2 Long Loops 67 4.5.2 The Constant Modulus Algorithm (CMA) 68 4.5.3 The Multi Modulus Algorithm (MMA) 71 4.5.3.2 Short Loops 73 4.5.3.2 Medium Loops : 74 4.5.3.2 Long Loops 76 4.6 The Combined M M A - L M S Algorithm 78 4.6.1 Short Loops 78 4.6.2 ' Medium Loops 79 4.6.3 Long Loops 80 Chapter 5 Conclusions and Suggestions for Future Work 82 5.1 Conclusions 82 5.2 Suggestions for Future Research 83 Glossary 84 Bibliography 87 Appendix A . Transmission parameters 91 Appendix B . R L C G Parameters 95 B . l R, L , C, G parameters of twisted pair cables 95 Appendix C. V D S L Loops 97 Appendix D. D F E Transceiver Structures and Performance 98 D. 1 Optimum DFE performance 98 List of Tables Table 2.1 various DSL reach profiles versus data bit rate [5], [6], [18] 5 Table 2.2 Reach versus bit rate (in a noise-free environment) for an upstream bit rate equal t o T l [38] 12 Table 2.3 CAP spectral efficiency for = 20% 22 Table 3.1 cyclostationary FEXT for V D S L loops 37 Table 3.2 Stationary FEXT power for V D S L loops 37 Table 3.3 V D S L capacity in a W G N environment 44 Table 3.4 V D S L capacity in a cyclostationary environment 46 Table 3.5 V D S L capacity in a 24-disturber environment 47 Table 4.1 SNR Requirement in the Presence of Gaussian Noise for Pe = 10"' 56 Table 4.2 Performance of R C A at the steady state over Short Loops 65 Table 4.3 Performance of R C A at the steady state over Medium Loops 67 Table 4.4 Performance of C M A at the steady state over Short Loops 71 Table 4.5 Performance of M M A at the steady state over Short Loops (h = 10"5) 74 Table 4.6 Performance of M M A at the steady state over Medium Loops (n = 10"5) 75 Table 4.7 Summary of M M A performance 78 Table 4.8 Summary of M M A - L M S convergence over V D S L loops 81 Table A. 1 Standard asymmetric bit rates 91 Table A.2 Standard asymmetric band allocation for downstream transmission 91 Vll List of Figures Figure 2.1 Data and Voice Distribution in DSL Loops 5 Figure 2.2 Schematic of a DMT transmitter 14 Figure 2.3 D M T Receiver 15 Figure 2.4 Structure of a Q A M transmitter 17 Figure 2.5 . Structure of a matched Q A M receiver for a distortionsless channel and a square root raised cosine transmitter shaping filter 18 Figure 2.6 CAP transmitter 19 Figure 2.7 Power Spectrum density of the CAP signal for different rolloff factors (0.2, 0.5, and 1) 20 Figure 2.8 CAP spectrum for different transmitter tap spans (a = 0.2) 20 Figure 2.9 Structure of a CAP linear receiver 21 Figure 3.1 VDSL0 insertion loss (left) and impulse response (right) 25 Figure 3.2 Insertion loss of VDSL1 (xTPl) to the left and Loop Impulse Responses to the right 26 Figure 3.3 Insertion Losses and Impulse Responses of VDSL2 26 Figure 3.4 Insertion Losses and Impulse Responses of VDSL3 27 Figure 3.5 Insertion Losses and Impulse Responses of VDSL4 27 Figure 3.6 Insertion Loss (left) and Impulse Response of VDSL5 (right) 28 Figure 3.7 Insertion Loss (left) and Impulse Response (right) of VDSL6 28 Figure 3.8 Insertion Loss (left) and Impulse Response (right) of VDSL7 29 Figure 3.9 Self-NEXT and self-FEXT interference 32 Figure 3.10 Stationary N E X T for symmetric long-range V D S L 32 Figure 3.11 N E X T and FEXT coupling through twisted pairs 33 viii Figure 3.12 Block diagram for crosstalk simulation 34 Figure 3.13 Cyclostationary Self-FEXT Loss (single disturber) over V D S L Loops 36 Figure 3.14 Stationary Self-FEXT Loss (24 disturbers) over V D S L Loops 38 Figure 3.15 A D S L (downstream) Power Mask : 39 Figure 3.16 A D S L Fext (24 disturbers case) into V D S L short loops 40 Figure 3.17 A D S L - N E X T noise 40 Figure 3.18 ISDN (top) and HDSL (bottom) crosstalk PSDs (PSD disturber only) 42 Figure 3.19 V D S L Communication Model 42 Figure 3.20 Contours of equal SNR for the cyclostationary F E X T environment - case of an equal disturber and disturbed loop 45 Figure 3.21 Capacity of V D S L test Loops 48 Figure 4.1 Signal space constellations of demodulated CAP signals 50 Figure 4.2 Structure of the NPDFE receiver 51 Figure 4.3 Structure of a conventional DFE receiver 52 Figure 4.4 Wrong DFE convergence for VDSL1 S 53 Figure 4.5 2D FIR Filtering using a 4-tap filter 54 Figure 4.6 ZFE for VDSL1 (left) and VDSL4, 5, and 6 (right) 55 Figure 4.7 Non-convergent and diagonal L M S solutions 58 Figure 4.8 Wrong L M S convergence 59 Figure 4.9 Signal constellations of a 16-CAP system tested over VDSL1 S using the L M S with a 3000-long 4-CAP training sequence - plots are made after 8,000, 15,000, and 250,000 iterations in the DD mode (^i= 10"4) 59 Figure 4.10 Eye diagrams of VDSL1 S equalized using the L M S filter after 8,000, 15,000 and 250,000 iterations (about 5 msec of setup time) 60 Figure 4.11 The inphase transfer function and inphase filter output for the L M S receiver 60 ix Figure 4.9 Eye diagrams for the R C A applied to VDSL1 Short after 30,000 (left), 50,000 (middle) and 500,000 (right) iterations 63 Figure 4.10 Signal Constellations for the R C A applied to VDSL1 Short after 30,000 (left), 50,000 (middle) and 500,000 (right) iterations' 64 Figure 4.11 R C A Learning Curves for Short Loops 64 Figure 4.12 Steady state signal constellations for R C A applied to short loops VDSL1 S, VDSL2 S, VDSL3 S, VDSL4 S, and VDSL5) 65 Figure 4.13 R C A Learning Curves for Medium Loops (n = icf 4) 66 Figure 4.14 Steady state signal constellations for R C A applied to medium loops (top left to the right: VDSL1 M , VDSL2 M , and VDSL3 M , bottom left to the right: VDSL4 M , and VDSL6) , 66 Figure 4.15 R C A Learning Curves for Medium Loops (n = l(T3) 67 Figure 4.16 Signal Constellations after 500,000 iterations for: a) V D S L 1 M , b) V D S L 2 M , c) V D S L 3 M , d) VDSL6 : 68 Figure 4.17 R C A Learning Curves of Long Loops: (left) and (right) 69 Figure 4.18 C M A Learning Curves for Short Loops 70 Figure 4.19 C M A Signal Constellations for short loops after a setup time of 1 second 71 Figure 4.20 C M A Signal Constellations for medium loops after a setup time of 5 mseconds .72 Figure 4.21 C M A Learning Curves for medium (left) and long Loops (right) 72 Figure 4.23 M M A Learning Curves for Short Loops 73 Figure 4.24 M M A Signal Constellations for short loops after 5 mseconds of setup time 74 Figure 4.25 M M A Learning Curves for Medium Loops 75 Figure 4.26 M M A Signal Constellations for Medium loops after 1 second of setup time 76 Figure 4.27 8-CAP signal constellations for VDSL1 S (middle) and VDSL4 S (right) 77 Figure 4.28 VDSL4 L at 25.92 Mb/s (left) and 12.96 Mb/s (middle and right) 78 Figure 4.29 Performance of the M M A - L M S algorithm for VDSL1 S, VDSL4 S and VDSL579 Figure 4.30 Performance of M M A - L M S for medium loops (top: VDSL1 M , VDSL2 M , bottom: VDSL3 M , VDSL4 M) 79 Figure 4.31 Performance of M M A - L M S for long loops after 1 second of setup time 80 Figure A . l Raised Cosine Pulse (left) and Square Root Raised Cosine Pulse (right) impulses.. 92 Figure A.2 Theoretical spectrum of Square root raised cosine with a roll-off factor of 0.2 ....92 Figure A.3 In-phase (left) and quadrature (right) filter impulse response over [-4T,4T] 93 Figure B . l Series Resistances and Inductances of TP1 (1), TP2 (2), TP3 (3) and FP (fp) twisted pairs 95 Figure B.2 Shunt Conductances and Propagation Losses for TP1, TP2, TP3 and FP copper lines 96 xi Acknowledgment I would like to thank my supervisor Dr. Samir Kallel for his fruitful discussions and friendly assistance during this thesis work, and for his financial support. I'm also very grateful to Mr. Gang Huang for all his advice, availability and enlightening help. Many thanks also to all the people involved in the V D S L standard development with whom I had discussions, for their patience and help. xii Chapter 1 Introduction Multimedia and interactive applications are creating an increase in demand for high-speed broadband services, both for the residential and business users. Examples of residential applica-tions are video on demand, tele-education, internet and database access. Examples of business oriented applications are video conferencing, intranet access (telecommuting) and L A N to L A N interworking. Typically, in all these applications, the bottleneck in the provision of high-speed data services to loop plants are the access networks. They present the major handicap from providing much demanded higher throughput services. To allow Broadband to the Home and enable high-volume data rates to reach the end user (residential or corporate), hybrid network solutions (FTTx) are being investigated before the ultimate Fiber To The Home (FTTH), allowing a data rate of 155.52 Mb/s or higher. These networks use xDSL modems to tackle the problem of delivering to the end user sustainable high volume rates over the available copper telephone wires. Making use of the current Unshielded Twisted Pairs (UTP) infrastructure is a cost-driven choice as the number of these loops rises today up to about 700 millions worldwide [25] and the upgrade of the current wiring to fiber would take up to 40 years according to certain forecast studies [18]. In a hybrid fiber/twisted-pair FTTx architecture, xDSL loops consist of UTP wires pulled out of the Optical Network Unit (ONU) in the last mile. Such an architecture expands the loop capacity as the signal propagates through a shorter copper medium and therefore it undergoes less attenuation, and makes a broader bandwidth usage possible (i.e. up to 30 M H z for certain propos-als of long-range VDSL). High data rates cannot be achieved without the use of complex receiver structures capable of adaptively adjusting to the severe line conditions at high frequencies and mitigating noises. 1 Chapter 1 Introduction 2 Noise sources of concern include crossatlk from other wire pairs (in the same binder) and surrounding radio frequency emitters. In addition, xDSL receivers suffer from the effects of both impulsive and background noises, but these are of a lesser damage. xDSL transceivers generally operate by adaptively equalizing the line to compensate for selective loss and group delay. They also perform echo cancellation to separate the overlapping signal frequency bands for the two directions of transmission, typically for multicarrier transmitters where frequency overlapping is meant to optimize the usage of bandwidth. Different linear and DFE (Decision Feedback Equalizer) receiver structures are being considered by the V D S L standardization bodies. These structures are dependent on the transmis-sion scheme used (single or multi carrier). We will present in the following chapters our results for. the C A P transmitter. A class of interesting receivers for us use efficient blind equalization algorithms before eventually switching to the optimum L M S algorithm to fine tune the data estimation process. Simulation results are presented for typical V D S L links. An interesting result would be to know how well our receivers work for each one of the T I E 1.4 transmission loops, which are the benchmarks towards which any V D S L receiver should be tested. 1.1 Thesis objectives and organization The objective of this thesis is to study different equalization algorithms for different receiver structures in the case of CAP-modulated V D S L communication links. The methods considered here are the L M S and the blind algorithms (RCA, C M A , M M A ) . We investigate the performance of the different techniques under various test loops and noise conditions, and decide on the best ways to mitigate them. The noise conditions that are studied here are the W G N and self-crosstalk. Chapter 1 Introduction 3 More precisely, the objectives of this work are as follows: 1) to present a solid simulation work which assists in the planning and deployment of V D S L service by looking at the best achievable rates over V D S L test loops, 2) to determine the best suited equalizer structure for V D S L loops with short, medium and long loop ranges for various impairment schemes, 3) to compute the performance of linear receivers using blind algorithms for V D S L chan-nel equalization, We should note that our work is done according to ANSI specifications for test loops, noise test conditions and the proposed data rates. The rest of this thesis is organized as follows. In Chapter 2, a background information on various DSL technologies and line codes is provided. In Chapter 3, we derive the channel and noise models relevant to our discussion from the transmission line theory and statistical noise models. In Chapter 4, we investigate DFE and linear equalization methods for V D S L receivers, namely we discuss the L M S , R C A , C M A and M M A adaptive equalization algorithms for the purpose of mitigating the severe ISI incurred by subscriber loops and noise effect along with the DFE structures using LMS-based conventional and noise predictive techniques. The conclusion and future works that we propose are presented in Chapter 5. Chapter 2 DSL Technologies and Line Codes 2.1 DSL Technologies and applications xDSL is an emerging wireline access architecture designed to support megabit-rate traffic transmission over Plain Old Telephone Service (POTS) lines (Figure 2.1). It uses adaptive digital filtering techniques and sometimes trellis coding to increase channel capacity in the presence of Gaussian noise, and forward error correction to provide immunity against impulse noise [1]. This section reviews the main broadband DSL techniques both for the business and residential catego-ries. We notice that business applications are usually symmetric while residential applications are asymmetric. For residential users, bandwidth asymmetry is due to the unbalance in traffic streams: typically very short messages flow in the upstream direction (i.e. submission of text queries) and heavy data in the downstream (i.e. multimedia files downloads). For a historical summary on DSL systems and compatibility, refer to [7], [25]. For an overview of some xDSL early trials and for network models refer to [6], [18]. Higher D S L data rates were able to be achieved because of better pulse shaping and multilevel encoding schemes (regrouped in the bandwidth efficiency coefficient shown in Table 2.1). The limiting factor to getting even higher rates is the severe propagation loss and the crosstalk effect between adjacent wires. We distinguish between two crosstalk types: Near End Crosstalk (NEXT) and Far End Crosstalk (FEXT). Symmetrical high data rate D S L systems suffer from N E X T impairments which are more damaging than FEXT. Therefore, Asymmetric services achieve a greater transmission distance than their symmetric counterparts, as expected. 