Module: Digital Communications. Experiment 784. DSL Transmission. Institut für Nachrichtentechnik E-8 Technische Universität Hamburg-Harburg

Transcription

1 Module: Digital Communications Experiment 784 DSL Transmission Institut für Nachrichtentechnik E-8 Technische Universität Hamburg-Harburg

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3 Table of Contents Introduction The DSL System Network Topology Transmission Path The DSL Channel The User Channel Crosstalk Discrete Multi-tone Technique (DMT) Bit Loading Frequency Domain Equalization Zero-Forcing Equalization for a User Crosstalk Cancellation Zero-Forcing Equalization for Multiple Users Channel Estimation Pilot-Based Channel Estimation Walsh-Hadamard Code Preparatory Problems Design of the Experiment Model Experiment One Active User Multiple Active Users Bibliography iii

4 Introduction In this practical course the digital subscriber line (DSL) system is presented, with which extremely high data rates can be transmitted over existing telephone lines. The special characteristics of the DSL channel will be demonstrated and a glimpse of the existing and newest DSL technologies will be provided. The technical task consists in transmitting binary data from a transmitting modem to a receiving modem over a copper cable bundle. The DSL system is based on digital wired transmission technology. Realistic wired transmission channels distort the transmission signal ( ) due to crosstalk activity within the cable, for example, so much so that error-free reception is usually prevented. Typical error-causing influences in a DSL channel include crosstalk, additive noise and impulse disturbances. Furthermore, the channel is characterized by path loss and is highly frequency-selective as a result of reflection. In this practical course we will focus on the treatment of frequency-selectivity and crosstalk. Frequency-selectivity is treated with digital orthogonal frequency-division multiplexing (OFDM) transmission technology with corresponding bit loading. For the execution of the experiment a suitable technical model will be utilized. Signal processing on the transmitting and receiving ends is digitally realized. Data transmission occurs analog over multiple copper lines. Further information regarding the theoretical context can be found in a number of textbooks [Ded06] [Bin00] [Sjö00] [Cio02] [Cio00] [Bel00]. 1

5 1 The DSL System Data transmission over copper lines utilizing DSL is a well-known and established digital transmission technology. DSL technology makes use of the already existent telephone network allowing for such applications as high-rate internet access among other digital services. As illustrated in Figure 1.1, speech and data signals are transmitted from the exchange to each user over the same twisted pair. Figure 1.1 The DSL reference model The frequency range up to is used exclusively for speech-signal transmission, whereas the frequency range of is reserved for DSL signals. On the user-end the superimposed signals are separated again via a splitter (a filter) and routed further to the telephone or DSL modem. This method of transmission works just as well from the exchange to the user (downstream) as it does the other way around (upstream). As illustrated in Figure 1.2, the entire frequency range is divided into frequency bands for upstream and downstream so that transmission in both directions is possible. In this practical course only upstream transmission is considered so that the entire bandwidth can be used for upstream transmission. 2

6 1 The DSL System Figure 1.2 Band layout 1.1 Network Topology Copper cable pairs are usually grouped together and together form a cable binder (Figure 1.3). As a consequence of the imperfect insulation of the individual cables there is crosstalk between adjacent cables. Here a distinction is made: crosstalk on the transmitting-end which is caused by the transmitter and affects all other cables is defined as near-end crosstalk (NEXT) and crosstalk on the receiving-end which is caused by the transmissions of other users is defined as far-end cross talk (FEXT). In this practical course only FEXT is considered, since NEXT can be prevented by perfect synchronization. The purpose of twisting the cables is to reduce crosstalk between the cables. Typically the power of the interferences is greater than the noise power. In the newest DSL systems these interferences therefore aren t tolerated and assumed as background noise, but rather treated separately and reduced using equalization techniques (crosstalk cancellation). As a result, bi-directional data rates of up to can be attained with the newest DSL system standards. Figure 1.3 Network topology The network topology adopted in this experiment is illustrated in Figure 1.3. What will be examined is the copper cable connection between the exchange and the user. Every user has a cable pair at his disposal, which directly links the user and the exchange. The cable pairs of multiple users are combined into cable binders, which in practice can contain up to 50 cables. The lengths of the individual lines vary. Current lines fall within the range of. 3

