Loop Qualification for xdsl

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1 Final Report for xdsl by Master of Science Thesis in Digital Signal Processing Department Applied Signal Processing Ericsson Telecom AB Document Number ETX/X/ARTP-2001: 002 And Department of Signals, Sensors & System at Royal Institute of Technology Document Number IR-SB-EX-0104 February 2001

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3 Abstract The enormous impact of the Internet in everyday life and the Telecommunications Act of 1996 opened up the global market for broadband data access. Today several types of Digital Subscriber Line (DSL) technologies are rapidly becoming standards for delivering this access on copper access network cables to the end user. In the competition of the available market for offering end users with new services like xdsl, operators face a number of challenges. These result from the fact that the cable network has a unique topology per user depending on type of cable, length of cable, splices and such. In order to offer the end user xdsl services in a cost efficient way, the operator needs to be able to pre-qualify the loop. At the initial stage of deployment the operators used to send out technicians both to the end user and the Central Office (CO) to pre-qualify the loop. This is a very costly exercise. The aim of this master thesis work is to simulate and implement models of copper network cables. The possibility to qualify the loop using single-ended testing should be investigated. Methods to investigate cable characteristics in presence of noise and estimates of channel capacity are to be developed and simulated. The results of the simulations show that the length of the cable can be estimated fairly accurate using single-ended testing. With the help of this length estimate and the input impedance of the loop, the transfer function of the loop can be estimated. With this at hand the channel capacity for e.g. ADSL can be estimated. This will enable the operators in the future to pre-qualify the loop. The operator can, based on this knowledge, give a go/no go to xdsl, and if possible, offer the end user a certain capacity (bit rate) on the connection. The reader of this report is presumed to have basic knowledge in signal processing, communication and electrical engineering. 3

4 Acknowledgements This master thesis work was done at the department of Applied Signal Processing, within Ericsson Telecom AB, Stockholm. First of all I would like to thank my colleagues Jonas Gustafsson and Stefan Allevad for their advice and for making everyday at the office a pure pleasure. Then I would like to thank my supervisor at Applied Signal Processing, Albin Johansson, for his enormous enthusiasm and support. A special thanks to Jan Boström, Access Application Lab, for his support and technical guidance. I would also like to thank Magnus Jansson, my supervisor at KTH, for his guidance and encouragement during the thesis work. Also, all the staff of both departments, Applied Signal Processing and Access Application Lab, deserves a big thanks for making the time during my master thesis interesting, inspiring and extremely funny. At last but certainly not least, personals thanks to my lovely girlfriend Anna for her support around the home during many late hours working on this report. 4

5 Abstract... 3 Acknowledgements Introduction Background Outline Purpose of this master thesis work Methodology Restrictions General xdsl information ADSL VDSL Telephone subscriber loop environment Subscriber loop structure General composition of the loop Problems with deployment Physical impairments Electrical impairments Testing Twisted pair channel modeling Model structure of the local loop Twisted pair cable Primary and secondary parameters Two port network ABCD parameters Transformer equivalent circuits Bridged taps Hybrid circuits Implementation and simulations Single ended testing Echo path Test pulse Bridged taps Distance estimation Noise model

6 4.6 Estimation of transfer function Capacity analysis Conclusions Future work Glossary of abbreviations Appendix A Calculation of primary constants according to ITU recommendations References

7 1 Introduction 1.1 Background Digital Subscriber Line (DSL) is rapidly becoming the standard for delivering broadband data access. xdsl is a copper loop transmission technology that makes it possible to deploy highspeed data access over millions of phone lines already in existence. Before this technology could be put into practical use, two things had to happen. First, the enormous impact that the Internet has effected our everyday life. Secondly, the Telecommunications Act of The fierce competition fostered by globalization of business makes it easy for even small companies to use Internet driven strategies. High-speed Internet connections are the future of business. Just as the Internet has changed the nature of global commerce, the information revolution has allowed non-technical people everywhere to become Web surfers. This new generation Web users have become accustomed by fast, constant and reliable access. The Telecommunications Act of 1996 had intent to deregulate the telecommunications industry and encourage competition in local services. The Act requires Incumbent Local Exchange Carriers (ILECs) e.g. Telia, to make Unbundled Network Elements (UNEs) and collocation space available to competitive service providers. This enables Competitive Local Exchange Carriers (CLECs) to offer broadband access to business and households. These major factors of course leads to a demand to offer the most cost effective means of highspeed connections. Since xdsl uses the existing telephone lines it is very attractive and cost saving technology for both ILECs and CLECs. Much better than the first far-reaching plans to connect every home with optical fiber cables. The general telephone line consists of a twisted pair, which is made up of two copper conductors (wires) twisted around each other. Thus, the high-speed data traffic will use the same set of copper wires that the analog voice band signal. This cable net is commonly known as the Public Switched Telephone Network (PSTN). The major idea however, is that the existing cables should be used the last distance from the Central Office (CO) to the subscriber and that fiber cables should be used for the long distance communication between the CO s. 7