4 Chapter 2 DSL Technologies and Line Codes 5 DATA DSL modem Splitter D ata Switch Voice Switch L A N Figure 2.1 Data and Voice Distribution in DSL Loops Table 2.1 various DSL reach profiles versus data bit rate [5], [6], [18] POTS Downstream Bit Rate (Mb/s) Loop range Km (Kft) Maximum Bandwidth efficiency (b/s/Hz) Line code Data rate ISDN-BRA 5.5(18) 2 2B1Q 144 Kb/s HDSL 3.7-5.5(12-18) repeaterless 6 2BlQor64-CAP or 128-CAP T l - E l (over two pairs) Chapter 2 DSL Technologies and Line Codes 6 Table 2.1 various DSL reach profiles versus data bit rate [5], [6], [18] Downstream Bit Rate (Mb/s) Loop range Km (Kft) Maximum Bandwidth efficiency (b/s/Hz) Line code Data rate HDSL2 3.7(12) 4 16-PAM T l - E l SDSL 3.7(12) 2 2B1Q from 144 Kb/s to TI - E l ADSL 2.6 - 5.5 (8.5 - 18) 8 CAP/DMT DS:1.554Kb/s-8.448 Mb/s US: 16-640 Kb/s RADSL 2.6 - 5.5 (8.5- 18) 8 CAP/DMT DS: up to 8Mb/s US: up to 1 Mb/s G.992.2 splitterless ADSL (formerly G.lite) 2.6 - 5.5 (8.5 - 18) 8 DMT DS: 1.5 Mb/s US: <384 Kb/s VDSL 0.3 - 1.4 (1-4.5) 4 CAP/DMT DS: 13 -52 Mb/s US: 1.5-2.3 Mb/s 2.1.1 DSL Loops We wil l define the different DSLs in terms of their targeted coverage range and loop conditions over which services are designed to operate. Generally, high bit rate DSLs cannot be supported by loaded loops because of the low pass filtering effect of the inductive and capacitive elements of the loading coil. Loading coils, which flatten the loop impulse response over the voice channel, were used at the early stage of telephone lines deployment when amplifiers were not feasible. Two major loop design architectures are found in the literature and known as Revised Resistance Design (RRD) and Carrier Serving Area (CSA): 1. RRD guidelines RRD loops are non-loaded twisted pairs not exceeding 18 Kft in length, with an overall loop resistance less than 1300 Q. (which is true for about 85% of all residential loops [19]). RRD rules emerged after the RD model1 and are better suited for DSL coverage design. Chapter 2 DSL Technologies and Line Codes 7 2. CSA guidelines C S A guidelines call for loops shorter than 9 Kft for 26 A W G pairs, and 12 Kft for 24 A W G pairs (with no load coils). Multigauges are limited to two. Other technical specs limit the bridged taps to two and their longest cannot exceed 2 Kft. The total briged taps length is less than 2.5 Kft. D S L receivers are expected to operate over at least C S A loops, which form a subset of RRD loops (in Bellcore SR-TSV-002275 [35]). CSA loops represent 50% of all loops and 75% of all business district loops [19]. In the following sections we will describe the main characteristics of xDSL flavors. We will summarize briefly some of the technical profiles of ISDN, HDSL (and within the same family HDSL2 and SHDSL), A D S L (with the variants R A D S L and G.992.2 splitterless or G.lite) and V D S L [1], [2], [29], [31], [38], [39]. Note that for internet-optimized asymmetric applications, the forward and reverse bit rate ratio is designed around 8, and would best be served with A D S L for the time being and jointly with V D S L in the next future. 2.1.2 ISDN The first technology of the DSL family is the ISDN Basic Rate Access (BRA). The second standard method of data and voice distribution is Primary Rate Access (PRA). B R A consists of up to three distinct channels (on a single UTP wire): one or two B (Bearer) Channels and one D (Delta) Channel. The B channel carries circuit-switched voice and/or data communications at speeds up to 64 Kbps, in the upstream direction. It uses on the overall 160 Kb/s full-duplex transmission throughput (the information pay load is 144 Kb/s). The ISDN-BRA used the 2B1Q 1 considered permissive for DSL applications as it allows loading coils and a loop resis-tance up to 1500 Q. for any loop length and any bridged taps. Chapter 2 DSL Technologies and Line Codes 8 modulation scheme (the symbol rate is of 80 Kbaud and the allocated bandwidth is 40 KHz). The 2B1Q modulation is designed to support transmission through loops meeting RRD rules. Practical ISDN-BRA implementations use either a half duplex transmission method (time compression multiplexing) or a frequency duplexing method with echo cancellation. The latter was standard-ized by ANSI (T1.601). Basic access doesn't require repeaters, pair selection or loop condition-ing 3 , as opposed to primary access, and can be used on a non-loaded loop up to 5.5 K m long. PRA is made out of 24B + ID and therefore has a capacity of 1.544 Mb/s. The B channels carry voice calls, circuit switched data, and video, whereas the D channel handles data and signaling informa-tion. ISDN bi-directionnality allowed some business oriented applications to be developed such as the two way conferencing using for example the H263+ codec. 2.1.3 HDSL HDSL handles a full T l payload using two pairs (24 B + O A M channels) over a distance of about 5 K m and doesn't carry POTS. It equally uses 2B1Q line code and echo cancellation for duplex operation. Symmetric T l leased lines implementation for C S A loops (see section 2.1.1) are successfully operating and make HDSL main applications for business customers (within a collocated CO). HDSL T l links are repeaterless and get rid of loop conditioning or pair selection. H D S L doublers can extend the reach to 24 Kft (7.32 Km) (providing that loop resistance is less than 900 Q. and the loop loss is less than -35 dB [29]). A splitterless variant of H D S L that keeps POTS has been developed (MVL) . Other HDSL variants include M D S L , IDSL and SDSL [29], loop's bridged taps removal requiring that no T l / E l links could be transmitted in the same bundle of the same cable Chapter 2 DSL Technologies and Line Codes 9 neither of the latter keeps POTS. HDSL2 is a single-pair HDSL flavor which accommodates symmetric TI and is cheaper than leased lines. It is also called the next generation HDSL and designed to operate over the same range (CSA loops). Another H D S L flavor is SDSL. It is defined as HDSL2 using a passband modulation scheme (still under debate) and will therefore allow an analog telephone channel on the same twisted pair. Using MPEG-4 algorithm, domestic V C R quality could be achieved with a data rate of TI . This is expected to make a good business opportunity for SDSL systems. 2.1.4 ADSL A D S L holds a big potential for residential customer deployment [6]. By allocating more bandwidth for downstream transmission, A D S L became very suitable for web access and is expected to deliver compressed digital video. It has been under field trial since 1994 and was standardized by the ANSI T1E1.4 working group in 1995. A second issue of the A D S L standard was more complete and addressed A T M over A D S L [35]. A D S L has 7 transport classes: 4 multiples of TI and three multiples of E l as downstream bandwidth. Using the M P E G - 2 algorithm, live broadcast quality can be reached with a data rate of about 6 Mb/s [6]. The minimum A D S L bit rate is TI (which permits to accommodate for a VHS video quality channel). A D S L TI transmission is targeted to a coverage over all non loaded loops that conform to the RRD set of rules. A D S L 6.14 Mbit/s transmission has a coverage target of all CSA loops4. Passive filters are used to keep POTS in cases of failure of the data network. American A D S L ranges are higher by about 10% compared to their european counter-parts because ETSI decided to run A D S L on an ISDN overlaid network. Chapter 2 DSL Technologies and Line Codes 10 Based on test measurements, DMT was chosen as the preferred line code after an ongoing debate which opposed it to CAP modulation. A D S L - D M T is discussed later on . A D S L modems implement FEC and support data in both interleaved and non-interleaved modes [26]. The damaging crosstalkers for A D S L are: ISDN, HDSL, A D S L (pairs in the same binder group) and T l lines [28]. HDSL common models use 10 or 20 disturbers. The other crosstalkers usually use 10 or 24 disturber models [35]. For A D S L links using overlapping US and DS frequencies, N E X T crosstalkers are more important than FEXT ones because they don't undergo the channel attenuation and have a stronger coupling path. A D S L frequency ranges from 25 to 138 K H z for the US spectrum and 25 to 1104 KHz for the DS spectrum. NBTel was able to provide video service over A D S L for a few hundred subscribers and plan to expand the service for about 20,000 more. NBTel proposed with the use of IP multicast-ing, 110 channels and VOD service [40]. 2.1.5 Other A D S L s R A D S L is one of the A D S L family with some added features. R A D S L data rate is varied automatically to adapt to line conditions. For RADSL, D M T (see 2.2.1) is better suited to smooth bit rate increments than C A P (it starts from 64 Kb/s, in steps of 32 Kb/s). C A P is coarsely adjusted from 640 Kb/s [26]. D M T codes up to 15 bits/symbol (with Q A M ) for R A D S L [29], which can also run symmetrically at 800 Kb/s. R A D S L upstream and downstream data rates are nearly equal, but US and DS bandwidth allocation is not symmetric [19]. R A D S L can adjust line speed based on the gauge of the wire, the distance between subscriber and the central office, and the noise condition of the line. R A D S L can also use C A P to Chapter 2 DSL Technologies and Line Codes ] ] deliver rates up to 51.84 Mb/s (OC-1) over a distance of up to 300 m [1]. The last member of the A D S L family is G.lite (G.992.2, also called UADSL) which is a downgraded version of A D S L designed only for a faster internet access with a rate in the 10% full A D S L capability range. Other variants of the A D S L family include the 1-Meg Modem (Nortel), C D S L (Rockwell) and EZ-DSL (Cisco). Interoperability between all these products is still an issue at the time of this writing. 2.1.6 VDSL V D S L has symmetric and asymmetric modes with very high transmission rates over very short distances. High V D S L rates are to be deployed only in very dense access environment areas where COs are close by. V D S L lines are mostly used in conjunction with hybrid access solutions over the frequency range 300 KHz-30 MHz (and over loops not exceeding 325 Q in resistance) because of a power supply constraint to avoid heating problems (1 W per unit). We distinguish two categories among VDSL: long-range V D S L and short-range V D S L . It was agreed that for any spectral plan proposal, the lower band edge is around 300 K H z indepen-dently of the other services supported. This is to avoid low frequency strong distortions and to relatively immune the service against impulse noise. For long-range V D S L , the copper drop is about 1 to 1.5 K m (sometimes called FTTSA), the transmission capacity in this case is increased to 26 Mb/s downstream and 3 Mb/s upstream. For short-range VDSL, the optical fiber is brought even closer to the subscriber (FTTC) and only the final copper drop (about 300 m) is made out of copper pairs. The transmission capacity reaches up to 52 Mb/s DS and 6 Mb/s US. For symmetric service deployment, long-range V D S L extends up to 13 Mb/s over 1 K m and 26 Mb/s over 300 m (see Table 2.2). We notice that the ANSI transmission rate proposals are chosen to be fractions of Chapter 2 DSL Technologies and Line Codes 12 the SONET rate (see Appendix A.). Because of its broad frequency, V D S L receivers have to resolve RF interference which overlaps with amateur radio and emergency services [18]. More importantly, V D S L has to mitigate coupling from other DSL crosstalkers. Receiver structures proposed for this purpose are transmission technique dependent and therefore we start by reviewing the available line code candidates for V D S L modulation and show why we kept C A P for our subsequent work (with 2B1Q, these are the whole set of candidates for DSL line coding that ANSI considers). V D S L rates depend on the carrier loop configuration of the subscriber and the noise environment in which the V D S L modem operates. Table 2.2 gives an idea about the typical achievable rate versus reach for non-noisy environments. Table 2.2 Reach versus bit rate (in a noise-free environment) for an upstream bit rate equal to TI [38] Downstream Bit Rate (Mb/s) Reach (Km) 13 1.5 26 1 52 0.3 2.2 VDSL line Codes: DMT and QAM/CAP Presently, the three major bandwidth-efficient modulation schemes considered by the standards bodies for V D S L are Q A M , C A P and DMT. Conventionally, Q A M and C A P are F D D based while D M T is T D D based, although the line code is independent of the multiplexing technology. FDD is used to avoid self-NEXT and echo-cancellation, at the expense of increased attenuation and self-FEXT (which follows an f 2 law) [7]. On the other hand, T D D based line codes were reported to undergo a greater degradation than FDD line codes in a mixed F E X T Chapter 2 DSL Technologies and Line Codes 13 environment. Therefore, FDD was considered as a better choice in [12] and is generally known to be easier to implement. TDD schemes are believed to present a very problematic issue of synchro-nization for operators, especially when multiple operators share the same cables and therefore F D D is the preferred scheme from the operator view [22]. In addition, adding users to an F D D system doesn't affect the other subscribers throughput. 