7 1.2 Transmission Path 1.2 Transmission Path The bit stream in a DSL system must first be processed in various steps in order to generate the transmitted signal. As illustrated in Figure 1.4 the bit stream is coded (Forward Error Correction, FEC), after which an interleaving is carried out. In order to minimize the number of bit errors, suitable channel coding methods (error-correcting codes) are implemented. Figure 1.4 Transmission path In DSL systems discrete multi-tone technology (DMT) is utilized, which partitions the entire bandwidth into a large number of subcarriers (Chapter 3). The DMT process is based on the OFDM transmission technology. Narrowband channel transmission can be realized on the individual subcarriers, whereby intersymbol interference (ISI) is virtually non-existent. Before the modulation the signal is converted with a serial to parallel converter and subsequently modulated to each subcarrier individually using the corresponding constellation (Chapter 4). The signal is transformed to the time domain with the inverse fast Fourier transform (IFFT) (Chapter 3). In order to completely prevent intersymbol interference a guard interval is added. Each DSL standard has certain specifications with respect to the power spectral density of the transmitted signal, which is why the transmitted signal must be configured before the transmission. This is done by the filter as illustrated in Figure 1.4. After the digital to analog conversion the transmitted signal is amplified and then transmitted over the copper cable. The steps carried out on the transmitting-end are reversed on the receiving-end with the distinction that the received signal is equalized before the demodulation, in order to compensate for the influences of the transmission channel. 4

8 2 The DSL Channel The transmission medium used in DSL systems is copper. Technically speaking these are twisted pairs of copper cable which exhibit special transmission characteristics. In the first part of this chapter these characteristics are described in more detail (Section 2.1). Section 2.2 goes into crosstalk, which occurs as a consequence of the arrangement of the cables in a cable binder and imperfect insulation. 2.1 The User Channel The user channel is viewed by the signal that is transmitted from transmitter to receiver over the copper cable that links them. In the frequency range used by DSL systems this cable can be viewed as a transmission line, and therefore many of the channel characteristics can be derived from transmission line theory [Ded06]. Figure 2.1 Channel attenuation over frequency for various line lengths and diameters The DSL user channel is affected by its frequency-selectivity. As depicted graphically in Figure 2.1, the attenuation of the channel increases as frequency increases. Additionally, the attenuation decreases with increasing line diameter and increases with increasing line length. 5

9 2.1 The User Channel Figure 2.1 shows the power transfer function in for cables with various lengths and diameters. The transfer function for the user channel of user is given by: ( ) ( ) (2.1) whereby ( ) represents the propagation constant of each cable, respectively length. the cable In addition, the frequency distortion depicted graphically in Figure 2.2 is characteristic of cables with bridged taps. They result from reflection of the signal at the discontinuities, whereby intersymbol interference occurs, which manifests itself as frequency-selective channel behavior. The branches of the bridged taps are connected to the line at the one end and are open on the other and thus reflections occur. Figure 2.2 Channel attenuation over frequency with bridged taps In addition to attenuation over the frequency the channel is also influenced by additive white Gaussian noise. If the channel transmission factor ( ) ( ) is known, then the received signal of user on the subcarrier is obtained analytically as: ( ) (2.2) whereby is the transmitted signal of user, is the noise, and is the subcarrier spacing. 6