8 The existing Plain Old Telephone Service (POTS) was not initially designed to carry broadband data access services. Therefore there are many potential difficulties that can rule out the deployment of xdsl in some regions. Some of these difficulties include old worn copper circuits, load coils, bridged taps, bad splices, broken cables and such. ILECs and CLECs have both relied on manual loop qualifications for giving a go/no go for xdsl deployment to the end user. This is an extremely costly procedure, since it requires several so called truck rolls (sending out technicians out on the field to make measurements). There are some previous efforts in making double-sided testing. This however requires equipment at the user side of the local loop. The equipment either has to be sponsored by the operator, or paid by the subscriber. This is not very likely since the customer will probably not buy any equipment if there is a risk it might not work. The most cost effective and customer friendly way to qualify the loop would be single-sided testing. This way the operator could quickly and easily respond to the customer question: Can I get xdsl?. A future answer might be: No you can t, because or Yes you can and since you live 1.5 kilometers from the nearest CO we can offer you a bit rate of, say 15 Mbit/s. Making the loop qualifying system advanced, and at the same time easy to use it can be used by a person with less insight in the complex world of xdsl, which also is a reduction of the deployment cost for the operator. Single-sided loop qualification shall to some extent be investigated within the scope of this master thesis work. 1.2 Outline The structure of the report will now be discussed briefly. The first chapter will contain some general xdsl information and background to the master thesis. Also the purpose, methodology and restrictions are discussed. In Chapter 2 a more detailed description of the telephone subscriber loop environment is presented. Deployment and problems such as cable impairments will be described. Also different methods of testing is discussed. In Chapter 3 twisted pair channel modeling will be stepped through. Chapter 4 deals with implementation and issues such as creating a test pulse, modeling the noise, examining the echo path and estimating distance, transfer function and capacity. 8

9 The conclusions of the simulations are presented in Chapter 5, together with suggestions for future work. A glossary of necessary abbreviations can be found in Chapter 6 and in Chapter 7 the references are listed. 1.3 Purpose of this master thesis work To be able to simulate and examine the pre-qualification of the local loop for DSL technologies, models of the copper network cables have to be constructed. Thanks to some previous research some modeling of twisted pair copper cables has already been performed. However, the adaptation this research for loop qualification purposes has not been conducted as of today. Therefore, the purpose of this master thesis work is to adapt the previous research in of twisted pair copper cables in [11] towards the loop qualification area. The thesis consists of building models of the copper network, which consists of analogue devices such as the hybrid, the transformer and the actual cable. Loop qualification to the extent of determining distance to customer and estimating the offered channel capacity should be simulated and analyzed for single ended testing. A suitable test signal for qualification should be determined and decided upon. The modeling should be verified by building a simulation chain for the test system using Matlab. The goal of the simulations is to determine if single ended testing can be used to determine distance to breakpoint/customer, and if an estimate of the channel capacity can be obtained from the test. The expected outcome of the master thesis is a simulation model and results for a loop qualification system. The aim is also to increase the knowledge within this expanding area within Ericsson Telecom AB so that Ericsson can position itself at the cutting edge of technology. 9

10 1.4 Methodology To get an understanding of xdsl in general and the deployment of such technologies, an initial literature study is conducted. This is carried on with an extensive literature study on the modeling procedures of twisted pair cables and analog front-end equipment. When the literature study is finished, the system model has to be worked out. Also test procedures have to be investigated. These shall be implemented, analyzed and be realistic. When the system model is finished a suitable test signal has to be constructed. Once the system is implemented, an algorithm for obtaining the distance of the cable from the received echo has to be developed. This has to work for a noisy environment so a noise analysis has to be made. Thereafter the channel capacity shall be estimated from an estimation of the true channel transfer function. Note that the channel transfer function is unknown since only single ended testing is investigated. 1.5 Restrictions As the simulations and theory will point out, the different combinations of faults or problems of deployment are innumerous. To be able to concentrate the master thesis on signal processing, system modeling and development, these faults and problems have to be limited. One concrete example of this is the choice of cables. Since there are several different types of twisted copper cables and each one has unique characteristics, only one type will be used in the simulations, the ETSI50 cable. The task is to conduct single ended testing. This will put some restrictions on the testing capabilities. What these are and suggestions to circumvent them will be suggested in the appropriate chapter. The noise models in existence are designed for the case when you have information about input/output relations from both sides of the loop, hence double sided testing. Therefore the noise will be modeled according to reasonable and measured known levels and then added to the echo from the transmitted pulse instead of using those models. 10

11 1.6 General xdsl information xdsl is a generic name for all DSL techniques. Some techniques currently progressing are ADSL, VDSL and HDSL. A short description of ADSL and VDSL will be given below to spur further reading. One of the main differences between xdsl modems and the old voice band modems is that a voice band modem operates over an end to end PSTN connection. The xdsl modems only operate over a transmission path named the local loop. The local loop can be described as the path in-between the CO and the customer premises. In-between the different CO s is a high-speed wideband optical network. This makes xdsl very cost effective compared to the far-reaching plans to install optical fibres to every customer. Another difference is that the copper wires normally carries analog voice-band traffic to make the POTS available. To serve POTS, a bandwidth of approximately 4 khz is necessary. This is sufficient even though the human audible range is roughly 20 Hz to 20 khz. The xdsl technologies however, take advantage of a great portion of the available bandwidth on the local telephone wire. The usable bandwidth on these cables can be as large as a couple of MHz and therefore able to serve a broadband communication ADSL ADSL is the first DSL technique to hit the market. ADSL stands for Asymmetric Digital Subscriber Line, which has its origin in the different up- and downstream data capacities. In the upstream, from customer to CO, a bit rate of up to 1 Mbit/s is used. For the downstream, from CO to customer, a bit rate of up to 8 Mbit/s is employed. ADSL also supports POTS simultaneously over the twisted pair cable. This is possible due to a splitter filter in the ADSL modem, which separates ADSL from POTS. ADSL uses Discrete Multi-tone (DMT), which is a QAM modulation method with 256 carrier waves. To separate downstream with upstream data two different methods can be used, Frequency Division Multiplexing (FDM) or Echo Cancelling (EC). For more information see further in [1]. 11

12 1.6.2 VDSL Very high bit rate Digital Subscriber Line (VDSL) has many similarities with ADSL, but offers higher transmission rates. The higher transmission rates are achieved by expanding the signal bandwidth and by limiting its reach. While ADSL offer a downstream data speed of up to 8 Mbit/s, VDSL can be as high as 52 Mbit/s. This of course limits its reach to about km instead of ADSL s reach of approximately 3.5 km. The modulation method for VDSL is yet to be standardized. Two different methods are currently under investigation, where one of them is similar to the ADSL case. The interested reader is referred to [2]. 12