2.2.1 The DMT The D M T is an adaptive modulation technique that uses orthogonal frequency and division multiplexing (FDM) as illustrated in Figure 2.2. The input bit stream is mapped into symbol blocks of b=RT bits. R is the bit rate and T is the symbol period. A subset of the k b-long block is transmitted on the subchannel i , such that b = ^ bi where N is the number of i= l subchannels. Each subchannel carrier is placed at a successive multiple of 1/T (half of the FFT size). Each subset b; is QAM-encoded into a subsymbol X; , transformed by the orthogonal IFFT into real-time transmitter sequence, after passing through the DAC (with an oversampling factor T/N). By decomposing the multichannel into a large number of channels, the original transfer function can be approximated by flat narrow portions. D M T permits to avoid carriers at selected frequencies by allocating very low bit rates over the noisy channels. The number of subcarriers used is determined by the channel analysis signal [35]. The encoding is done by a bit loading table which determines the number of bits carried by each tone. This table reflects the SNR variation of the loop and avoids RF interference. Therefore, D M T doesn't require the use of notch filters (as opposed to the case of single carrier modulation technique). D M T minimizes the effect of variable Chapter 2 DSL Technologies and Line Codes 14 Input data Serial to Parallel encoding N QAM symbols Time domain samples T/N (anaphase) overselling Figure 2.2 Schematic of a DMT transmitter frequency impulsive noise interference. For large N, the spectrum of the receiver input signal is written as: hk = HiXi,k + Ui,k (2.1) i designs the index of the subsymbol k. For a large FFT size (2N), each subchannel can be assumed to be independent of the others and can be individually decoded. The construction of the transmitted data out of these FFT samples is done by a memoryless decoder for each of the successive independent subchannels (see receiver structure in Figure 2.3). D M T still present some sensitivity to RFI and the zipper method is one of the tested proposals presented to solve this problem. It optimized the transmit spectrum by overlapping subcarriers. Further details are explained in [30]. Chapter 2 DSL Technologies and Line Codes 15 received data LPF T sampling A D C Serial to Parallel encoding FFT N = 2N 'Hi Decoder detected Time domain samples Figure 2.3 DMT Receiver Wavelet-DMT A different D M T implementation is the discrete wavelet multitone (DWMT). It uses wavelet-based transforms rather than FFTs to achieve multi-channel modulation. D W M T has been proposed for a V D S L upstream link jointly with an F D M CAP for the downstream link [27]. D W M T implementations were reported robust against RFI ingress. A narrowband RFI interferer wil l only damage the subcarriers near its transmission frequency because of the bit loading technique, which was reported to be working for most of the AM-broadcast transmitters but not for RFI from amateur radio users (HAM) [30]. The difference with D M T is that D W M T uses overlapping in the time domain as well. ADSL-DMT A D S L - D M T consists of 256 4KHz-wide carriers in the DS link (26 KHz-1.1 MHz). Each carries T C M encoded data streams up to 15 bit/s/Hz. The carrier spacing is Af = 4.13125 kHz and Chapter 2 DSL Technologies and Line Codes 76 the subcarrier 16 is reserved for a pilot. A D S L using D M T is limited to 10.24 Mbps (40 Kb/s*256 carriers). There are 25 channels in the upstream direction over the range 26-133.8KHz. Echo cancellation is used to allow duplex transmission over the 24 overlapping frequencies. D M T could avoid crosstalk (self-NEXT) by separating the two directions of transmission into non-overlapping time intervals or non-overlapping frequency bands. 2.2.2 QAM/CAP Modulation Q A M (and CAP) is a single carrier, passband modulation5. It is a bandwidth efficient two-dimensional encoding scheme which superimposes modulated in-phase and quadrature waveforms. A typical QAM/CAP-DSL link is presented in Figure 3.19. Q A M impresses two different incoming m-bit symbols from the input stream on two quadrature carriers. Multilevel encoding is used to achieve spectral efficiency6 and allows the mapping of fractional bits into symbols. For a discussion on multilevel encoding (and pulse shaping) refer to [16]. Encoding blocks of m bits reduces the utilized bandwidth by the same factor m (for a given bit rate). Multilevel encoding has two different effects. The first is an increase in the receiver sensitivity to noise, as the number of levels augments. The second has an opposite effect and consists in a reduction of the signal loss through the channel as a result of the reduction in the bandwidth utilized. Referring to Figure 3.19, the resulting QAM-modulated signal waveform can be expressed as X a n S ( t - n T ) cos(o) t) X bn8(t-nT) sin(GW) (2.2) 5 to allow POTS and ISDN 6 equal to ( log 2 M)/ ( 1 + a ) , where M is the number of multilevel symbols Chapter 2 DSL Technologies and Line Codes 17 where g(t) is the transmitter's pulse shaping function, generally chosen to be a square root raised cosine (see Appendix A, section 4) with a small rolloff factor (0.2 to 0.3 for D S L applica-tions) and / = coc/(27i) is the center frequency of the spectrum of the downstream Q A M / C A P signal, as we're interested in the V T U - R receivers only. cos£27if ct) Data Generator Symbol Encoder Lowpass filter Lowpass filter Bandpass filter QA.M sinf27lf<.t.) Figure 2.4 Structure of a QAM transmitter Equation (1.1) can be re-written as: y o = Re\ I Ang(t-nT) (2.3) where An = an + jbn is the complex symbol transmitted at time nT. For flat channels, the recovery of the transmitted Q A M signal (shown in Figure 2.5), is obtained by the following operations [16]: [yox«~M'®s(OW = K (2.4) Using the mathematical equation (2.5), we can deduce an equivalent passband implemen-tation of Q A M (using passband inphase and quadrature shaping filters) which uses a phasor Chapter 2 DSL Technologies and Line Codes 18 cos(27if c€) l/T l/T 2£> Decision Device sinf^27ifct) ( e™ct ) at the transmitter and the opposite rotator (e J'~c") at the demodulator. Figure 2.5 Structure of a matched QAM receiver for a distortionsless channel and a square root raised cosine transmitter shaping filter Sq{t)®g(t)eJ \xe '(2.5) t = nT The idea behind C A P is to get rid of the two phasors in (2.5) as this leads to simpler receiver structures (although theoretically the same performance is achieved). The (phase-splitting) 2D filter structure above, provides the best performance in steady-state operation with the least amount of complexity [1]. C A P Modulation C A P stands for Carrierless Amplitude and Phase modulation. The word carrierless in C A P follows from the fact that the carrier doesn't contain any information. CAP is very closely related to Q A M and can mathematically be derive from Q A M equations [13]. The C A P signal can be expressed as: Chapter 2 DSL Technologies and Line Codes 19 Data Generator k. Symbol Encoder w Figure 2.6 CAP transmitter Bandpass filter > CAP W O = X anp(t-nT)-^ bn~p(t-nT) (2.6) or equivalently, W O = R e \ S AnP«-»T) where (2.7) P(t) = p(t) + jp(t) = g(t)e (2.8) p(t) and p (t) are the respective passband in-phase and quadrature transmitter filters impulse responses. They form a Hilbert transform (under the assumption that the carrier frequency is larger than the largest frequency of the baseband pulse g(t)). Their Fourier transforms (using obvious notations) satisfy: P(f) = -j • sign(f) • ~P(f) (2.9) The C A P signal is easily proven to be cyclostationary with a bandwidth of 1 + a The lowest and highest frequencies of the downstream spectrum are therefore given by: Chapter 2 DSL Technologies and Line Codes 20 1 + a 1 + a fww ~ fc 2f~ m ^ ^ H I G H ~ f ° + 2T (2.10) The C A P spectrum is displayed in Figure 2.7. Higher rolloff factors result in wider Figure 2.7 Power Spectrum density of the CAP signal for different rolloff factors (0.2, 0.5, and 1) Figure 2.8 CAP spectrum for different transmitter tap spans (a = 0.2) spectra. The out-of-band lobes are suppressed with additional analog filtering. Notice the attenua-tion of the side lobes with the span increase ([-3T,3T], [-5T,5T], and [-10T,10T]) in Figure 2.8. The psd of the CAP signal is given by: PSDCAP(f) = • \P(ft = %f [\G(f-fc)\+\G(f + fc)\2] (2.11) Chapter 2 DSL Technologies and Line Codes 21 for positive frequencies we retain (see appendix A for the expression of G(f)), PSDcAp(f) = ^-\G(f-fc)\2 (2.12) where a is the complex symbols variance given by L L k = \ k= 1 p k is the probability of the symbols a k and b k and L is the number of multilevels for each CAP dimension. By adjusting the value of L , the CAP transceiver can scale its bit rate to lower or higher speeds while using the same digital and analog front end filter structure. The transmitted in-phase and quadrature data sequences can be recovered using (2.14), which is implemented in the receiver shown in Figure 2.9. Notice that (2.14) is simpler than (2.5). [SCAP(t)fg(t)eia'\snT = An (2.14) AID ?T l/T In-phase filter Quadrctiure filter 1/7 2D Decision Device Figure 2.9 Structure of a CAP linear receiver Spectral efficiency C A P and Q A M have the same theoretical performance and spectral efficiency, which is Chapter 2 DSL Technologies and Line Codes 22 reported in Table 2.3. It was reported though that "for a given complexity of implementation, C A P usually performs slightly better than Q A M " [24]. Table 2.3 CAP spectral efficiency for a = 20% Constellation size) Spectral efficiency (b/s/Hz) 4 1.67 16 3.33 32 4.17 64 5 128 5.83 256 6.67 Applications of CAP: CAP has been proposed as the line code for several data communication applications [2], [8], [20]. 32 C A P was reported to provide an FDD rate of 125 Mb/s over 100 meters of voice grade UTP wiring in a channel bandwidth of 30 MHz [20]. 16 C A P is the DAVIC's 52 Mb/s (OC-1 = 51.84 Mbit/s) specification to fiber to the curb [8]. 64 C A P is the 155.52 Mb/s A T M L A N standard for category 3 UTP wiring (duplex operation over two twisted pairs). Future ( A T M L A N ) V D S L applications include 622.08 Mb/s duplex operation over 100 m UTP (category 3) loops using 64-CAP line coding and 4 twisted pairs for each direction of transmission [20]. Over new high performance category 5 UTP loops, the above rates can be achieved only over two pairs for each directional link. We believe that because of its lower computational complexity and therefore lower power consumption of its signal processing unit, CAP will be chosen to meet the rigid power constraints of the V D S L environment. Chapter 2 DSL Technologies and Line Codes 23 2.2.3 Comparison between DMT, QAM and CAP The only difference between C A P and Q A M is the absence of a symbol rotator in CAP. This makes an easier C A P implementation. Both Q A M and C A P receivers can be made compati-ble if the carrier frequency is an integer multiple of the symbol rate. A blind dual mode receiver for C A P and Q A M has been developed in [13] for any carrier/symbol rate combination. More on the discussion of the interoperability between C A P and Q A M as well as the complexity of implementation of DFE receiver can be found in [16]. It was also explained in [16] that the errors derived in the Q A M transceiver must be rotated before being used to update the tap-weight values. C A P outperformed Q A M [14] because of its receiver simplicity that doesn't require correction for carrier jitter and offset. C A P was reported to have an advantage over D M T in services requiring fast switching for its low latency [26]. During the rest of the thesis we will only consider C A P modulation. 2.3 CAP-VDSL V D S L lines form a point to multipoint network, therefore no training sequence could be tolerated in order to avoid disrupting other receivers when a new modem is turned on. Under this assumption, receiver blind equalization is needed. This equalization process has to operate under severe impairments generated from the adjacent lines within the same cable binder. These impair-ments depend on the distance and frequencies of the disturbers, as well as the loop configurations (with possible gauge change and bridged taps). Signal levels of A D S L systems are much higher than their V D S L counterparts. Therefore foreign crosstalk (NEXT and FEXT) impairments are essential to our study. Self-FEXT is the dominant impairment in C A P - V D S L (as opposed to self-N E X T for baseband transmissions) and will be investigated in chapter 3. Chapter 3 Channel and Noise Modeling In this chapter we wil l model V D S L channel loops and noise sources. The channel impulse responses and the noise sequences generated will be used in Chapter 4 for V D S L perfor-mance evaluation. We will show in the following that with our assumptions stationary self-FEXT is the most damaging noise source for short loops, whereas for longer loops W G N is the most significant. Finally, we present numerical results on the achieved capacity over these loops in A W G N and self-FEXT environments. 3.1 VDSL test loops In order to be able to test transceiver architectures and DSP algorithms for V D S L loops, accurate channel models were developed by the ANSI T1E1.4 working members based on the electromagnetic results of infinitesimal copper line R L C G representations (see appendix B). These models were tested against extensive loop transmission characteristics gathered from measurements of different independent sources [18]. In this context, the two-port network A B C D method, developed by Werner [17] [33], is used as a means to compute the impulse responses of different V D S L channels. These channels are used later on in the simulation of V D S L communi-cation links. We made use of the linemod program [37] to compute the channel impulse responses and insertion losses, that we checked independently using the parameters of Appendix B . Typically, V D S L lines are short and formed out of UTP wires. A set of representative V D S L transmission media have been proposed [14]. We will develop our study in conformance to these proposals, approved by ANSI's T I E 1.4 working group. This set of loops is attached in Appendix C for reference. For a discussion on loop qualification and testing possibilities related to xDSL, refer to [29]. 24 Chapter 3 Channel and Noise Modeling 25 V D S L test loops present severe impairments to the transmitted signal because of loop attenuation caused by the propagation loss and bridged taps. Certain bridged tap combinations can introduce an additional propagation loss of up to 30 dB [33] which degrades the performance of the channel especially in noisy environments (see section 3.3). Figure 3.1 VDSLO insertion loss (left) and impulse response (right) According to the system specification draft for V D S L [1], the input voltage levels propagate through a channel with a characteristic referred to as the insertion loss (instead of the transfer function). In other words, the power constraints are applied to the loop's input not includ-ing the source impedance [1], [33]. For VDSLO, the insertion loss (Figure 3.1) is mild and the impulse response spans over around 20 symbol periods (assuming a symbol rate of 12.96 Mbauds). For VDSL1 , we notice from Figure 3.2 that the attenuation is more important and the spreading of the impulse responses is wider as we extend the loop's length, which means more ISI exists for longer loops and makes the signal detection more difficult. This remark applies to all of the remaining V D S L loops, where we adopted the notation L to designate long loops, M to designate medium loops and S to refer to the shorter loops. We present our results, out of the Chapter 3 Channel and Noise Modeling 26 long loop | \ medium loop j 'i x 10" 5 Figure 3.2 Insertion loss of VDSL1 (xTPl) to the left and Loop Impulse Responses to the right Werner's model, in the figures Figure 3.1 through Figure 3.7. 