10 2 The DSL Channel 2.2 Crosstalk In the case of multiple active users the user information signal that is transmitted over a DSL channel is heavily influenced by interference. The interference concerned is so-called crosstalk. As a consequence of the imperfect insulation between cable pairs in a bundle the signal transmitted on one cable interacts with the signal transmitted on another, and vice versa. This happens on both the receiving-end (FEXT) and on the transmitting-end (NEXT) (Section 1.3), whereby only FEXT is considered in this course. The interferences are also frequency-selective and typically range from noise level. Figure 2.3 shows a user channel experiencing interference. over the Figure 2.3 Channel attenuation of the user channel and crosstalk channel In addition, the strength of the crosstalk depends on the distance between the user and the receiver. If the user is close to the receiver relative to the disturber, then interference is marginal because the interference signal is heavily attenuated by the path loss, whereas the user information signal is only slightly attenuated (Figure 2.4 a)). If the user is far away from the receiver and signals from a disturber located close to the receiver cause crosstalk, then the interference is greater (Figure 2.4 b)). If the channel coefficient of the user channel ( ) and the disturbing channel ( ) are given, then the received signal on the subcarrier can be described analytically by: ( ) ( ) (2.3) 7

11 2.1 The User Channel whereby is the number of users, is the transmitted signal on the user channel and designates the transmitted signal of the disturber. Figure 2.4 Dependence of the strength of crosstalk on the network topology: a) disturber is farther from exchange, b) user is farther from exchange The channel matrix on the subcarrier [ ( )] [ is then given by: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ] (2.4) for active users. ( ) specifies the influence of user on user. 8

12 3 Discrete Multi-tone Technique (DMT) In DSL systems DMT transmission technology is utilized. This is a form of multicarrier transmission technology, which is known as orthogonal frequency division multiplexing (OFDM) in mobile communications. In this case the entire bandwidth is partitioned into a large number of orthogonal subcarriers, which don t mutually influence each other due to their orthogonality. This is illustrated in Figure 3.1. Since only amplitude and phase are distorted in the DSL channel, orthogonality is retained on the receiving end as well. Figure 3.1 DMT spectrum In order to realize an equal data rate compared to a single carrier system, a longer symbol duration is provided in a multicarrier system. By extending the symbol duration on the individual subcarriers a narrow band channel transmission is made possible and intersymbol interference is greatly reduced. If a guard interval is implemented as well, then intersymbol interference can be completely eliminated. Figure 3.2 compares single carrier transmission to multiple carrier transmission with DMT. 9

13 3 Discrete Multi-tone Technique (DMT) Figure 3.2 Comparison of a) single and b) multicarrier methods (red: ISI) An efficient creation of the discrete transmission signal at time is possible with the inverse fast Fourier transform (IFFT). The transmitted signal on the subcarrier is then given by: ( ) (3.1) with, whereby represents the number of subcarriers, respectively the symbol duration. 10

14 4 Bit Loading When more than one subcarrier is used for the transmission, the question always arises, how should the data be distributed on the individual subcarriers? The constellations on each subcarrier used for the transmission should be chosen dependent on the transmission quality so that the user data rate is maximized. For this purpose an SNR, respectively SINR measurement is carried out on each subcarrier during an initialization phase. Based on these SNR or SINR measurements the constellation is subsequently chosen such that the previously determined bit error probability won t be exceeded. Figure 4.1 Constellation diagrams for a) BPSK, b) 4QAM and c) 16QAM 11

15 4 Bit Loading SNR/SINR in db number of loaded bits Table 4.1 SNR/SINR limits for bit loading A QAM up to a QAM will be used for data transmission in this experiment s set-up. A BPSK will be used for the channel estimation. Table 4.1 provides an overview of the SNR/SINR limits for various constellations. In Figure 4.1 constellation diagrams for a BPSK, 4QAM and a 16 QAM are depicted. As can be seen in the figure, exclusively quadratic constellations with gray mappings are used in this course, which is otherwise not the case in common DSL systems [06]. 12