13 2 Telephone subscriber loop environment This chapter will give a deeper understanding of the telephone subscriber loop channel. This is necessary to get an understanding of the technical assumptions for the DSL deployment. 2.1 Subscriber loop structure Digital Subscriber Lines (DSLs) are developed based on the existing telephone copper network originally developed for POTS. Hence, these basic networks were designed to carry analog voice services and lately with the consideration of carrying digital extensions, such as Digital Loop Carriers (DLC), of analog services. The transmission characteristics of the telephone subscriber loop environment and the proper utilization of these transmission characteristics determine the performance potential of a DSL system General composition of the loop The twisted pair infrastructure, known as the loop plant, consists of twisted pair cables connecting a local Central Office (CO) to a customer (the telephone subscriber) premise. The twisted pair telephone loop connecting a subscriber to a CO is therefore called a subscriber loop. The subscriber loop is often up to 3 km long and consists of sections, typically 153 meters long, of copper twisted pair cables of different sizes. An individual subscriber loop can be divided into portions consisting of the following cables going from the CO towards the subscriber. First there are the Feeder cables. They provide links from a CO to a concentrated customer area. Then there are the Distribution cables that provide links from feeder cables to potential customer sites. The last bit, connecting the customer premises to the distribution cable is called Drop wires. 13

14 The distribution cables are bundled into binder groups. Depending on the cable type there could be 10, 15 or 50 twisted pairs in a binder group, and up to 50 binder groups per cable. Figure 2.1, shows a schematic overview of the loop plant. Subscriber Subscriber Central Office Bridged tap Bridged tap Feeder cable Distribution cable Drop wires Drop wires load-coil Loaded loop (unusable) Figure 2.1. Loop plant 2.2 Problems with deployment When deploying DSL there are many technical obstacles to overthrow. Some of these obstacles are easy to deal with, some decrease the possible performance and some totally rule out the possibility of DSL deployment. Too easier get an overview of these copper loop impairments they are divided into two subgroups, physical and electrical impairments Physical impairments The physical impairments arise from the local subscriber loop being engineered and optimized for analog voice. In order to extend the reach for telephony so called loaded coils were added, mainly in the US. These extend the reach of the voice passband, but at the same time cut off higher frequencies. Since DSL techniques use the extra bandwidth above POTS normally available, loaded coils totally rule out xdsl deployment. Because loop plant construction usually occurs ahead of customer service demands, cables are usually made available to all potential customer sites. Hence, a common practice in the US is to connect more than one distribution cable. 14

15 This maximizes the probability of reaching a potential customer, but often results in unused cable ends. These cable ends, often referred to as bridged taps, create reflected signals that cause interference at the higher xdsl frequencies. The physical location of a subscriber loop could be Aerial (hung on poles) Buried (directly in the ground) Underground (protected within a dedicated conduit) These locations each cause direct threats to xdsl communication. Splices, usually made by hand, are especially sensitive in the aerial case. They bend and flex in the wind, causing micro-outages of short duration. Sometimes splices are not always done properly among pairs within the same bundle. Although each pair is color-coded, various factors make it possible to splice wires from separate pairs together. Such split pairs are seldom fatal for voice, but a real problem for digital services. For the cables buried in the ground, as well as the cables hung in the air, dampness always poses a threat. Finally, short but untwisted drop cables to the premises, had a minimal effect on overall voice quality, but are a concern in xdsl environments Electrical impairments Electrical impairments are also called interferers or disturbers. At xdsl frequencies, a major concern is Radio Frequency Interference (RFI). Many Amplitude Modulation (AM) radio stations broadcast in the same range as xdsl methods operate. Aerial cables are much more at risk, especially in areas where AM stations are particularly dense, such as the northeastern US. Even amateur radio can be a concern for xdsl schemes that operate on aerial cable above 1 MHz or so. Another major concern is crosstalk, the unwanted electrical coupling between transmitters and receivers. This is an effect from the deployment of cable bundles containing multiple twisted pairs each. 15

16 There is both Near-End crosstalk (NEXT) from a receiver pair s adjacent transmitter and Far- End crosstalk (FEXT) from a remotes pair s transmitter. NEXT is often the most severe disturbance of the two types. Figure 2.2 shows how a near-end transceiver i, would experience NEXT noise from a near-end transceiver j if the two transceivers share the same frecuency spectrum within the same cable. Transmitter Disturbing near-end Receiver pair j pair i NEXT Disturbed near-end Cable Figure 2.2. Near-end crosstalk, NEXT There is also Self-NEXT from the same types of xdsl running in the same cable binder and Foreign-NEXT from adjacent types of xdsl. Figure 2.3 shows how a near end transceiver i would experience FEXT noise from the far-end transceiver j if they share the same frequency spectrum within the same cable. Transmitter Disturbing far-end pair j FEXT pair i Receiver Cable Disturbed near-end Figure 2.3. Far-end crosstalk, FEXT Finally there is background noise from many sources: thermal noise, semiconductor noise, impulse noise from local exchange equipment and premises equipment such as light dimmers and refrigerator compressors. 16