4 X 10" S Figure 3.3 Insertion Losses and Impulse Responses of VDSL2 Notice the nulls in Figure 3.5, Figure 3.6 and Figure 3.7 introduced by the bridged taps at certain notch frequencies (which depend on the loop length). Chapter 3 Channel and Noise Modeling 27 X 10" 5 Figure 3.4 Insertion Losses and Impulse Responses of VDSL3 Figure 3.5 Insertion Losses and Impulse Responses of VDSL4 3.2 PSD masks The ability of V D S L to tolerate other systems crosstalk operating over the same access network is discussed in the T1E1.4 and ETSI spectrum management drafts (formerly, spectral compatibility) [25]. Spectrum management deals with coordinating the behavior of V D S L and Chapter 3 Channel and Noise Modeling 28 Figure 3.6 Insertion Loss (left) and Impulse Response of VDSL5 (right) Figure 3.7 Insertion Loss (left) and Impulse Response (right) of VDSL6 other systems sharing the same cable binder. A reasonable condition for compatibility would be to cancel out alien-NEXT (discussed in 3.3.4). This is achieved by limiting the spectral power that each transmitter injects into the cable through masks. Instead of comparing each V D S L technique to all existing xDSL technologies and evaluating the performance degradation for each, an effort has been made to define a common PSD mask which is "minimally restrictive" and compatibility Chapter 3 Channel and Noise Modeling 29 Figure 3.8 Insertion Loss (left) and Impulse Response (right) of VDSL7 has only to be gauged to it. Practically, the transmit power has to be shaped by the PSD mask to ensure that it remains below the PSD power. In other words, the power output of the transmitter is less than the mask level at each frequency. We assume a flat mask of -60 dBm/Hz for the C A P transmitter and a flat background noise mask of -140 dBm/Hz. 3.3 Noise sources We try in the following to catalogue the different noises that might appear in a V D S L link and disturb the communication system. 3.3.1 W G N Background noise is well approximated by a Gaussian distribution [1] [14]. It is in the range of 10-30 micro-volts with a power density of about -140 dBm/Hz, according to a Bellcore survey [18]. This background noise level is higher than that achieved by a receiver front end electronic circuit [25] and is considered as the result of background radio noise and other electri-cal and electronic devices contributions. Chapter 3 Channel and Noise Modeling 30 3.3.2 Impulse Noise Impulse noise is stated here for reference only. It results from electronic and electrome-chanical devices such as poor switching equipment at COs, household electronics, light dimmers, lightning strikes, power lines etc. It can be narrow band or wideband. Forward error correction codes are proven effective to handle impulse noise [25]. Impulse noise effect is known to be important only over low frequencies, so we will not consider it in our simulation work. An investi-gation of impulse noise effect usually includes an SNR noise margin of 6 dB at the receiver. 3.3.3 Radio Frequency Interference (RFI) RFI noise comes from broadcasting and radio transmitters. We distinguish two types: ingress (radio frequency energy entering a wire pair and interfering with the transmission system) and egress (energy radiating from the twisted pair and interfering with a radio service). A M radio signals are strong (-80 dBm/Hz) and occupy 10 KHz-wide bands in the frequency range 560-1600 KHz. They generate serious harmful ingress to V D S L receivers. Ham radio interferers are narrow-band signals (2.5 kHz wide) in the frequency ranges: 2 M H z , 3.5 M H z , 7 M H z and 10 M H z . H A M radio interferers also receive electromagnetic radiation from V D S L transceivers which can cause audible interference for H A M radio receivers [31]. RFI interferers are generally consider-ably diminished by V D S L transceivers with a receiver front-end analog filter, therefore we wouldn't keep radio frequency interference in our communication model. 3.3.4 Crosstalk A serious challenge for D S L communications is crosstalk. It is an important limiting factor to the achievement of better transmission throughputs over the copper lines. At high frequencies, twisted-pair lines become like antennas, both receiving from and transmitting to the Chapter 3 Channel and Noise Modeling 31 outside environment. Crosstalk comes from capacitive and inductive coupling of adjacent channel loops collocated in the same cable binder (generally a group of 10, 25 or 50 pairs [18]). Therefore, each pair generates crosstalk (NEXT and FEXT) in the adjacent pairs. The effect of crosstalk is minimized by adopting different twist lengths for the surrounding cable pairs. Crosstalk is called self-crosstalk if it is generated by transmitters using the same DSL technology. Otherwise, it is called foreign or alien-crosstalk. In the following we will be interested in self-crosstalk and in foreign-crosstalk caused by ISDN, HDSL and A D S L in V D S L channels. It is clear that raising the signal level for the transmitter doesn't necessarily improve the SNR, as the other signals egress interference amplifies. Raising the level of the V D S L signal alone would violate the spectral compatibility of other DSLs with V D S L and rule out the sharing of mixed DSLs of the same cable binder. 3.3.5 N E X T N E X T is the crosstalk effect which appears at the same end of a loop (Figure 3.9). It is important when the receiving and transmitting paths (opposite directions) share a common frequency spectrum. Typically, this is always the case for symmetric applications. It is instructive to know what noise levels could be added to the transmitted signal for symmetric services by looking at Figure 3.10. We focus only on residential services and consider throughout the rest of our development asymmetric stream flow in the local loops. A good study of the effects of self-N E X T in A T M L A N applications can be found in [32] where different receiver structures for N E X T equalization were also simulated. Self-NEXT coupling is obviously not an appropriate disturbance scheme for C A P - V D S L as the DS and US spectra are disjoint (see Appendix A). In other terms, the central office end Chapter 3 Channel and Noise Modeling (VTU-C) transmits at a higher frequency than the customer end at the user's side (VTU-R). 32 pair 1 VTU-C2 VTU-R2 VTU-C1 N E X T VTU-R1 p air 2 Figure 3.9 Self-NEXT and self-FEXT interference - 4 5 | — 1 1 1 1 1 r F r e q u e n c y ( M H z ) Figure 3.10 Stationary NEXT for symmetric long-range VDSL For asymmetric services, self-NEXT coupling occurs for C A P - V D S L when the transmit-ting source V d i s t ( t ) is collocated with another V D S L receiver. In this case, the DS flow intended for VTU-R2 is leaked through N E X T coupling into VTU-R1. This case is unlikely to happen as collocated subscriber transmission units are generally pulled out of the same CO. Therefore, we will only consider foreign NEXT, which will be discussed in sections 3.3.8 and 3.3.9. The power of the N E X T disturbance in V D S L lines is given by: Chapter 3 Channel and Noise Modeling 33 PSDNEXT(f) = PSDdisturber(f) • \XNEXT(f)\2 (3.1) \XNEXT(ff = KNEXT • d • fh5 • ^ J " 6 (3.2) K N E X t is the N E X T coupling parameter, equal to 8.818 10~14 (for category 3 UTP wires), according to the ANSI T I E 1.4 specifications. Two techniques are used to mitigate NEXT: equalization and cancellation. N E X T cancel-lation consists in the (adaptive) synthesis of the interfering N E X T signal out of the transmitted and received signal (this clearly applies only to self-NEXT as the only available transmitted signal to the N E X T canceler is the one of the same twisted pair, generated by the local transmitter). N E X T cancellation was shown in [32] not to be efficient in the case of multiple interferers under a bandwidth constraint of 30 M H z 1 . Therefore, as far as N E X T is concerned, we should only be interested in the equalization of foreign-NEXT. VTU-Cl VTU-R2 VTU-R3 Figure 3.11 NEXT and FEXT coupling through twisted pairs 3.3.6 F E X T F E X T is the crosstalk effect that appears at the opposite end of the loop. It undergoes the For this case, the transmitter and receiver bandwidths overlap. Chapter 3 Channel and Noise Modeling 34 channel attenuation as the F E X T signal propagates through the loop connected to the V D S L transceiver (see Figure 3.9 and Figure 3.11). For C A P - V D S L applications, FEXT crosstalk disturbance should be accounted for, since downstream data in adjacent pairs flow in the same direction and V D S L loops are relatively short (so the F E X T signal doesn't fade considerably). In the following, we will be mainly interested in F E X T modeling. FEXT equalization will be dealt with in the next chapter. The block diagram used for modeling crosstalk disturbance is shown in Figure 3.12. Over WGN YTU-C1 symbols 1 VTU-C2 symbols CAP Transmitter Xtalk(f) Channel(f) Receiver Figure 3.12 Block diagram for crosstalk simulation the lower link, the C A P transmitter is fed by the V T U - C 1 symbols which represent the downstream link. To this is added the crosstalk noise with a transfer function Xtalk(f) equal to the F E X T PSD. Two disturbance schemes are possible. In the first, a similar modulated signal is fed to the C A P transmitter and then to the crosstalk filter. The output represents the additive noise for the case of a single disturber. The second scheme is when the link operates in a multi-disturber environment. Using the central theorem a W G N signal at the input of the crosstalk filter is a more appropriate representation of a real shared cable-binder environment. Chapter 3 Channel and Noise Modeling 35 3.3.7 Self-FEXT F E X T can be modeled by a linear filter having a transfer function Xpg^T defined by \XFExT(f)\2 = KFEXT • \H(ff -d-f2- (JtJ6 (3.3) The overall PSD FEXT is obtained by replacing (3.3) into (3.4). PSDFEXT(f) = PSDdisturber • \XFEXT(f)\2 (3.4) where KpgxT 1 S t n e FEXT coupling constant (equal to 810"20). N is the number of disturbers and d is the coupling path length of the loop (in feet). In the following two subsections, we have considered both cyclostationary and stationary FEXT. Stationary power corresponds to 24 disturbers and cyclo-stationary power corresponds to a single disturber. We assume a maximum transmit PSD of -60 dBm/Hz at all frequencies. 2 (N\0-6 Note that the term PSDdisturber • KFEXT • d • f 1^1 1 S l e s s t n a n o n e f ° r t n e frequency range [0, 30MHz], therefore the F E X T effect is always less than the loop attenuation for VDSL. 3.3.7.1 C y c l o s t a t i o n a r y F E X T Simulation results plot in Figure 3.13 show that some F E X T levels of VDSLO, V D S L 5 , VDSL1 S, VDSL2 S, VDSL3 S and VDSL4 S are above -140 dBm. The loops order reflects their decreasing interference power. In these cases, cyclostationary F E X T is more important than W G N and the disturbance signal from a single disturber propagating through each of these loops is more important than background noise for at least a part of the frequency spectrum. It should therefore be included in further receiver performance work involving single disturber systems. Chapter 3 Channel and Noise Modeling 36 -100 - 1 2 0 -140 -160 E sa -180 -200 -240 -260 -280 -300 o VDSLO X VDSL1 S VDSL1 M • VDSL1 L VDSL2 S VDSL2 M VDSL2 L X VDSL3 S VDSL3 M • VDSL3 L X VDSL4 S * VDSL4 M • VDSL4 L VDSL5 VDSL6 VDSL7 8 10 12 Frequency (MHz) 14 16 ' 1 18 Figure 3.13 Cyclostationary Self-FEXT Loss (single disturber) over V D S L Loops For all loops, we still can recognize the shape of the CAP transmitter PSD in Figure 3.13. From Table 3.1, we reported the cyclostationary FEXT power interference over the whole long-range V D S L spectrum. The effects of cyclostationary F E X T on long loops is not of any importance to us (the F E X T signal fades considerably before reaching the receiver at the opposite end). For reference, we state that VDSLO cyclostationary power is -46.30 dBm, under the constraint of a maximum input PSD to the FEXT filter of -60 dBm/Hz. Chapter 3 Channel and Noise Modeling 37 Table 3.1 cyclostationary F E X T for V D S L loops Frequency range (MHz) Cyclostationary FEXT Power (dB) relative to VDSLO VDSL1 S VDSL2 S VDSL3 S VDSL4 S VDSL5 2.42 - 17.97 -3.92 -9.16 -10.15 -22.25 -0.07 3.3.7.1 Stationary FEXT Stationary FEXT is the contribution of all surrounding important disturber loops. Simula-tion results plot in Figure 3.14 show that stationary FEXT is more damaging than cyclo-stationary F E X T for all the loops, as expected. The interference level for short loops increases in this case and F E X T levels from V D S L 2 M and VDSL3 M can be damaging up to 8 M H z . V D S L 1 M stationary FEXT interference is important up to 4 MHz. Other loops interferences are comparable to background noise levels at low frequencies and are of no threat at higher frequencies. Table 3.2 Stationary F E X T power for V D S L loops Frequency range (MHz) Stationary FEXT Power (dB) relative to VDSLO VDSL1 M VDSL2 M VDSL3 M 2.42 - 17.97 -33.65 -25.08 -25.96 Remarks: 1. For Table 3.2, VDSLO reference stationary power is -38.00 dBm. 2. It is useful to know that for 24 disturbers the power of stationary F E X T is merely a 3.8 dB add up to the level of the power of the 10 disturber case. Stationary self-FEXT is kept for transceiver performance testing for short loops as it represents a serious challenge and it can exceed the background noise. Chapter 3 Channel and Noise Modeling -100 -150 -200 -250 -100 -105 -110 £ CD CD > CD 115 120 -125 -130 -135 -140 8 10 12 Frequency (MHz) Figure 3.14 Stationary Self-FEXT Loss (24 disturbers) over V D S L Loops Chapter 3 Channel and Noise Modeling 39 3.3.8 A D S L crosstalk A D S L crosstalk spectral compatibility is ensured with a set of tests and simulations of the interference incurred by the coupling from A D S L systems offered over pairs within the same cable binder. A D S L crosstalk is discussed here using the mask of Figure 3.15. F r e q u e n c y in M H z ( l o g s c a l e ) Figure 3.15 ADSL (downstream) Power Mask ADSL-FEXT we showed in Figure 3.16 the PSD of the transmitted signal with and without an A D S L disturber (respectively before and after 11.04 MHz). A D S L F E X T level is equal to background noise levels in the most dangerous cases and therefore it should be discarded from further simula-tion. ADSL-NEXT The PSD of A D S L - N E X T is plotted in Figure 3.17. Since This level is higher than -140 dBm/Hz, A D S L - N E X T is a noise factor for all V D S L loops which should be accounted for in the design of any CAP-receiver. We will not be considering A D S L - N E X T any further in our work, Chapter 3 Channel and Noise Modeling 40 —AO i 1 1 1 1 1 r Figure 3.16 ADSL Fext (24 disturbers case) into VDSL short loops Figure 3.17 ADSL-NEXT noise though. Partly, this is because the mask proposed by T1E1.4 at the time of this writing (Figure 3.15) is contested by committee members and should be changed possibly with a much narrower mask and a lower transmit level. 