16 5 Frequency Domain Equalization The newest DSL standards (VDSL2) utilize the knowledge of all channel transmission factors and carry out signal processing for all users combined. By doing so, crosstalk can be cancelled, which up until now has limited the data rate, and a substantial increase in the data rate can be attained. Crosstalk cancellation by equalization methods is possible for both the upstream as well as the downstream. In this course the upstream equalization methods will be used for the entire bandwidth, and therefore only this technology is treated here. 5.1 Zero-Forcing Equalization for a User In the experimental set-up a zero-forcing equalizer in the receiver is used to remove the influence of the user channel. Here, each user s line is equalized separately. Figure 5.1 shows the corresponding block diagram exemplary of the th user. Before demodulation the received signal is equalized so that the influence of the user channel is compensated for. Figure 5.1 Block diagram with frequency domain equalization The received signal ( ( )). is multiplied with the inverse of the user channel coefficient The equalized received signal for user on subcarrier is then given by: ( ( )) ( ( )) (5.1) whereby and are the equalized received signal, respectively transmitted signal for the th user on subcarrier, and is the noise signal. 13

17 6 Crosstalk Cancellation The newest DSL standards (VDSL2) utilize the knowledge of all channel transfer factors and carry out signal processing for all users combined, that way crosstalk can be eliminated, which up until now has limited the data rate, and a substantial increase in the data rate can be attained. Crosstalk cancellation by equalization methods is possible for both the upstream as well as the downstream. In this course the upstream equalization methods will be used for the entire bandwidth, and therefore only this technology is treated here. 6.1 Zero-Forcing Equalization for Multiple Users In the experimental set-up a zero-forcing equalizer in the receiver is used to eliminate crosstalk. Figure 6.1 shows the corresponding block circuit diagram. Before demodulation and frequency domain equalization the received signal is additionally equalized and thereby the crosstalk is eliminated. Figure 6.1 Block diagram with crosstalk cancellation (upstream) The channel matrix is partitioned into: whereby the matrix: [ ( )] [ ( )] [ ( )] (6.1) [ ( )] [ ( ) ] (6.2) ( ) is diagonal, and specifies the influence of the user channel. Its inverse is given by: ( ( )) [ ( )] [ ( ( )) ] (6.3) 14

18 6 Crosstalk Cancellation The crosstalk matrix [ given by: ( )] specifies the influence of the crosstalk channels. The crosstalk matrix is [ ( )] [ ( )] [ ( )] (6.4) The received vector is multiplied with the inverse of the crosstalk matrix [ ( )]. The equalized received vector on subcarrier is then given by: [ ( )] [ ( )] [ ( )] (6.5) whereby [ ( )] represents the inverse channel matrix on subcarrier. and are the equalized received vector and transmitted vectors on subcarrier, and is the noise vector. The channel matrix is an matrix and the transmitted, received and noise vectors have the length, where represents the number of users. 15

19 7 Channel Estimation In a DSL system data transmission occurs over copper cable. The channel behavior of the cable is never known a priori, however channel state information is required to equalize the received signal and eliminate crosstalk, for example. Therefore each user s channel must be measured. Many methods are known to measure the channel. Here only the pilot-based channel estimation technique is treated since this method is also employed in the experimental set-up. 7.1 Pilot-Based Channel Estimation Pilot-based channel estimation methods are the established methods for measuring the channel transfer factors. Predefined pilot symbols or sequences, which are known to both the transmitter and receiver, are transmitted at specified times on predetermined subcarriers. As stated in Chapter 3, the multicarrier process DMT is used in DSL systems. The entire bandwidth is partitioned into a large number of subcarriers, whose bandwidths are so small that the transmission on a subcarrier can be carried out over a narrowband channel. Since the channel transfer function of each cable is dependent on the frequency, as was determined in Chapter 2, channel transfer functions need to be determined for all subcarriers. Figure 7.1 illustrates how the measurement for an active user occurs, in this case user 1. A pilot symbol is transmitted on subcarrier. The received signal on each subcarrier results in: ( ) (7.1) whereby ( ) represents the channel transfer factor for the user channel 1 on subcarrier, and is the additive Gaussian noise. The estimated channel transfer factor ( ) therefore results in: ( ) ( ) (7.2) 16