17 To sum up this section, there are many sources of impairment. Four of those associated with local loops have been found crucial for the success of xdsl. First and foremost is the loop length including bridged taps. Second is the existence of loaded coils. General background noise is a factor, and finally other xdsl noise (Self-NEXT and Foreign-NEXT) is key elements. 2.3 Testing Until recently, all xdsl testing was done by adapting old tools for new needs. The most useful tool is the Time Domain Reflectometer (TDR), but others are needed. A technician used a load coil detector and TDR to locate the first load coil and mixed gauges. The combined use of a TDR and an open meter determined the length of the loop. A wideband frequency sweep found bridged taps and the TDR determined their distance. When it came to turn-up verification, only double ended testing could find operational margins, usually by installing and testing the proper xdsl equipment on both ends and hoping for the best. It should be pointed out that load coil detectors, TDRs and so on still work for xdsl testing but is very costly. This limits the profit possibility for the operator, and slows down the deployment rate. There is a need for new equipment specifically for that task. There are two major approaches to testing. The first is double-ended testing, as seen in Figure 2.4. This requires either one technician at each end of the local loop, or one technician at the CO and some test equipment at the subscriber. It is easily understood that sending out a technician to the subscriber is a very costly exercise. However, sending some cheap and passive plug-in equipment to the potential subscriber seems to be the best way for double-sided testing. This equipment could easily be connected by the subscriber and thereafter automatically respond to provisioning signals from the CO. 17

18 Test unit CO Loop Double ended testing Subscriber Test unit Test unit Network operation center Double ended testing Single ended testing Remotely controlled Test unit Open end Figure 2.4. Test approaches The other alternative is single-ended testing. This is of course the most cost-effective approach since no additional equipment or truck rolls are needed. Unfortunately there are no good solutions for this yet. The restriction of only getting information from one side of the cable is thought to be insufficient when a total loop qualification test is to be carried out. 18

19 3 Twisted pair channel modeling Twisted pair channel modeling plays an important role when designing and evaluating xdsl systems. With accurate channel models, computer simulation studies can be carried out to understand the transmission performance potential of the telephone subscriber loop plant under different system assumptions. This chapter explains model structure of the local loop as well as the basic concepts and techniques of twisted pair channel modeling. After the models of the twisted pair copper cables are presented, models for the transformer, bridged taps and the hybrid are presented. 3.1 Model structure of the local loop To model the local loop on its path from the CO to the subscriber you have to consider the building blocks along the way of transmission. An overview of the local loop can be viewed in Figure 3.1 below. Transmitter Central Office Bridged tap Subscriber (opened end) Hybrid Transformer Receiver Twisted pair loop Figure 3.1. A model of the local loop. The main building blocks to consider when constructing this model is the hybrid, the transformer, bridged taps and the actual twisted pair copper cable. 19

20 3.2 Twisted pair cable The transmission characteristics of a twisted pair cable can be accurately described by primary and secondary parameters as defined for a distributed equivalent circuit of a transmission line Primary and secondary parameters The primary parameters of a twisted pair copper cable are the R (resistance), L (inductance), C (capacitance) and G (conductance) which all are variables of frequency. The twisted pair cable is modeled as a transmission line, which in turn can be described with a transmission line equivalent circuit built up with a series resistance (R), a series conductor (L), a parallel capacitance (C) and a parallel conductance (G). For a clearer view of an element dx of a transmission line, see Figure 3.2 below. The values of the primary parameters are expressed per unit length and are frequency dependent. I I + di R dx L dx V G dx C dx V + dv Figure 3.2 The transmission line equivalent circuit. For calculation of the primary parameters of a certain cable the models in the recommendations from the International Telecommunications Union (ITU) is used. For a more detailed description of this, see Appendix A. Now the secondary parameters of a twisted pair copper cable will be derived. The secondary parameters are also called the propagation constant and the characteristic impedance. 20

21 Consider an element dx of the transmission line equivalent circuit in Figure 3.2. Let the ω transmission line equivalent circuit be exited with a sinusoidal frequency of f =. 2π Then let R, L, C and G be the primary parameters per unit length, and functions of frequency. If Kirchhoff s equations are applied to the circuit, the following two differential equations will be obtained: dv = ( R + jωl)i dx di = ( G + jωc )V dx (3.1 a) (3.1 b) where V ( x,ω ) V = and I = I( x, ω ) are the voltage and current at distance x in the transmission ω line for the given frequency f =. The two equations (3.1 a) and 2π (3.2 b) can be rewritten in the following way. 2 d V 2 = γ V 2 dx 2 d I 2 = γ I 2 dx (3.2 a) (3.2 b) where the complex quantity ( R + jωl)( G jωc ) γ ( ω) = α ( ω) + jβ ( ω ) = + (3.3) is the transmissions line propagation constant, which is the first of the secondary parameters. As seen in (3.3), the propagation constant is a complex number and can be expressed in α (ω ) and β (ω), which are the attenuation constant and the phase characteristic of the line respectively. The general steady state solution for the differential equations in (3.2 a) and (3.2 b), are given by V + γx γx ( x, f ) = V0 e + V0 e (3.4 a) and I( x, f ) + γx I e γx + I e (3.4 b) =

22 + Here V 0 and are the positive- and negative-going current. V 0 are the positive- and negative-going voltage. In a similar way, + I 0 and By insertion of either of these solutions (3.4 a) or (3.4 b) into the appropriate first order voltage/current differential equation (3.2 a) or (3.2 b) the following will be obtained. + V V R jωl Z ω = ( ) = = (3.5) + I I G + jωc 0 0 This is equal to the constant characteristic impedance of the transmission line. This is the second parameter of the secondary parameters. Please observe that R, L, C and G are still parameters per unit length and frequency dependent. For a deeper explanation of these parameter the interested reader is referred to [1] and [2]. I Two port network ABCD parameters A common and practical way to model transmission lines is by using the two-port network representation. In this representation the electronic circuit in Figure 3.2 can be abstracted by the black box shown in Figure 3.3. I 0 I d A B V 0 V d C D Figure 3.3 Two port model of a section of a twisted pair cable The function of any electronic circuit, or if you want the transfer function of a twisted pair copper cable can be derived by the input/output current/voltage relationships in the two-port equivalent. In the figure V 0 and I 0 are the input voltage and current respectively at x = 0. Vd and I d are the output voltage and current at distance x = d respectively. 22