3.3.9 I S D N a n d H D S L c ross ta lk For the remaining foreign crosstalks (other than ADSL) , we distinguish between ISDN, Chapter 3 Channel and Noise Modeling 41 and HDSL N E X T and FEXT interferences. To compute the PSD of ISDN and HDSL crosstalkers, we replace ¥SDdisturber in (3.3) and (3.1), which are single-sided PSDs by one of the respective following expressions [14]: 2 P S D ISDN -disturber^) = &ISDN ' T~ JO 2 P S ® HDSL-disturber^) = ^HDSL'~T JO where sinc(jc) = — , f0 = 8 0 k H z > a n d K ISDN = 25.7210"3. Figure 3.5 and Figure 3.6 suggest that the transmitted ISDN and H D S L pulses are assumed to be passed through low-pass shaping filters. These are chosen to be second and fourth order butterworth filters. Equation (3.5) represents the PSD of an 80 ksymbols/sec 2B1Q signal (with equiprobable levels) with a second order butterworth filtering at f0. Equation (3.6) represents the PSD of a 392 ksymbols/sec 2B1Q signal with random and equiprobable levels and a fourth order butterworth filter at f 3 d B . These two low-pass filters attenuate the foreign interfer-ence at high frequency and marginate their effect. Figure 3.18 permits to conclude that the N E X T and F E X T disturbances from ISDN and HDSL do not affect downstream V D S L links. 3.4 Simulation Model Our model is described in Figure 3.19. The transmitter is fed with random equiprobable data symbols (assuming the values ± 1 , ± 3, ± 5... ). This data passes through i/T over-sampled in-phase and quadrature filters (see Figure 2.6). The difference between the in-phase and quadra-ture signals is the CAP signal, which we feed to a V D S L channel. At the output of the channel, we 2 sine ( / / / o ) ^—^j (3.5) l + ( / / / 0 ) 2 sine ( / / / n ) 0 (3.6) 1 + ( / / / W Chapter 3 Channel and Noise Modeling 42 - 1 2 0 Figure 3.18 ISDN (top) and HDSL (bottom) crosstalk PSDs (PSD disturber only) add crosstalk and background noises. The resulting signal if fed to the receiver (see Figure 2.9 for the linear receiver structure and Chapter 4 for DFE structures). crosstalk WGN Transmitter Data generator Low-pass filter K 2D Modulator l/T noise VDSL Loop |. l/T' l/T 2D Receiver ^ ^estimated data Figure 3.19 VDSL Communication Model The transmitter filter operations were described in Chapter 2. We abide by a maximum Chapter 3 Channel and Noise Modeling 43 transmit PSD of -60 dBm/Hz at all frequencies. The noise generation process was detailed in the previous section. Before we present our simulation results, let's look at the achievable data rates over V D S L loops under A W G N and self-FEXT conditions. 3.5 Channel capacity and Receiver Input SNR The achievable data rates over the V S D L loops are upper-bounded by Shannon's capacity formula: CLooP(d' w) = lBB2\og2^+SNR(f)]df (3.7) W = B 2 - B] is the utilized channel bandwidth (DS-VDSL spectrum) and SNR is the Signal-to-Noise Ratio at the input of the receiver, which we will derive for A W G N and stationary-F E X T conditions. 3.5.1 A W G N e n v i r o n m e n t In this case, the SNR is expressed as follows: PSDCAP(f) • \H(d,f)\2 SNRReceiverInput{f) = C A P N (3-8) where N 0 is the PSD of the background noise. The capacity under W G N conditions is computed from (3.7) and reported in Table 3.3. Chapter 3 Channel and Noise Modeling Table 3.3 VDSL capacity in a WGN environment 44 .Loop Capacity (Mb/s).; over long range VDSL VDSLO 371.16 VDSL1 L . 3.74 VDSL1 M 38.69 VDSL1 S 246.22 VDSL2 L 18.76 VDSL2 M 71.32 VDSL2 S 196.34 VDSL3 L 17.42 VDSL3 M 67.56 VDSL3 S 190.84 VDSL4 L 0.93 VDSL4 M 16.92 VDSL4 S 121.01 VDSL5 260.08 VDSL6 36.42 VDSL7 5.28 3.5.2 Self-crosstalk environment Following Figure 3.12, the SNR at the receiver input is given by [3]: SNR Receiverlnput (f) = PSDVTUAf)-\H(d,f)Y (3.9) PSDdisturber(f) ' \Xxtalk(f">\ X x t a l k is to be replaced with X s e i f _ F e x t (stationary or cyclostationary). 3.5.2.1 Case of a single interferer (Cyclostationary FEXT) This case applies only for cables using pair selection techniques which does not allow the sharing of multiple interfering DSLs of the same binder. Assuming a single interferer and self-crosstalk, the SNR formula in (3.9) simplifies to SNRReceiverInput(f) = \H(d,ff/\Xxtalk(f)\2 (3.10) Assuming the crosstalk is generated from a loop of the same type as the disturbed one Chapter 3 Channel and Noise Modeling 45 (connected to the VTU-R), we can write using (3.2) and (3.10) the SNR at the receiver input as: 1 SNR C y d o F E X T (/) = Receiverlnput d'f2- KFEXT • (|Q (3.11) which we show in Figure 3.20 1 \ j I J * V r 1 J SNR = 30 dB SNR = 2 0 d B SNR = 10 dB ! \ i \ i s i s •i "V •• - \ \ - - - '• \ 8 10 12 Loop length (in Kfeet) 16 18 Figure 3.20 Contours of equal SNR for the cyclostationary FEXT environment - case of an equal disturber and disturbed loop we notice that the SNR value is independent of the loop's insertion loss and of the transmitter's spectrum. It is also inversely proportional to the overall length d and to f . In a cyclostationary FEXT environment, the V D S L test loops capacities are given in Table 3.4. Chapter 3 Channel and Noise Modeling Table 3.4 VDSL capacity in a cyclostationary environment 46 Loop Capacity (Mb/s) over long" range VDSL VDSLO 278.22 VDSL1 L 131.63 VDSL1 M 140.69 VDSL1 S, VDSL5 165.29 VDSL2 L, VDSL3 L 130.42 VDSL2 M, VDSL3 M, VDSL6 138.90 VDSL2 S, VDSL3 S, VDSL4 S 152.75 VDSL4 L 128.19 VDSL4 M 135.70 VDSL7 129.50 3.5.2.1 Case of multiple interferers (Stationary FEXT) For multiple interferers, (3.9) is written as: SNR Receiverlnput (f) = PSDCAP(f)-\H(d, f t NWGN ' \Xxtalk(f) (3.12) Where N W G N , I s the PSD of the W G N signal fed to a transmit mask which level is equal to -60 dBm/Hz. N W G N cancels out with the mask applied at the output of the C A P signal as both transmit filters have the same power constraint. We wil l still write P S D C A P to designate the spectrum of the CAP without the scaling value of -90 dB/Hz. The SNR expression is reduced to: SNR S t a t F E X T (/) = Receiverlnput PSDCAP(f) K rl f2 (H FEXT a J I 49 ,0.6 (3.13) which can be more explicitly expressed for the following frequency ranges (assuming a < 1): Chapter 3 Channel and Noise Modeling 47 1. 0 < | / - / c | < ^ ( i + a ) statFEXT , „ s SNR (f) Receiverlnput a2T 2 ' KFEXT • d • f2 ' (j| ,0.6 (3.14) 2. ^ ( l - a ) < | / - / c | < 2 y ( l - a ) SATC S M F E X T ( / ) Receiverlnput -/Mir (3.15) Table 3.5 VDSL capacity in a 24-disturber environment Loop ' .. :[ '•')V. '• Capacity (Mb/s) oyer long range VDSL 1 VDSLO 225.24 VDSL1 L 81.07 VDSL1 M 89.63 VDSL1 S, VDSL5 113.33 VDSL2 L, VDSL3 L 79.93 VDSL2 M, VDSL3 M, VDSL6 87.93 VDSL2 S, VDSL3 S, VDSL4 S 101.18 VDSL4 L 77.85 . VDSL4 M 84.90 VDSL7 79.07 We notice from (3.12) how the multi-disturber case is far more damaging than the single case. We also notice from Figure 3.21 that for short loops crosstalk effect is more important than for longer loops and the difference between single and multiple interferers is about 50 Mb/s. These results are in accordance with our expectation in that for short loops, F E X T doesn't attenu-ate much and the capacity under the FEXT impairment scheme is higher than that under the W G N Chapter 3 Channel and Noise Modeling scheme. For higher loops, the opposite happens. Figure 3.21 Capacity of VDSL test Loops Chapter 4 Linear and DFE Equalization of VDSL Communication Links 50 Chapter 4 Linear and D F E Equalization of V D S L Commu-nication Links The channel amplitude and phase distortion broadens the transmitted pulses and causes symbols to interfere. The purpose of the receiver is to recover the transmitted data sequence with the minimum possible number of errors. To achieve this goal, the receiver should compensate for the channel distortion and additive noise. A V D S L equalizer should not be pre-designed and is required to work for a different channel and in different noise environments. Therefore, V D S L receivers should use adaptivity to continuously adjust the internal settings of the filter taps in an effort to minimize a certain cost function. Different receiver structures can be found in the litera-ture, each is generally well suited to a certain type of applications and mitigates only certain noises (for which some cost function has been optimized). We are concerned in this chapter with linear and DFE structures of V D S L receivers. The importance of a good equalizer could be seen from Figure 4.1, showing the received signal constellations at the output of some short V D S L loops. Except from VDSLO, the received samples cannot be readily interpreted after a simple demodulation, even in a noise-free environment. For VDSLO (null loop), there's still a need for a simple rotator to adjust the phase offset and a matched filter to compensate for the real-world noises. Signal constellation diagrams of other channels are not reproduced here because they are displays of random points (and emphasize the need for an ad-hoc equalizer). The general receiver structure combines bandpass filtering, phase splitting and adaptive equalization (Figure 2.9). We retain the phase splitting F S L E structure as opposed to cross-coupled and four-filter structures. After filtering the received signal, a sheer maps the equalizer output to its nearest (in the Euclidean sense) neighbor symbol from the signal space constellation. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 51 Practical receiver filters are implemented as direct form FIR filters, as illustrated in Figure 4.5. Figure 4.1 Signal space constellations of demodulated CAP signals We are interested in long range V D S L with the highest speed (51.84 Mb/s). Different linear receivers will be tested in this chapter and over certain loops the bit rate might have to be downgraded to some of the lower values shown in Appendix A. 4.1 DFE filtering Different types of Decision Feedback Equalizer (DFE) structures could be considered for V D S L equalization. Hybrid DFEs are costly, complex to implement and will not be investigated in this work. The noise-predictive DFEs and the conventional DFEs are examined instead. Optimum D F E filter performance was reproduced from the literature in Appendix D. for the reader's reference. The Feed Forward Filter (FFF) is a Fractionally Spaced Linear Equalizer (FSLE) which provides an eminent role in V D S L equalization. For the NPDFE (shown in Figure 4.2), the transfer function synthesized by the FFF is the same as that of the optimum FSLE. The feedback filters of the NPDFE do not carry channel equalization any further and only act as noise predictors to cancel out the noise effect, using the correlation between the successive noise samples (notice that the noise sequence reaching the DFE filter is highly colored). We thought that Chapter 4 Linear and DFE Equalization of VDSL Communication Links 52 the equalization stage for V D S L still needs some more refining and should be carried further in the DFE stage. Therefore, only the conventional DFE could be of interest to us. J/T FFIF l/T FFQF eV»> | «'jC»J Figure 4.2 Structure of the NPDFE receiver 4.2 Conventional DFE The inphase and quadrature feed forward filter taps are updated according to the equations in (4.1) and (4.2): Cn + 1 = C n - « - e i ( n ) - r n ( 4-D d n + i = d n - c c - e q ( n ) - r n The feedback taps are updated using the following equations: fn + i = fn + M e j ( n ) - a n - e q ( n ) - b n ) (4.2) (4.3) Chapter 4 Linear and DFE Equalization of VDSL Communication Links 53 efn) Figure 4.3 Structure of a conventional DFE receiver g n + i = g n + P-(e (n ) -a n + e i ( n ) - b n ) (4.4) Simulation results in a noise free environment show that the conventional D F E needs a special tap weight initialization and is very sensitive to step size values. Its convergence was difficult to obtain and usually exceeded the 1 second setup time desired. Therefore DFE structures are not investigated in the remainder of our work as we think that in our context linear receiver structures could be better suited to equalize V D S L channels. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 54 0.06 0 -0.02 -0.04 -[ I l l I l 1 1 - • W ^ K . ; . •.• '•J.: 1 . . . ' *• i i i i -.• > ;.4V.->.'/: * • •«,*•* J 1 1 1 • ? * . 0 0 6 l , 1 1 1 1  '  z -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 REAL Figure 4.4 Wrong DFE convergence for VDSL1 S 4.3 Linear Filtering It is known that linear filters provide a suboptimal equalization result. Because their computational complexity increases only linearly with the channel dispersion length (or equalizer number of taps), the use of linear filters for equalization is widespread. The first equalizer that comes to mind for V D S L is the well-known linear matching filter. Since it only compensates for noise, it is not of practical use in typical V D S L environments where the severe channel distortions cause significant ISI. Therefore, matched filters wil l not be considered any further. Another possible V D S L linear receiver could be the Zero-Forcing Equalizer (ZFE), which is optimum in the sense of minimizing the peak distortion criteria (ISI). The ZFE eliminates ISI at the input of the receiver slicer by inverting the channel. It doesn't compensate, even partially, for the noise though. The magnitude of the inphase and quadrature ZFE is plot for various V D S L loops in Figure 4.6. Since the normalized transfer functions of VDSL1 L , V D S L 2 L and V D S L 3 L are Chapter 4 Linear and DFE Equalization of VDSL Communication Links 55 Receiver Input _ Sentence Equalized Quadrature Sequence Equalized Inphase Sequence F i g u r e 4 .5 2 D F I R F i l t e r i n g u s i n g a 4 - tap filter similar, the corresponding ZFE spectra were not reproduced. In crosstalk noisy environments, the Z F E results in unacceptable decoding errors as it amplifies the signal level at high frequencies where the relative noise level is important compared to the propagated signal level. This results in noise enhancement at the receiver output. The magnitude of the transfer function synthesized by the ZFE is also small at low frequencies (small noise) and doesn't try to amplify the transmitted signal level at this range (as a way to increase the SNR level at the slicer). For these reasons, the ZFE is not reliable and it is ruled out of any practi-cal implementation for VDSL. Let's consider again the phase splitting equalizer of Figure 2.9. Typically, the inphase and quadrature equalizer filters are implemented as tapped delay lines with adaptive weighting coeffi-cients. The weight updating law depends on the cost function minimized. Let us define r n as the vector of M recent received signal samples at time n. M is the span of the equalizer. Similarly, c n is the inphase filter tap weights vector, and d n the quadrature filter tap weights vector. The outputs Chapter 4 Linear and DFE Equalization of VDSL Communication Links 56 10 12 14 16 18 Frequency (MHz) 10 12 Frequency (MHz) Figure 4.6 ZFE for VDSL1 (left) and VDSL4, 5, and 6 (right) of the in-phase and quadrature equalizers can be written in the following respective compact form: y n = c n r n y n = d n r n (4.5) (4.6) Before we develop any of the receiver filters, let's have a look at the SNR requirements first. Using the fact that the CAP signal can be considered as a superposition of two independent line codes, the probability of error for a C A P signal in the presence of Gaussian noise is double the probability of error for a ID P A M line code [24]: P = 2 1-- Q /VSNRM A °1D ) (4.7) where L is the number of multilevel symbols and o ] D is the ID standard deviation of the Chapter 4 Linear and DFE Equalization of VDSL Communication Links 57 transmitted symbols. From (4.7), we can derive the theoretical SNR requirement at the slicer input: Table 4.1 SNR Requirement in the Presence of Gaussian Noise for P e = 10 Signal Constellation 4 16 32 64 SNR (dB) 14.5 21.5 24.5 27.7 For 51.84 Mb/s we retain 21.5 dB since the additive noise signals are Gaussian (see later). 