20 7 Channel Estimation Figure 7.1 Transmission for an active user If multiple users are simultaneously active, then the received signal for each user doesn t just comprise the signal that was transmitted over the user channel. As exemplified in Figure 7.2 for 3 users, the received signal for each user is comprised of the user information signal and the interference of multiple crosstalk signals. Figure 7.2 Transmission for multiple active users The received signal for each user is given by: ( ) ( ) ( ) (7.3) ( ) ( ) ( ) (7.4) ( ) ( ) ( ) (7.5) In order to obtain all necessary channel state information both the channel transfer factor of the user channel ( ) and the channel transfer factors of the crosstalk channels ( ) need to be measured. In the case of multiple active users it is more difficult to formulate the estimation, since interference of the user information and crosstalk signals is encountered in the receiver. One possible solution to this problem would be for each user to have his pilot 17

21 7.1 Pilot-Based Channel Estimation symbol transmitted exclusively, during which all other users wouldn t be permitted to transmit. The estimated channel transfer factors for each user are then given by: ( ) ( ) (7.6) ( ) ( ) (7.7) If the measurement takes place for all users simultaneously, as it will be done in the experiment, then the use of orthogonal pilot sequences is necessary. These pilot sequences don t interfere with each other due to their orthogonality. In this course the Walsh-Hadamard Code is used as an orthogonal sequence, which is explained in detail in Section 7.2. With the aid of a correlation receiver the received user information and crosstalk signals can be separated again, so that the channel transfer factors can be calculated. With the use of orthogonal pilot sequences these are given by: ( ) [( ( ) ) ] (7.8) ( ) [( ( ) ) ] (7.9) whereby is the length of the pilot sequence, and the pilot sequence for user on subcarrier is given by: [ ] (7.10) 18

22 7 Channel Estimation 7.2 Walsh-Hadamard Code Walsh-Hadamard codes can be created with lengths of. The pilot sequences which are transmitted for the various users are given by the Hadamard Matrix. With: (7.11) the code sequence is given by: [ ] (7.12) Walsh-Hadamard codes with lengths of 16 or 64 are used for channel estimation in this course. 19

23 8 Preparatory Problems The following problems must be worked on at home and shown at the course sessions so that further participation in the course is permitted. Problem 1: DMT System The following system parameters are given: Bandwidth ; number of subcarriers ; guard interval a) Calculate the subcarrier spacing. b) Calculate the symbol duration on a subcarrier. c) Calculate the data rate, for transmission with a 4QAM on all subcarriers. Problem 2: Matlab Commands So that during this course you re in the position to solve the presented problems you should have basic Matlab skills. Furthermore, you need to know some Matlab commands. Look into the application of the following Matlab commands. a) plot, title, figure, xlabel, ylabel b) abs c) transpose d) size, squeeze 20

24 9 Design of the Experiment 9.1 Model For the execution of the experiment a computer, on which Matlab is installed, and a DSL demonstrator are used. The DSL demonstrator consists of a transmitting and a receiving modem, which are attached to a long cable bundle with 8 copper twin wires. The wires of the twin wire each have a diameter of. Both modems are connected to the USB port of the computer. Matlab is found on the computer. The flow diagram of a Matlab program is depicted in Figure 9.1. The gray colored blocks are carried out by the Matlab program. The blue colored block represents the transmission over the cable. As can be seen in Figure 9.1 the Matlab program can carry out the transmission of a preamble, the modulation, the channel estimation, the crosstalk cancellation, the SINR measurement and the bit loading. These steps are repeated for each transmission. Furthermore, after the second transmission the number of bits remaining to be loaded that was obtained from the bit loading of the previous transmission is used. The experiment set-up can carry out a complete DSL transmission, whereby all of the signal processing is accomplished in Matlab. The transmission over the cable, however, is accomplished with the aid of the transmitting and receiving modem. 21