23 In the model, input voltage/current and output voltage/current are related to each other by the so called ABCD parameters. If a segment of a transmission line of length d has the solution V L = Vd and I L = I d and thus V I L L + γd γd = V ( d, f ) = V0 e + V0 e + γd γd = I d, f ) = I 0 e + I 0 e ( (3.6) Since the two voltage waves in each direction are related to the same-direction current waves by the characteristic impedance Z ( ), one can solve the two equations (3.6) for + V and 0 ω to get + 1 γd V0 = ( VL + I LZ0 (ω )) e 2 1 γd V0 = ( VL I LZ0 ( ω )) e (3.7) 2 By substituting these constants into the general solution and evaluating for the voltage and currents at x = 0 in terms of those at x = d, one obtains the following two-port representation 0 V 0 V 0) = I(0) Z cosh( γd) 1 sinh( γd ) ( ω) ( 0 o Z ( ω)sinh( γd) V( d) A cosh( γd ) = I( d) C B V ( d) D I ( d) (3.8) Hence, the ABCD parameters can be expressed in terms of the secondary parameters as A( s) = D( s) = cosh( γ ( s) d ) B( s) = Z0( s)sinh( γ ( s) d) C( s) = 1 sinh( γ ( s) d ) Z ( s) 0 (3.9) where s = jω = j2πf is the complex frequency and d is the length of the cable. The ABCD parameter modeling is a very useful method when modeling the whole cable section from the CO to the subscriber. Each section along the transmission path can be represented by its own ABCD matrix. For instance, one ABCD matrix for the hybrid, one for the transformer, one for bridged taps (if present) and one for the actual cable. 23

24 The ABCD parameters for the whole transmission path are then obtained by simply cascading all the sections in series. The ABCD matrix information of a twisted pair telephone loop can be easily converted into its input impedance or cable transfer function. Corresponding calculations can be put into a computer program to generate channel models in conjunction with a few tables of twisted pair cable primary parameters. For a loop with terminal impedance Z t (s) the following input impedance will be obtained B( s) A( s) + Zt( s) Zi( s) = D( s) C( s) + Z ( s) t (3.10) in which A, B, C and D are the complex frequency dependent ABCD parameters of a twisted pair telephone loop. For a complete two-port network model both a source and terminal impedance has to be added. A complete two-port network is depicted below, in Figure 3.4. Z S A B V S V t Z t C D Figure 3.4. Two-port network model The transfer function of a twisted pair loop with source impedance Z s (s) and terminal impedance of Z t (s) can then be obtained as H( s) = Z ( s) s Z ( s) ( C( s) Z ( s) + D( s) ) + A( s) Z ( s) + B( s) t t t (3.11) 24

25 3.3 Transformer equivalent circuits The device connecting the hybrid circuit to the twisted pair loop is the transformer. The transfer function of a transformer can be determined according to its equivalent circuit, see Figure 3.5. R p R S L l C i R c L p C 0 Figure 3.5. Transformer equivalent circuit. The key parameters for the transformer equivalent circuit include the following: Rp R R L L l C C s c p i o - The resistance of the primary coil. - The resistance of the secondary coil - The core resistance - The primary inductance - The leakage inductance - The input capacitance - The output capacitance The ABCD matrix of the transformer equivalent circuit is A C B 1 = D sc i R p 1 1 R c sl p 0 1 Rs + sll sc o 0 1 (3.12) 25

26 The key parameters are different depending on which DSL technique that is used. In [2] the key parameters for the transformer are listed for ISDN, HDSL and ADSL. These values are presented in Table 3.1 below. R p R s (ohm) R c (kohm) L p L l (mh) C i (pf) C o (pf) (ohm) (mh) ISDN HDSL ADSL Table 3.1. Transformer parameters 3.4 Bridged taps Bridged taps are unterminated twisted pairs, also known as laterals, that is connected to a feeder cable with more than one distribution cable pair. Thus a bridge tap is a length of wire that is connected to a loop at one end but is unterminated at the other end. If we consider the expression for the input impedance to a twisted pair cable, equation (3.10), we can clearly see what happens if the far end of the cable would be left open. The terminal impedance will be infinity and the expression for the input impedance would simplify to A( s) Z i,0( s) = C( s) (3.13) A bridge tap can simply be considered as a two-port network with only a shunt impedance. The ABCD matrix representation of a shunt impedance is derived in [2], and can be put on the form as follows A C B = D Z = CBridge( s) 1 ( ), 0 s ABridge( s) i 0 1 (3.14) The values of A Bridge (s) and C Bridge (s) are parts of frequency dependent ABCD parameters of the section of twisted pair cable connected as a bridged tap. 26

27 3.5 Hybrid circuits In all existing telephone systems there are hybrids at both ends of communication. This is a device that enables real-time, full-duplex transmission of voice signals over the twisted pair copper loop. A hybrid circuit is basically an electrical bridge. There is little signal from the transmit path coming back to the receiving path when the electrical bridge is properly balanced. The balance condition, however, requires the impedance match to the telephone subscriber loop. This condition cannot really be satisfied because the input impedance of a telephone loop is not exactly fixed, due to bridged taps and temperature variations etc. In [2] there are some models of both single ended hybrids and differential hybrid circuits. Both these models were evaluated, but since none of them were chosen in the system model, neither will be discussed in this report. The interested reader is referred to [2] for further reading. Another reason for not choosing any of the discussed models was that no parameter values were given for the electrical components in the models. Since a hybrid is supposed to be matched to the telephone loop to minimize unwanted reflections, using the described models in [2], would mean an extensive impedance matching for various loop conditions. Therefore the considered model within this thesis is picked from reality. A line-card board assembly from a modem built by Ericsson AB was studied, and the hybrid used there was later modeled. This was very practical since the hybrid used there were already optimized for different loop scenarios. This offers a pretty good matching to the cable for almost any scenario. 27