4.3.1 F r a c t i o n a l l y S p a c e d E q u a l i z a t i o n Using a higher sampling rate than required is a common practical procedure in order to avoid aliasing distortion. This technique is known as Fractionally Spaced Equalization and could be associated with any type of the equalization schemes considered in this thesis [10]. Generally, the performance of an equalizer is sensitive to the sampling phase for baud spaced signal sampling. FSLE uses a sampling rate of 1/T' = i/T. Typically, i is 3 or 4 and provides relatively robust results against degradations caused by variations in phase sampling compared to baud-spaced filters. FSE receivers are also more flexible than a baud sampler for receiver synchroniza-tion (time recovery). A more general result is that a fractionally spaced equalizer was shown in [32] to provide optimum filter performance for any receiver. 4.4 The Mean Square Error (MSE) algorithms The M S E minimizes the joint effect of ISI and noise and allows both residual ISI and noise. This ensures a better probability of error than the zero forcing equalizer and the matching equalizer. The equalizer weights are adjusted to minimize the mean square value of the error between the sequence of transmitted symbols and their estimates. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 58 4.4.1 The L M S algorithm The simplicity of this algorithm is behind its wide spread use and sets it as the benchmark to which adaptive equalization algorithms are usually compared. The L M S minimizes the cost function in (4.8), which is the mean of the 2D squared error. The derivation of the L M S algorithm from (4.8) is closely related to the steepest descent minimization of J, except for the randomiza-tion of the cost function's gradient. This leads to the tap-weight update algorithm of (4.9). J = E { ( y n - a n ) 2 + ( y n - b n ) 2 } (4.8) w k (n + l ) = w k ( n ) - i a - ^ - (4.9) Using an instantaneous estimate of the gradient in (4.9) leads to the well known L M S algorithm: c n + i = c n - a ( y n - a n ) r n (4.10) d n + i = d n - a ( y n - b n ) r n (4.11) where a is called the adaptation step size parameter. Computer simulations show that when the L M S algorithm was initially adapted without a training sequence we cannot obtain convergence even for the noise-free environment and assuming the best V D S L propagation conditions (through short loops). When the transmitted sequence is not available to the DSL receiver, the latter has to make estimates of the sent symbols using the tap-update equations: c n + l = c n - a ( y n - a n ) r n ( 4- 1 2) d n + 1 = d n - a ( y n - b n ) r n (4.13) where the "hat symbols" are the outputs of the receiver slicer in the Decision Directed (DD) Chapter 4 Linear and DFE Equalization of VDSL Communication Links 59 -5 -4 -3 -2 5 - 5 - 4 - 3 -2 -1 1 2 3 4 5 Figure 4.7 Non-convergent and diagonal LMS solutions mode. The type of wrong solutions we found is reported in Figure 4.7 and in Figure 4.8. Diagonal solutions are the most frequent among all wrong final states. They are obtained when both the inphase and quadrature filters synthesize the same transfer function as shown on the two most right plots of Figure 4.7. In the Decision-Directed mode, the L M S behavior is dependent on the initial tap-weight values. We noticed that with initializing the inphase tap weights with the transmitter inphase impulse response we can get sometimes the convergence over the inphase dimension. Other wrong convergence lead to a different signal constellation as illustrated in the right of Figure 4.8. The divergence of the L M S is not surprising as it is a feedback system and needs special attention to converge. Since the L M S doesn't blindly converge for short loops, no tests for longer loops is necessary and its usage for V D S L in the DD mode is ruled out. 4.4.2 The Four-CAP trained LMS Using a 4-CAP training sequence, we were able to produce the results shown in Figure 4.9 and Figure 4.10. We notice a very fine convergence from the neat final signal constellation and Chapter 4 Linear and DFE Equalization of VDSL Communication Links 60 -v «, ».* * '> f. #. * « * * * * V *• », * "» * * ?. * f." \ • « V at. 4* •t * "# a .'* 4 - - - f» « < V- * --4 -3 -2 -J 0 I Z 3 Figure 4.8 Wrong LMS convergence 1 ^$&^M$M>::'-Figure 4.9. Signal constellations of a 16-CAP system tested over VDSL1 S using the LMS with a 3000-long 4-CAP training sequence - plots are made after 8,000, 15,000, and 250,000 iterations in the DD mode(u = 10"4) eye diagram plots. The PSD of the filtered signal at the output of the L M S equalizer was also plotted in Figure 4.11 for VDSL1 Short. The flat channel output spectrum indicates that channel distortion was fully compensated for, as its shape is similar to that of the transmitted C A P signal. The type of inphase transfer function synthesized by the L M S receiver is also shown at the left of Figure 4.11. It shows an amplification of the signal level at high frequencies to compensate for the channel attenuation. From the last section, we mentioned that blindly converging the L M S is tedious and Chapter 4 Linear and DFE Equalization of VDSL Communication Links 61 Figure 4.10 Eye diagrams of VDSL1 S equalized using the LMS filter after 8,000, 15,000 and 250,000 iterations (about 5 msec of setup time) Figure 4.11 The inphase transfer function and inphase filter output for the LMS receiver usually doesn't succeed to mitigate the ISI corrupting the equalizer's input. In this section, we see how the convergence of the L M S is very attractive when it happens. The need of a training sequence with the L M S rules out its practical usage for V D S L transmission because of the reasons stated in 4.5. The alternative to a training sequence is to set the equalizer initial mode with a blind algorithm and then switch to the L M S as explained later. 4.5 B l i n d E q u a l i z a t i o n For a brief reference on the history of blind equalizers and some of its interesting issues Chapter 4 Linear and DFE Equalization of VDSL Communication Links 62 refer to [14]. At least two incentives are behind blind equalization for VDSL[8]: 1. Blind start-up increases the receiver compatibility with other transceivers and makes point-to-multipoint network restart easier after failure, since the transmitter doesn't have to interrupt its broadcast transmission each time a new receiver starts. This way, we avoid the use of a costly bandwidth overhead. 2. Training sequences are often vendor specific and might lead to a non interoperability of service. Three steps are involved in blind equalization and can be summarized in [14]: 1. Setting the automatic gain control and performing the timing recovery. This gain stage consists in normalizing all signal constellations to a unit energy and compensating for the analog front end disturbance. 2. Adapting the equalizer's tap coefficients with a blind equalization algorithm until the eye diagram is open (or the M S E between the slicer input and output is below a threshold). 3. Switching to Decision-Directed mode and decoding the output of the slicer. Blind convergence is affected by two factors: the ISI amount and the residual value of the cost function (after convergence). Among the blind algorithms in use we distinguish the R C A , C M A and M M A . During initial training, ISI is the major problem rather than noise and it will be our focus for the upcoming three subsections. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 63 4.5.1 The Reduced Constellation Algorithm (RCA) The R C A is a generalized 2D form of the Sato algorithm [11], which minimizes the following cost function: J R C A = E { | Y n - R r c a c s i g n ( Y n ) | 2 } (4.14) where csign is the complex sign function and R r c a is the R C A modulus, which is a function of the first and second order statistics of the symbols given in (4.15). E{a 2 } E{b 2 } R = 1 " J = 1 N J (4 15) c a E{|a n |} E{ |b n | } 2^ and b n are the transmitted inphase and quadrature symbols, considered independent and identi-cally distributed. Y n is the complex output of the 2D equalizer. The tap-weight update equations are derived from the minimization of (4.14). C n+1 = C n - « [ y n - R r c a S g n ( y n ) ] r n ( 4 - 1 6 ) d n + l = d n - « [ y n - R r c a S g n ( y n ) ] r n ( 4 - 1 7 ) R C A introduces correction terms to the tap-updating equations by computing the errors with respect to a reduced signal constellation made out of four points ( ± R r c a , ± R r c a ) • Because of the use of a reduced constellation size, the probability of making errors is reduced and this leads to an initial convergence, contrarily to the LMS algorithm, as illustrated in the next three sections. 4.5.1.2 Short Loops During the first few tens of thousands iterations, the outperforming of R C A to L M S is clear as we succeed to see some opening in the eye diagram. Since we use 16-point constellations, Chapter 4 Linear and DFE Equalization of VDSL Communication Links 64 a 4-point fixed reference constellation wil l result in initial big error values for the R C A . The learning curves are still meaningful in this case and have half the values of the R C A cost function. Figure 4.10 shows that after about 50,000 iterations all short loops converge and the algorithm -4 reaches a steady state (for \x = 10 ). Therefore, the algorithm's performance can't be improved any more and the R C A doesn't fine converge. The signal space diagrams would look "broad" even after a longer number of iterations. This is illustrated by the similarities in the two right figures of the eye diagrams (Figure 4.9) and signal constellation (Figure 4.10). After convergence, the signal Figure 4.9 Eye diagrams for the RCA applied to VDSL1 Short after 30,000 (left), 50,000 (middle) and 500,000 (right) iterations constellations are less clear than the L M S , as expected. This can further be seen by comparing the right most eye diagram plot of Figure 4.9 and that of Figure 4.10, illustrating the L M S conver-gence. Comparison of the signal constellations is also readily interpretable (refer to the right plots in Figure 4.10 and Figure 4.9). Another performance characteristic for R C A is the normalized difference between the R C A cost function and the wiener mean squared error, which is defined as: (4.18) Chapter 4 Linear and DFE Equalization of VDSL Communication Links 65 3 •jifi*' 1*9 • -die' 2 a *3T -f? -^ F 1 ;# • 1 2 -2 Figure 4.10 Signal Constellations for the RCA applied to VDSL1 Short after 30,000 (left), 50,000 (middle) and 500,000 (right) iterations 6 8 Iterations VDSL1 VDSL2 VDSL3 VDSL4 VDSL5 Figure 4.11 RCA Learning Curves for Short Loops where e is a measure of the variance discrepancy between the sequences at the transmitter ( o d ) 2 and receiver filter output (0"~). It is zero for the wiener optimum filter. The highest e is reached for VDSL4 , to no surprise, as it has the worst propagation condition. Table 4.2 shows that for short loops, £ is between 6% and 18.4%. The final convergence of the rest of the short loops is plot in Figure 4.12 Chapter 4 Linear and DFE Equalization of VDSL Communication Links Table 4.2 Performance of RCA at the steady state over Short Loops 66 Loop VDSL1 VDSL2 VDSL3 VDSL4 VDSL5 £ (%) 6 14.8 12 18.4 17.3 4* '# * •*. * * * * * * * *• * (dE M 0 * 0. * .*» '^ §r ;5#/. Figure 4.12 Steady state signal constellations for RCA applied to short loops VDSL2 S, VDSL3 S, VDSL4 S, and VDSL5) 4.5.1.2 Medium Loops For short loops we only considered the case where p, is equal to 10 because it's small enough to lead to a convergence and its speed is acceptable for V D S L set up times (less than 5 msecond). For medium loops, we shall see two different cases corresponding to two different values of |0.. 1. |X = 10~4: In this case, the M S E decreases slowly but keeps improving to a lower value until reaching its steady state. This is illustrated in Figure 4.13. The speed of convergence is slow and is classi-fied in the following order (with obvious notations): Vvdsl4M < Vvdsl6 < V vdsllM < Vvdsl2M < Vvdsl3M (4-19) The longest number of iterations we have chosen to go up to is about 3.5 106 (about 13 Msymbols in a four times oversampled system). This is equivalent to a setup time of around 1 second, which is a reasonable tolerance for V D S L blind start-up. The signal constellations after this large Chapter 4 Linear and DFE Equalization of VDSL Communication Links 67 P f S A V K _ _ - 5 V D S L 1 V D S L 2 V D S L 3 V D S L 4 " 4 I V D S L 6 i i i— i .4 I I ' ' ' >-O 0.5 1 1.5 2 2 .5 3 Iterations X 1 QH Figure 4.13 R C A Learning Curves for Medium Loops ((i = 10~4) number of iterations is plotted in Figure 4.14. As a consequence of the worse propagation conditions, we found poorer e values than previously (Table 4.2). Choosing a smaller n leads to an even slower convergence and makes the blind start-up not attractive for VDSL. % % :* * • * • * *. » I 1 :%r 1, « * * | 10 * •* * =?#- 3 * i * * * * % #> * » •* * a . • ;A.-> • "\:"/k-' j ^ •••r.-.r.sc • • >'•":•. • .- ' • ' * -Figure 4.14 Steady state signal constellations for R C A applied to medium loops (top left to the right: VDSL1 M , VDSL2 M , and VDSL3 M , bottom left to the right: VDSL4 M , and VDSL6) Chapter 4 Linear and DFE Equalization of VDSL Communication Links 68 Table 4.3 Performance of R C A at the steady state over Medium Loops Loop V D S L l VDSL2 VDSL3 VDSL4 VDSL6 e (%) 34.61 31.07 33.07 35.40 35.71 -0.5 -1 sa U -1-5 CO .M | -2 Z -2.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Iterations x 1 0 s _ 3 Figure 4.15 R C A Learning Curves for Medium Loops (u = 10 ) 2. n = l ( f 3 : The convergence in this case is about 10 times faster (see Figure 4.15) but does not lead to the right solution all the times as shown in Figure 4.16. Choosing an even bigger [i doesn't converge the algorithm. 4.5.1.2 Long Loops The convergence of the R C A in this case is even more difficult to get than the previous _4 case because of the stronger channel attenuation and distortion. | i = 10 is considered a relatively large value, for which the algorithm diverges quickly. The M S E reaches its steady state value in about 15,000 iterations, after which the algorithm doesn't improve (see left of Figure VDSL6 Chapter 4 Linear and DFE Equalization of VDSL Communication Links 69 • p v 3 0 ; ; # r V f^ei-: •iSfe; - # i • # : ' < fc i f Figure 4.16 Signal Constellations after 500,000 iterations for: a) VDSL1M, b) VDSL2M, c) VDSL3M, d) VDSL6 4.17). For | i = 1 0 - 5 , the convergence is slower and better but wasn't enough to lead to interpret-able signal constellations. For the case where \i = 1 0 - 6 , the algorithm diverges quickly. From the above three sections, we found out that the R C A has a drawback of converging to wrong solutions when applied to V D S L loops. For some medium and for all long loops, the R C A conver-gence is not possible to obtain for a rate of 51.84 Mb/s and under a blind setup time constraint of 1 second. The C M A is known to be a more robust algorithm (as it uses fourth order statistics of the signal) and is beforehand a better algorithm. C M A will be investigated in the following section as an alternative to RCA. 4.5.2 The Constant Modulus Algorithm (CMA) In this case, the filter is set to minimize the cost function of (4.20), which is a measure of the dispersion of the complex receiver output around a circle with a radius given by (4.21). Chapter 4 Linear and DFE Equalization of VDSL Communication Links 70 2 2.5 Iterations -4 -5 Figure 4.17 RCA Learning Curves of Long Loops: (X = 10 (left) and \i = 10 (right) W = E { ( | Y n | 2 - R c ) 2 } BIN 4 } E { | A n | 2 } (4.20) (4.21) where A n is the transmitted complex symbol. The inphase and quadrature tap-weight iterative update equations are respectively: c n + l = c n - a ( | Y n | 2 - R c 2 ) y n r n d n + i = d n - a ( | Y n | 2 - R c 2 ) y n r n (4.22) (4.23) C M A uses both channels for the tap update, and for that it is a true 2D cost function, in the sense that quadrature channel information is used for the equalization of the inphase channel, and vice versa. C M A differs from R C A by referring to a circle rather than a four-point constellation in order to minimize the cost function. It tries to fit the equalizer output into a ring of constant Chapter 4 Linear and DFE Equalization of VDSL Communication Links 71 modulus. Even higher statistics can be defined with C M A , but we limit this work to only practi-cally manageable computational load. We start by evaluating the performance of C M A over short loops. For short loops the speed of convergence is comparable to that of R C A (using M-CMA = 10 - 5)- This convergence is more robust, though, as C M A is found to be better poised to avoid wrong diagonal solutions. From Table 7 we notice that for short loops, the wiener mean squared error shows an outperforming of C M A over R C A after reaching the steady state. " o 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Iterations x 1 D * Figure 4.18 CMA Learning Curves for Short Loops Table 4.4 shows that for short loops £ is between 2.41% and 9.24% which presents a clear improvement over the performance of RCA. The disadvantage of C M A is that it converges to the wrong phase and therefore needs an adaptive rotator (see Figure 4.19 and Figure 4.20). This makes the C M A algorithm an expensive solution for V D S L and rules out the usage of C M A as a blind algorithm for VDSL. Chapter 4 Linear and DFE Equalization of VDSL Communication Links Table 4.4 Performance of CMA at the steady state over Short Loops 72 Loop VDSL1 VDSL2 VDSL3 VDSL4 VDSL5 8 (%) = ID" 4 9.72 7.24 9.55 - 3.25 5.21 5.54 6.46 . 9.24 2.41 r 1 = 10 5 & •#/ •m. * •*> ^ ^ ' J'i\h' ' • .-.'-A &*-^  Figure 4.19 CMA Signal Constellations for short loops after a setup time of 1 second We see no need for further developments on the application of C M A for subsequent loops and the curves of Figure 4.21 concerning longer loops are shown only for reference. No conver-gence was obtained for long loops within a setup time specifications of 1 second. 4.5.3 T h e M u l t i M o d u l u s A l g o r i t h m ( M M A ) We consider the M M A algorithm, as defined in [8], mostly for square and non-dense j applications. The M M A cost function is a measure of the dispersion of the equalizer output around multiple linear moduli. The cost function we retain for V D S L is given by: Chapter 4 Linear and DFE Equalization of VDSL Communication Links 73 * * to % •« m •* •* * * -• • • • Figure 4.20 C M A Signal Constellations for medium loops after a setup time of 5 mseconds Figure 4.21 C M A Learning Curves for medium (left) and long Loops (right) J M M A = E [ y n - R La ( y n ) ] 2 + [ y n - R m m a ( y n ) ] 2 (4.24) where y and y n are the respective inphase and quadrature filter outputs. The R m m a value depends Chapter 4 Linear and DFE Equalization of VDSL Communication Links 74 on the region of the complex space in which the equalizer output is located. For square C A P constellations, R m m a is given by (4.25). (4.25) The update equation for the inphase and quadrature dimensions, derived from J M M A A R E : c n + l = C n - a ( y n - R m m a ) y n r n (4.26) d n + l = d n - a ( y n - R m m a ) y n r n (4.27) We notice that applying a phase rotation to y n and y n yields a different value for the cost function in (4.24). Therefore, unlike C M A we reach the right signal phase after convergence. 4.5.3.2 Short Loops We found that for this set of loops, M M A converged slightly more quickly but more often Figure 4.23 M M A Learning Curves for Short Loops than R C A . Our performance index of Table 10, along with Figure 4.23 and Figure 4.24 highlight Chapter 4 Linear and DFE Equalization of VDSL Communication Links 75 this result. V D S L applications requiring a short setup time and running over VDSL4 S or VDSL5, I # * * • * * *-.*• * * -•# * * • -» ,* * * » I, I * * * •m * Figure 4.24 MMA Signal Constellations for short loops after 5 mseconds of setup time should be accommodated with a slower rate to get a comfortable convergence. For both loops, the receiver has some difficulty to cancel out the nulls of the spectrum caused by the bridged taps. Comparing Table 4.5 and the previous results shows that the M M A performance over short loops is somewhat intermediate between R C A and C M A but all three algorithms perform well for these short range channels. Table 4.5 Performance of MMA at the steady state over Short Loops (pi = 10~5) Loop VDSLl VDSL2 VDSL3 VDSL4 VDSL5 e (%) 3.01 4.86 3.87 8.05 5.86 4.5.3.2 Medium Loops This case is more difficult to converge and the final signal constellations are broader given the same setup time. For V D S L 4 M , more training time is needed to reach convergence. Therefore, the bit rate of 51.84 Mbit/s should be downgraded. Again, the difficulty of convergence Chapter 4 Linear and DFE Equalization of VDSL Communication Links 76 Iterations x 1 n e Figure 4.25 M M A Learning Curves for Medium Loops is perfectly described by the normalized M S E curves (Figure 4.25), in the sense that curves with smaller values represent loops over which the receiver works better and the eye diagram is more open. Comparing Table 4.3 and Table 4.6 shows a clear improvement of performance of M M A over R C A and the value of e is better by at least 17% at the 51.84 Mb/s rate. Table 4.6 Performance of M M A at the steady state over Medium Loops (U, = 10 ~5) Loop V D S L l VDSL2 VDSL3 VDSL4 VDSL6 e (%) 9.47 2.20 4.01 18.4 12.98 VDSL4 M converged for a bit rate of 25.92 Mbit/s and a 4-CAP constellation (as shown in the bottom right of Figure 4.26). V D S L applications running over V D S L l M , VDSL4 M and VDSL6 , for which setup time is a stringent requirement should be accommodated with a four point constellation and a slower rate of at most 25.92 Mbit/s. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 77 r?ii< :p0 :v$it*. "4^i\ 'SB'' Ife- sfe > "i#>: si 3 i Figure 4.26 MMA Signal Constellations for Medium loops after 1 second of setup time 4.5.3.2 Long Loops No convergence at a rate of 51.84 Mbit/s was obtained for any of the loops in this set. We tried a lower rate system using an 8-CAP signal constellation and a bit rate of 38.88 Mb/s. The M M A is demonstrated in [8] to work better than R C A for non-square signal constellations and would be a good choice here again. Simulation results show that the 8-CAP M M A system didn't converge for long loops and was prone to wrong diagonal convergence. Actually, even for short loops its performance wasn't as good as the 51.84 Mb/s 16-CAP system, as illustrated in Figure 4.27. A 25.92 Mb/s system using a 4-CAP constellation is now tested. We found that the M M A was able to equalize long loops as shown in Figure 4.28. The convergence is sometimes only rough, and we barely see some opening in the eye diagrams, but it is enough for the L M S to converge if switched to, and if the setup time is allowed to exceed 1 second. For V D S L 4 L , no convergence was obtained and we see again the diagonal solution. Even slower rates should be tested for this case. The highest V D S L rate we were able to get V D S L 4 L convergence for is Chapter 4 Linear and DFE Equalization of VDSL Communication Links 78 12.96 Mb/s (the symbol rate was 6.48 Mbauds), as shown in Figure 4.28. The third column of Figure 4.27 8-CAP signal constellations for VDSL1 S (middle) and VDSL4 S (right) Figure 4.28 shows the signal constellation of a 12.96 Mb/s rate over long loops. These signal constellations were drawn for the same setup time (1 second) and using the same number of symbol points (2000), as for all of the signal constellations in this thesis. M M A is well suited for applications of equalization and carrier recovery, but as it tries to do both at the same time, it is subject to wrong solutions as well. For all V D S L loops, linear receivers were able to provide convergence in a noise-free environment, at least at one of the V D S L rates. To fine converge our results we will make use of the L M S in the remaining of this chapter and then look at the system performance in a noisy environment. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 79 Table 4.7 Summary of MMA performance Data Rate (Mb/s)/ Loop Short Medium Long 51.84 1,2, 3 4, 5 (broad) 2,3 1 (broad) 6 (very broad) None 25.92 , - 4(broad) 1,2, 3, 7 (very broad) 12.96 - - 4 Figure 4.28 VDSL4 L at 25.92 Mb/s (left) and 12.96 Mb/s (middle and right) 4.6 The Combined MMA-LMS Algorithm M M A wil l be used in conjunction with the L M S . Its use serves to blindly recover the transmitted sequence. Once converged, the receiver switches to the L M S . The first step leads to a partially open eye diagram. The second step is meant to completely open the eye. We consider the M M A - L M S receiver performance in the presence of self-FEXT and A W G N . Our results are best described by the graphical illustrations of convergence in the next three sections. 4.6.1 Short Loops From our simulations, we notice a neat recovery of the transmitted symbols for the first three loops. Figure 4.29 illustrates the clarity of convergence for VDSL1 S at a data rate of 51.84 Mbit/s. For VDSL4 S and VDSL5, the L M S needs more setup time to get a better convergence as shown to the right of Figure 4.29. A system operating at 25.92 Mb/s over these two channels will provide a much better convergence during the same setup period. Chapter 4 Linear and DFE Equalization of VDSL Communication Links 80 1 ^ > • if T*f .' i - •; . # •••:^ r -i|v -^ p:'-•$f; ^ Figure 4.29 Performance of the MMA-LMS algorithm for VDSL 1 S, VDSL4 S and VDSL5 4.6.2 Medium Loops We were able to get an acceptable convergence of V D S L 1 M , V D S L 2 M , and V D S L 3 M at the data rate of 51.84 Mbit/s as shown in Figure 4.30. For VDSL4 M and VDSL6, a neat conver-gence couldn't be reached with a rate higher than 12.96 Mb/s after about 1 second of running the L M S in the DD mode (and a setup time of 1 second for M M A ) . Figure 4.30 Performance of MMA-LMS for medium loops (top: VDSL1 M, VDSL2 M, bottom: VDSL3 M, VDSL4 M) Chapter 4 Linear and DFE Equalization of VDSL Communication Links 81 4.6.3 L o n g L o o p s The highest convergent data rate we were able to obtain is 25.92 Mbit/s using a four-point Figure 4.31 Performance of MMA-LMS for long loops after 1 second of setup time constellation, except for VDSL4 L , for which this rate is only 12.96 Mbit/s. The signal constella-tion plots in Figure 4.31 only evaluate the quality of convergence of each loop at the lower rate of 19.44 Mbit/s, as the L M S wasn't able to work out a neat convergence even after a total of 1 second in the DD mode. Generally, the LMS by itself wasn't able to work out a convergence for a divergent case (within our time limitations at least), but it made the symbol decoding much easier and less error prone for the decision device. The M M A - L M S receiver showed robustness against noise and converged for all loops. This result comes to no surprise as the main challenge for V D S L channels is the ISI distortion. Chapter 4 Linear and DFE Equalization of VDSL Communication Links Table 4.8 Summary of MMA-LMS convergence over VDSL loops Loop Data Rates (Mb/s) Short Medium Long 51.84 1, 2, 3 neat 4, 5 broad None None 25.92 - 2, 3 neat 1 broad 1, 2, 3, 7 neat 12.96 - 4, 6 neat 4 neat Chapter 5 Conclusions and Suggestions for Future Work 82 Chapter 5 Conclusions and Suggestions for Future Work 5.1 Conclusions In this thesis we investigated the performance of linear and DFE V D S L transceivers under self-FEXT and W G N conditions. We found that receiver performance is more affected by the channel ISI rather than additive noise impairment. Noise effect depends itself on the channel type and the cable binder in which the V D S L service is provided. Different test loops are proposed by the ANSI T1E1.4 standardization working body and they present the benchmark against which our receivers are tested. Simulation results show that among this set of loops full rate V D S L links could be established with the R C A , C M A and M M A linear