28 The hybrid used is depicted in Figure 3.6. Transmitter R R s Receiver + - C 1 C 2 R 1 R 2 Z in Loop Figure 3.6. A model of the hybrid. Due to the fact that single-ended testing was to be investigated, there is no need to calculate the ABCD matrix representation of the hybrid. It is sufficient to describe the electrical coupling model, see Figure 3.6, and derive the expression for the needed characteristics from there. This derivation will be made in the following chapter, implementation and simulations under the section echo path, due to its relevance there. 28

29 4 Implementation and simulations In this chapter the implementation and simulations is described and explained in detail. To get an idea about the necessary steps, a brief explanation of the single ended testing procedure will be given in the first section of this chapter. When the necessary steps have been presented, each step will be described in more detail. 4.1 Single ended testing When single ended testing is to be employed, the possibilities of testing are restricted. The echo impulse response and the input impedance are the only known features about the local loop. These features however have to be constructed in the simulation environment. Therefore the first step in the implementation of the system is to build the modules described in Chapter 3. These include the actual twisted pair cable, the transformer and bridged taps The local loop can be terminated in an innumerous number of ways, typically a telephone or a modem. The big problem with terminations is that each and every kind of termination has individual characteristics and will cause different echoes. Therefore, it is assumed that the local loop is unterminated, which actually also might be the case. This will cause a clean reflection echo at the subscriber end of the loop. The assumption seams reasonable since the subscriber could perhaps be asked to remove the connected equipment before the test can be performed. This is accepted today when the telephone lines are qualified for POTS. After the transformer, the bridged taps and the twisted pair cable have been modeled with their ABCD matrix representation, the input impedance of the local loop will be determined. Thereafter the echo path transfer function will be calculated with the help of the model of the hybrid and the knowledge of the input impedance. By transforming the calculated echo path transfer function to the time domain the echo impulse response is obtained. Now everything is known about the loop that will be available when initializing a single ended test in the field. 29

30 A test system also has to be implemented. The first step is to design the test pulse that shall be transmitted on the local loop. From the received signal the length of the loop can be determined. Using this distance the real transfer function of the loop can be estimated. The test system should also work in a noisy environment. Therefore a noise model have to be constructed and implemented. When the system is robust and operates in a noisy environment a capacity analysis is carried out. The possibility to calculate offered capacity to the customer is a very attractive attribute for the operators. To calculate the offered capacity you have to use the channel transfer function in combination to an expected noise floor. Also the spectrum of the DSL technique has to be considered. 4.2 Echo path The echo path is the path that a transmitted pulse travels along on its way to the receiver. To visualize the different echo paths, the many possible paths are depicted in Figure 4.1 below. Transmitter Bridged tap Hybrid Subscriber Receiver Figure 4.1. Echo paths. To be able to simulate single ended testing, an expression of the echo path has to be obtained. This is possible using the model of the hybrid described in Chapter 3, Section 5 and some circuit analysis. For the reader s convenience, the model of the hybrid is shown again in Figure 4.2, together with the suitable notations for the calculation. 30

31 Transmitter U S R U R R s Receiver + - C 1 C 2 U Ztot Loop R 1 R 2 Z in U L U R1 Ztot Figure 4.2. The hybrid. The first step in the calculation of the echo path transfer function is to formulate some basic relations. H U U U U U U echo L S R1 Z tot R S UL U ( f ) = U Z in = R + Z S in 1 S jωc1r1 = 1+ jωc R R = R + Z tot 1 R1 (4.1) (4.2) (4.3) (4.4) With the help of (4.4) the following relation can be formed U Z tot = U S U R Ztot = R + Z tot U S (4.5) Combining (4.3) and (4.5) gives 31

32 U U R1 S Z tot = R + Z tot jωc1r1 1 + jωc1r 1 (4.6) Finally, using (4.1) and (4.6) gives H echo U ( f ) = L U U S R1 = R S Zin + Z in Z tot R + Z tot jωc1r1 1 + jωc1r 1 (4.7) where 2 1 ω C1R1C2 R2 + jω ( C1R1 + C2R2 ) Z tot = 2 ω C C ( R + R ) + jω ( C + C ) (4.8) The importance of the echo path transfer function comes from the fact that it will serve as a base for the model of the echo impulse response. In a real system the echo impulse response will be one of the known features about the total loop. It serves as a description of the channel that an eventual test pulse would experience on its way from the transmitter in the CO towards the subscriber and back again. The echo impulse response is obtained by an inverse Fourier transform of the echo path transfer function from the frequency to the time domain. To achieve a realistic impulse response that corresponds to reality, the echo path transfer function has to be manipulated. First of all the echo path transfer function is constructed discrete, and in the frequency domain. The number of points of its representation will determine the number of samples in the time domain. The resolution in the time domain should therefore be detailed enough to find echoes. Good enough is a vague term but is determined through testing. The resolution in the frequency domain therefore has to be high. The echo path transfer function obtained from the models above will contain high frequency components. This is not very realistic in a real system, since the cable attenuates the higher frequencies. The models for the system can not take this into account because the behavior of the transformer is hard to model correctly. These high frequency components will also result in unrealistic ripples on the echo impulse response. To combat these ripples the frequency region, in which the transfer function is constructed, has to be extended about eight to ten times compared to the interesting interval. If the interesting interval is for example 0-1 MHz, the echo path transfer function has to be derived for the interval 0-10 MHz. Thereafter the transfer function will be low pass filtered to combat the high frequency components causing the ripples. 32

33 The filter that is used is a Butterworth filter of order 6. The cut off frequency for the filter is determined by the interesting frequency interval. If ADSL is studied, the signaling bandwidth is 0 to approximately 1.1 MHz. A cut off frequency of 10 MHz is sufficient, but further restrictions on this will be imposed in Section 4.3 when the frequency content of the transmitted test pulse has to be taken into account. For a deeper description about the butterworth filter and filters in general, the reader is referred to [4]. To get an idea of these effects three cases will be described in the following. For these cases the echo path transfer function versus the impulse response will be plotted. The cases will also be explained adjacent to Figure 4.3.a-c. Figure 4.3.a. Case 1. Echo path transfer function versus impulse response. Case 1. High frequency components in the transfer function. It can be seen that a short interval in frequency causes ripples in the echo impulse response. 33

34 Figure 4.3.b. Case 2. Echo path transfer function versus impulse response. Case 2. Extended interval in frequency domain. The ripples in the echo impulse response can still be seen because of the presence of high frequency components in the echo path transfer function. Figure 4.3.c. Case 3. Echo path transfer function versus impulse response. Case 3. Long interval in frequency domain. The high frequency components are removed by the filter. This gives a clean impulse response without the ripples. 34

35 After these manipulations the impulse response and the input impedance are sent to the test module where everything else about the cable is assumed unknown. The fact that the single ended test system makes all testing depending on these two features justifies the accuracy with which they are constructed. 4.3 Test pulse The operator qualifying the loop wants to be able to test short as well as long cables without having to change parameters in the test program. This is a reasonable assumption since the operator does not know how long the loop is in beforehand. It is very useful to know whether the possible problem on the cable is within the CO or half way to the subscriber. This offers a cost saving possibility both when pre-qualifying a loop and when assessing possible errors during maintenance. The ability to test both short and long cables poses some demands on the chosen test pulse. It also implies some requirements on the resolution of the echo impulse response. When testing short cables, the pulse has to have a short extension in time to minimize the interference of the transmitted pulse in the echo pulse. Here is an example. If an impulse is transmitted from the CO at t = 0, the reflection will arrive in the receiver in the CO after approximately t = 1µ s. This is under the assumption that the impulse travels with a speed of approximately 3 2 of the speed of light, that is * m / s. This speed serves as a rule of thumb for the propagation speed on twisted pair cables. This case is shown in Figure 4.4.a. However, an impulse is not very useful to send on the cable. Instead a pulse of some kind has to be transmitted. Normally a pulse has to have infinite length to have a frequency response without sidelobes and ripples in the passband. It is however sufficient to have a pulse width of about ± 4T from the main peak, if the main lobe has an extension of 2 T. This will give an idealized echo looking like the pulses in Figure 4.4.b. These echoes are pure imaginary and not transmitted over an attenuating loop. 35

36 Amplitude Amplitude Propagation time Propagation time 10T T Time Time Figure 4.4.a and 4.4.b Idealized echoes. If we continue the example there will now be about 10 T between the main peaks of the pulses. This gives a value of T of about 0.1µ s, which leads to a small value of T S, the time between T 9 each sample. If we use a value T s = = 5 *10 s, each pulse will be represented with samples, which is sufficient for a decent representation. This gives the requirement on the sampling frequency that is used when constructing the echo path transfer function. For long cables there is a demand for a pulse with a low fundamental frequency. This comes from the fact that long cables attenuate higher frequencies more. For the pulse in Figure 4.4.b, the fundamental frequency, f fund, is defined as 1 f fund =, were T is defined as half the main T lobe. Lowering the fundamental frequency will cause a decrease in the transmitted power, which is not good, if you want to see far into the cable. This can be adjusted for by increasing the amplitude of the transmitted pulse. When implementing a system that is going to be standard compliant it is important to limit the transmitted power in order not to disturb other DSL connections within the same cable bundle. This will not be considered in this master thesis, due to the non-existent standards within the area of power control for loop qualification. To conclude the discussion above, there is a need to develop a test system, which in some way adapts to the length of the cable. The approach within this master thesis is to start with a pulse that has a short duration in time and if no echo is detected for a certain threshold value, tries a pulse with a longer duration. The system simply increases the duration of the pulse until an echo is detected. 36

37 How should one choose a good pulse? The major criterion is the frequency characteristics of the pulse. The frequency response of the pulse should be well defined with few and small sidelobes. It should also have a nice clean peak without ripples, so that it does not distort the transfer function. A family of pulses known to have these characteristics is the raised cosine family, which concludes the choice of test pulse. The raised cosine is formed with the help of the expression below. cos( απn) r( n) = sinc ( n)*, 0 α 2 1 (2αn) 1 (4.9) where α is a design variable that controls the roll off in frequency domain. To visualize the characteristics of the raised cosine pulse, a description the pulse form and frequency response is given in Figure T Main lobe Bandwidth 1 B r cos 2T Figure 4.5. Pulse form and frequency response of raised cosine pulse. If the echo path transfer function in Figure 4.6 is studied, it becomes clear that the raised cosine pulse has to be modified. 37

38 Peak Oscillations Figure 4.6. Echo path transfer function for a 1 km loop. It can be seen that the echo path transfer function first has a high peak and then some oscillations, which are a result from the echo, and then finally flattens out. The peak represents some low frequency components in the echo impulse response. This will cause an unwanted DC-offset, which has to be removed by a filter. Shifting the frequency content of the raised cosine pulse to higher frequencies will cause the pulse to serve as the desired filter when sending the pulse onto the cable. This frequency shift is accomplished by a multiplication in the following way. p( n) = r( n)* sin( 2παn ) (4.10) Some care has to be taken in the filtering. The echo causes the oscillations seen in the echo path transfer function in Figure 4.6. Hence, this information is vital when qualifying the loop. Therefore it is important that the raised cosine pulse is not shifted too high in frequency. The most desired area to be covered by the frequency response of the pulse is shown in Figure