receivers. Noise predictive and conventional DFE structures are found to be difficult to converge and very sensitive to the setup parameters. It wouldn't be appropriate for them to work at V D S L rates in a noisy environment. Blind receiver startup is a desired feature for VDSL. The M M A algorithm was proven to be the optimum in terms of its speed and quality of convergence. The M M A steady state performance is not satisfactory for low error rate. Switching from the M M A to the L M S after initial blind startup improves the overall performance because of the fine final state of the L M S . Simulation work for long range V D S L showed that for a combined M M A - L M S algorithm, 52 Mbit/s can be supported over short loops and for some medium loops and even under self-FEXT and W G N impairments. For medium and long loops, comfortable convergence happens at lower rates (i.e. 25.92 Mbit/s and 12.96 Mbit/s). Intermediate rates between 51.84 Mbit/s and the latter two bit rate values were not able to be reached successfully because of their non-square constellations, which makes them error-prone and difficult to converge. Chapter 5 Conclusions and Suggestions for Future Work 83 5.2 Suggestions for Future Research In this thesis we only considered a single carrier modulation technique as our line code (CAP). Performance evaluation of the DMT code would be helpful in assisting the standardization process of VDSL. As mentioned in the thesis, noise impact over V D S L rates is important. Further work has to be carried on to test the effect of A D S L Next and RFI interference. These noise models should be updated according to the emerging services that wil l share the same V D S L environment. Receiver algorithms using higher order statistics were not simulated. Simulation and/or building of such receivers would be useful. Another area of research for V D S L is to find new techniques and cost functions that would avoid converging V D S L receiver algorithms to the wrong solutions. Finally, throughout this whole work we only considered issues that concern the subscriber side (i.e. V D S L Transmission Unit at the remote side). Similar investigation and research has to be done at the Central office side (VTU-C terminals). Glossary 2 B 1 Q Two Bits per Quaternary symbol (baseband) line code A D S L Asymmetric Digital Subscriber Line ANSI American National Standards Institute A W G American Wire Gauge A W G N Additive White Gaussian Noise B E A Blind Equalization Algorithm B R A Basic Rate Access BSR Basic Symbol Rate C A P Carrierless Amplitude and Phase modulation CSA Carrier Serving Area CO(s) Central Office(s) DA Distribution Area D A C Digital to Analog Converter DD Decision Direct DFE Decision Feedback Equalizer D M T Discrete Multi-Tone DS Down-Stream DTV Digital TV D W M T Discrete Wavelet Multi-Tone FDD Frequency-Division Duplex F D M Frequency-Division Multiplexing FEC Forward Error Correction 84 F E X T Far End Cross-Talk FFF Feed Forward Filter FFIF Feed Forward Inphase Filter FFQF Feed Forward Quadrature Filter FTTC Fiber To The Curb FTTSA Fiber To The Serving Area FTTx Fiber To The Neighborhood, Cabinet, Curb etc. HDTV High-Definition T V HDSL High-bit-rate Digital Subscriber Line IDSL ISDN - DSL ISDN Integrated Services Digital Network Mbit/s Mega bits per second M D S L Moderate Bit Rate DSL M S E Mean Square Error M V L Multiple Virtual Lines N E X T Near End Cross-Talk O A M Operations And Maintenance O N U Optical Network Unit POTS Plain Old Telephone Set PSD Power Spectral Density PSTN Public Switched Telephone Network Q A M Quadrature Amplitude Modulation R A D S L Rate Adaptive Digital Subscriber Line 86 RRD Revised Resistance Design SDMT Synchronized D M T SDSL Symmetric Digital Subscriber Line SNR Signal to Noise Ratio U A D S L UniversAl DSL UTP Unshielded Twisted Pair US Up-Stream V D S L Very-high-bit-rate Digital Subscriber Line V T U - C V D S L Transmission Unit - at the Central office VTU-R V D S L Transmission Unit - Remote (subscriber site) xDSL Generic term referring to all D S L technologies (i.e. ISDN, H D S L , A D S L , VDSL) Bibliography [I] W. 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J., "An Introduction to Blind Equalization", V D S L Project, ETSI/STS TM6 TD-7, 26/1-30/1 1998, Madrid, Spain [15] Umari, M.H. , "Effect of colored noise on the performance of L M S adaptive equalizers and predictors", ISCAS Proceedings, vol. 5, pp. 2565-2568, 1992 [16] Chen, W.Y., Im, G.H., and Werner, J.J, "Design of Digital Carrierless A M / P M Transceivers", ANSI T1E1.4 Contribution T1E1.4/92-149, August 19, 1992 [17] Werner, J.J., "The HDSL environment", IEEE JTSC, vol.9 , no. 6, pp. 785-800, August 1991. [18] Chen, W.Y., "DSL Simulation Techniques and Standards Development for Digital Susbcriber Line Systems", Macmillan Technical Publishing, Indianapolis, Indiana, 1998. [19] Zimmerman, G.A., "Achievable Rates vs. Operating Characteristics of Local Loop Transmission: HDSL, HDSL2, A D S L and VDSL" , Signals, Systems and Computers, vol.1, pp. 573-577, nov. 2-5, 1997 [20] Im, G.H., and Werner, J.J., "Bandwidth-Efficient Digital Transmission up to 155 Mb/s over Unshielded Twisted Pair Wiring", Conf. Record ICC, 1993, pp. 1797-1803. [21] Wang, A. , "Effect of Bridged Taps on Channel Capacity at V D S L Frequencies", M.A.Sc. thesis, Dept. of Electrical and Computer Engineering, U B C , 1998 [22] Working Group ANSI T1E1.4, "Recommendation for V D S L Duplexing Method", ANSI T I E 1.4 Contribution T1E1.4/99-059R2, Costa Mesa, C A , March 8-12, 1999 [23] V D S L Coalition, "Very-High-Speed Digital Subscriber Lines (VDSL) Draft Technical Specification", Revision 0.01, April 1999. [24] Werner, J.J., "Tutorial on Carrierless A M / P M - Part II: Performance of bandwidth-efficient line codes", Austin, Feb. 16, 1993. [25] Rezvani, B. and McDonald, D., "Spectral Management", T1E1.4 Spectrum Compatibility for twisted pair loop transmission systems, February 1-5, 1999, Hissimmee, FL . Bibliography 89 [26] Papir, Z., and Simmonds, A. , " Competing for throughput in the local loop", IEEE Commun. Magazine, May 1999, pp.61-66. [27] R. Baines, "Discrete Multitone (DMT) vs. Carrierless Amplitude/Phase C A P Line Codes", Analog Devices Inc. whitepaper, May 20, 1997; http://www.analog.com/publications/ whitepapers/whitepapers.html [28] J. W. Cook, R. H. Kirkby, M . G. Booth, K. T. Foster, D. E. A . Clarke, and G. Young, "The Noise and Crosstalk Environment for A D S L and V D S L systems", IEEE Commun. Magazine, May 1999, pp.73-78. [29] W. Goralski, "xDSL Loop Qualification and Testing", IEEE Commun. Mag., May 1999, pp. 79-83. [30] F. Sjoberg, "High Speed Communication on Twisted-pair Wires and Low Complexity Multiuser Detectors", Master Thesis, Lulea University of Technology, April 1998, Sweden. [31] J. Cioffi et al., "Very High Speed Digital Subscriber Lines", IEEE Commun. Mag., April 1999, pp. 72-79. [32] K. Sistanizadeh and D. Jones, " Channel Equalization for Very High-Speed Digital Data Communication", IEEE Transactions on Circuits and Systems, 1991. [33] A . Wang, "Effects of Bridged Taps on the channel capacity of very high-bit-rate digital subscriber lines", M.A.Sc. thesis, Department of Elec. and Computer Eng., U B C , June 1999. [34] J. M . Cioffi, "A Multicarrier Primer", tutorial paper, Amati Communications, avaialble at http://www-isl.stanford.edu/~cioffi/papers.html [35] T 1.413 Editor: F. Van der Putten, "T 1.413 Issue 2", Standards Project for Interfaces Relating to Carrier to Customer Connection of Asymmetrical Digital Subscriber Line (ADSL) Equipment, revision 4, June 12, 1998 (T1E1.4/98-007R4). [36] L . Garth, J. Yang, and J. J. Werner, "Blind Equalization Algorithms with automatic constellation phase recovery for dual-mode C A P - Q A M reception", IEEE 1999. [37] D. G. Messerschmitt, "linemod software", available at http://www-isl.stanford.edu/~cioffi/ linemod/linemod.html. Bibliography 90 [38] T1E1.4 Editor, "Draft Technical Report for Single-Carrier Rate Adaptive Digital Subscriber Line (RADSL)", Revision 3, Document No. T1E1.4/99-161, available at the T1E1.4 online database files: http://www.tl.org/index/0346.htm [39] Bellcore, "The spectral compatibility of SDSL with T1.413 A D S L and G.922.2-G.lite", T1E1.4 online database, project: Spectral compatibility, Orlando Florida, February 2-3 1999. [40] K . J . Bannan, "Video-Over-Copper gets northern exposure", Inter@ctive Week Online, 30/8/ 1999, available at: http://www.zdnet.com/intweek/stories/news/0,4164,2323854,00.html Appendix A . Transmission parameters A . l . Data Rates Different asymmetric transmission profiles have been defined in [23]. Our simulation work followed the standard North American baseline and downgraded downstream transmission profiles summarized below. The carrier frequency as well as downstream and upstream rates have to be scalable to integer multiples of a certain Basic Symbol Rate (BSR), set to 67.5 (Khz and Kbaud respectively). Table A. 1 Standard asymmetric bit rates Symbol Rate (Mbaud) DS/US Constellation size DS/US Carrier rate(Mb/s) DS/US(^f ratio) 12.96/1.08 16/64 51.84/6.48 (8) 12.96/1.08 8/16 38.88/4.32 (9) 12.96/1.08 4/8 25.92/3.24(8) 6.48/0.81 16/16 25.92/3.24 (8) 6.48/0.81 8/8 19.44/2.43 (8) 6.48/0.81 4/4 12.96/ 1.62 (8) 3.24/0.81 16/16 12.96/3.24 (4) 3.24/0.81 8/8 9.72 / 2.43 (4) 3.24/1.08 4/4 6.48/ 1.62 (4) Table A.2 Standard asymmetric band allocation for downstream transmission Carrier frequency (MHz) Lowest frequency / Highest frequency (MHz) Maximum transmit PSD (dBm/Hz) 10.1925 2.42/17.97 -60 5.9775 2.10/9.88 -57 4.0500 2.11/5.998 -54 We notice that applications optimized for internet access would probably be best served with the first 6 profiles of Table 1. 91 Appendix A. Transmission parameters 92 A . 2 . S p e c t r a l s h a p i n g filters Square root raised cosine pulse shapes are used in order to minimizes inter-symbol interference. A rolloff factor of 0.2 was recommended [94]. The use of square root raised cosine Km. Figure A . l Raised Cosine Pulse (left) and Square Root Raised Cosine Pulse (right) impulses. pulses is motivated by the desire to get an overall nyquist shaping filter (Figure A . l ) . Notice that the square root cosine spectrum doesn't have sidelobes (Figure A.2). Practical hardware implementations of truncated versions of square root raised cosine pulses usually suffer from side-lobe effects. 0.2 0.4 O.B 0.8 1 1.2 1.4 1.6 1 B 2 Figure A.2 Theoretical spectrum of Square root raised cosine with a roll-off factor of 0.2 Appendix A. Transmission parameters 93 Figure A.3 In-phase (left) and quadrature (right) filter impulse response over [-4T.4T] The raised cosine impulse response is given by: sin(7U/r) cos(ant/T) n t / T \-(2at/TY (1.1) The implemented impulse response will be an approximation to the actual square root raised cosine equation (1.2) over a fixed time interval. _ sin(7t( 1 -a)t/T) + 4af/7/cos(TC(l +a)t/T) %t/T[\-{4at/T)2} The theoretical spectrum of the square root raised cosine is given by: G(f) = (T_ T for 0<\f\<^(\-a) (1.2) (1.3) For a 20% excess bandwidth system, a filter time span of [-4T.4T] could be considered adequate (32-tap filter in a 4 times over-sampled implementation). Appendix A. Transmission parameters 94 For C A P filtering, the choice of the square root raised cosine is motivated by the fact that: 1. in the structures where the pulse shaping is implemented at the transmitter only (raised cosine filter), the receiver filter only filters the out of band noises. 2. when implementing the pulse shaping at the transmitter and the receiver, the receiver filter performs noise filtering and also attenuates the frequency components of the noise present at the rolloff regions. More on this is discussed for CAP implementations in [24]. Appendix B. RLCG Parameters 95 Appendix B . R L C G Parameters B.l R, L, C, G parameters of twisted pair cables V D S L loops are modeled using certain primary and secondary parameters called R, L , C, and G. In this section, these parameters are being sketched for different gauge loops over the V D S L bandwidth range (0-30 MHz). Using these parameter models, it is easy to compute the transfer functions and insertion losses for all V D S L test loops proposed by the technical group T1E1.4 of ANSI in [14]. As a general rule, the insertion Loss in dB increases linearly with distance and logarithmically with frequency [19]. Figure B . l Series Resistances and Inductances of TP1 (1), TP2 (2), TP3 (3) and FP (fp) twisted pairs Appendix B. RLCG Parameters Conductance (mH/m) ( Conductance (mrfm) Frequency (Hr) „ , „ ' Frequency)*) , , „ ' Figure B .2 Shunt Conductances and Propagation Losses for TP1, TP2, TP3 and FP copper lines Appendix C. VDSL Loops Appendix-G»-A^DSL Loops VDSLO (null loop) 6.5 ft (2m) TP2 TP1 - .4mm or 26-gauge - see appendix for rlcg TP2 - .5mm or 24-gauge - see appendix for rlcg TP3 - DW10- see appendix for rlcg FP - flat untwisted pair - see appendix for rlcg VDSL1 (range test for given data rate) x (ft) TP1 ; y (ft) TP2 underground cable VDSL2 (flat wire in drop) z (ft) of TP2 aerial cable VDSL3 u(ft)ofTP2 aerial cable (reinforced tp in drop - "Kevin's Castle") VDSL4 (bridge tap) v(ft)ofTPl aerial cable 250ft (76.2m) FP (vertical) 250ft (76.2m) TP3 (vertical) s f-. m s 150 ft (45.7m) T P 2 ^ VDSL5 550 ft (167m) TP2 100 ft (30.4m) TP2 250 ft (76.2m) TP2 (short The Little Demon-) (underground cable (underground. 5-20-pair) pair) (overhead aerial) 50 ft (15.2m) TP3 horizontal YDSL6 1650ft (503m) TPl _ 650ft (198m) TP2 (medium) (underground cable 100-pair) (underground cable 100-pair) -VDSL 5-VDSL7 1 6 5 0 f t ( 5 0 3 m ) T P 1 2300ft (701m) TP2 (underground cable 100-pair) Flgmr* 5 - VDSL test loops. VDSL5 Appendix D. DFE Transceiver Structures and Performance 98 Appendix D. D F E Transceiver Structures and Performance D.l Optimum DFE performance The transfer function of the optimum CAP equalizer can be shown to be [24]: 2 * * „ ( / > - N ( S ) . | Z ( / _ „ / r ) | 2 T ^ n N(f-n/T) n = 0 w where Z ( / ) - FFTlsi.) + r.(01 = (20S</) «-2> and N(f) is the noise transfer function. The denominator in (1.1) sums all the folded spectra (m depends on the rolloff factor). S(f) is the desired signal's transmit power spectral density. Finally, rj is the 2D variance of the CAP signal. The optimum performance of a DFE based receiver is: M a r g ' " ^ = 7 ^ J 1 0 1°4 1 + I *(/-«•/w) 1 |d/ + ( - O V K r e , ) ' (1.3) For C A P / Q A M this simplifies to: Margin = 10 • l o g 1 0 f e x p f - ^ - • f/^/V^1 + SNRfitUedCf))]]-SNRreq (1.4) where S N R j o W e ^ is the ratio between the folded received signal and the noise, given by: SNRfolded(f) = I n = 0  A N(f + n-fbaud) 

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