39 Desired area Figure 4.7. Desired frequency interval to be covered by transmitted pulse. The lowest carrier frequency, f c, for the sinus is determined by the Nyqvist anti-alias criterion. This gives 1 f c (4.11) 2T This serves as a minimum frequency for the sinus for each and every individual pulse that is transmitted onto the loop, and guarantees no aliasing effects. To ensure that the sidelobes of the pulse does not overlap the frequency region containing the peak in the echo path transfer function it is chosen according to 1 1 f c = 2 = (4.12) 2T T The different pulse characteristics used in the system are based upon simulations and are presented in Table 4.1 below. Pulse duration (T ) [s] 0.1*10 0.2*10 0.3*10 1.2*10 1.8*10 2.3*10 4*10 f c [Hz] d min [m] d max [m] 10* * * * * * * Table 4.1. Pulse characteristics. 39

40 In the table the maximum and minimum values of measurable distance for each of the pulses are given. The stated distances are the lengths from the CO to the subscriber. This shows that the shortest cable can be as short as 110 meters. A cable that is 110 meters is normally still inside the CO, and therefore enables fault location within the CO. The maximum distance is 5300 meters, which corresponds to a very long loop length. A problem that was encountered was the fact that the frequency region for some the pulses overlapped the region that was filtered away when the echo path transfer function was adjusted. This resulted in very strange received signals and had to be adjusted for. The cut-off frequency for the echo path transfer function was simply put larger than the highest frequency content of any of the test pulses. An example of one transmitted pulse, both in time and frequency domain, as well as the received signal will now be depicted in Figure 4.8 and Figure 4.9. The case shown is when a 6 pulse with T = 0.3 *10 s is transmitted over a cable with the length of 1 km. f c Figure 4.8. Transmitted pulse. In the graph showing the frequency response of the transmitted pulse, the frequency shift caused by the multiplication in (4.10) can be seen. This to give an idea where the actual frequency interval of the pulse for one specific pulse actually ended up. 40

41 Transmitted pulse Echo from pulse Figure 4.9. Received signal. Both the transmitted pulse and the echo are clearly visible in the received signal, which looks promising for the distance estimation. 4.3 Bridged taps A bridge tap is an unused wire that is connected to a loop in one end and unterminated in the other. They are modeled as described in Section 3.4, and defined by their ABCD representation. On a cable without bridge taps there are some oscillations in the echo path transfer function. If there are bridge taps on the cable, further oscillations will be introduced. This is shown in Figure 4.10, where the echo path transfer function is plotted both with and without bridged taps. 41

42 Figure Echo path transfer functions with and without a bridged tap. The cable without a bridge tap is 1 km long. The cable with the bridge tap is also 1 km, but has a bridge tap 0.8 km down the line from the CO. This is a reasonable assumption since bridge taps normally are located near the end of the subscriber. To visualize the decrease in performance that bridge taps introduce on a local loop the transfer function from the CO to the subscriber have to be studied. If we assume that the transfer function for transmission from the CO towards the customer is known or correctly estimated the graphs for a loop with a bridge tap and one without can be plotted. This is shown below in Figure

43 Loss of SNR Figure 4.11 Transfer functions with and without bridge taps. The capacity for a local loop is dependent on the available Signal to Noise Ratio (SNR) as described later in Section 4.7. It will be shown that the available SNR is calculated as the area in-between the transfer function, H ( f ), and the noise frequency characteristics, N ( f ). Then it is obvious, see Figure 4.11, that the area decreases if bridge taps are introduced in the local loop. The main problem with bridge taps when employing single-ended testing is that they have identical characteristics with the subscriber loop end. This is a result from the fact that they have unterminated ends, which also the subscriber loop end is assumed to have. Hence, it will be fundamentally impossible to discern the loop characteristics to the subscriber, from the bridge tap properties. Therefore the possibility to estimate the distance to the subscriber, and from that estimate the capacity of the loop, will be impossible. This leads to the fact that the system in this master thesis has to be restricted to the case without bridge taps. However this can lead to further work in a future master thesis where subscriber location on a cable with bridge taps might be the main task. Considering that bridge taps mainly exist in North America the system will still be able to handle most of the world market. The interested reader is referred to [8], [9] and [10] for more information about bridge taps. 43

44 4.4 Distance estimation When the cable, transformer and hybrid is modeled and implemented the only known parameters of the total system are the echo impulse response and the input impedance. When these parameters have been obtained the test pulse has to be constructed. We could read in Section 4.3 that the test system is designed to start transmitting pulses designed for short cables and thereafter increase the time duration of the pulse to enable testing of longer cables. The distance estimation block is designed to find an echo on the received signal, and if no echo is found, tell the test program to increase the time duration of the pulse. To send a pulse over the cable the pulse is simply convolved with the echo impulse response in the way described below. If the transmitted pulse is denoted p (n) and the echo impulse response is called h echo (n) the received signal will be y rx N 1 ( n) = h k= 0 echo ( k) p( n k) (4.13) where N is the maximum sequence length. The received signal, y rx (n), when a pulse with T = 0.3*10 s is transmitted over a 1 km cable looks like in Figure Here both the transmitted pulse and the echo is clearly visible. 6 44

45 Transmitted pulse Echo from pulse Figure Received signal for 1 km cable and pulse with T = 0.3*10 6 s When the received signal is available, the distance of the cable can be estimated. This is done by first locating both the peak of the transmitted pulse and the peak of the reflection. In Figure 4.12 this looks like a rather easy task, but this has to be made robust against noise. A method that works well both with and without noise are to filter the received signal with a matched filter and form the decision vector, d vec. The filter is matched to the transmitted pulse and is simply the flipped version in time of the transmitted pulse. A more thorough description seems unnecessary here, but the interested reader is referred to [5]. The matched filter is simply s( n) = p( N n) (4.14) if p (n) is the transmitted pulse and N is the length of the transmitted pulse. Both p (n) and s (n) are depicted below in Figure

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