25 9.1 Model Figure 9.1 Flow diagram of a Matlab program 22

26 9 Design of the Experiment 9.2 Experiment One Active User The first part of the experiment is concerned with becoming familiar with the DSL system when one user is active. Problem 1: Equalization This problem involves the analysis of the user channel of the DSL system. The effects of equalization of the user channel shall be demonstrated. For this problem all subcarriers are modulated with a 4 QAM. Furthermore, only one line is active and no bit loading takes place. The channel estimation is carried out only for one line, meaning no orthogonal codes will be used. num_of_lines and test_num shall therefore each be set to 1. a) Look at the Matlab program. Carry out the transmission of a data burst by starting the program. Draw a block diagram that reflects the processing steps of the signal that are carried out in the program. b) Plot the constellation diagram in Matlab of the transmitted and received signals for the subcarriers and. Compare the constellation diagrams for the transmitted and received signal as well as for the 1000th and 4000th subcarriers. Write down what you observe. Save the plotted images. c) Carry out the channel estimation in Matlab by removing the comments of the corresponding program section and starting the program. Sketch the block diagram. Plot the square of the absolute value of the channel transfer function ( ) over the frequency. Write down what you observe. Save the plotted images. d) Carry out the equalization of the user channel in Matlab by removing the comments of the corresponding program section and starting the program. Plot the constellation diagrams of the equalized received signal for the subcarriers and. Compare these results with the results from part b). Write down what differences you observe. Save the plotted images. How does the block diagram look now? Sketch it. 23

27 9.2 Experiment Problem 2: Bit Loading a) Carry out the calculation of the bit error rate and the data rate for the transmission of a data burst in Matlab by removing the comments of the corresponding program section and starting the program. Display the bit error rate (BER) and the data rate and write them down. In the following part bit loading that is based on the measured SNR values is carried out. The system adapts itself with each transmission and chooses according to the SNR values the constellation to be used for each subcarrier individually. The first transmission is transmitted with the lowest constellation and an SNR measurement is carried out. Not until the second transmission are the other constellations used. test_num shall therefore be set to 2. b) Carry out the bit loading based on the measured SNR values, by removing the comments of the corresponding program section and starting the program. Sketch the block diagram. Plot the number of loaded bits over the frequency using the Matlab function stairs, and then save the plotted image. Also plot and save the SNR over the frequency and then compare both graphs. Write down what you observe. c) Write down the displayed data and bit error rates, and compare these results with the results from part a). Write down which differences you have discerned. 24

28 9 Design of the Experiment Multiple Active Users The second part of the experiment involves the analysis of the DSL system when multiple users are active. To do this set the variable num_of_lines equal to 2 or 3 in the program. Problem 3: Crosstalk cancellation The purpose of this problem is to demonstrate the effects of crosstalk cancellation. Bit loading won t be implemented here, and therefore test_num shall be reset to 1. a) Run Matlab. Plot the SINR over the frequency on the receiving-end. Write down the data rate and the bit error rate for all users. b) Carry out the channel estimation for the user channel and the interference channel. To do this, use the part of the program. Plot the square of the absolute value of the channel transfer function ( ) of the user and interference channels over the frequency for all active users. Write down what you observe. Save the plotted images. c) Carry out the crosstalk cancellation based on the channel transfer matrix measured in part b). Write the Matlab code necessary for the crosstalk cancellation. Additionally, carry out the equalization of the user channel. Plot the constellation diagrams before the crosstalk cancellation and after the equalization of the user channel. Compare them and write down what you observe. Save the plotted images. d) Plot the SNR over the frequency after crosstalk was cancelled and the user channel was equalized. Write down the bit error rates. Compare these values with the results from part a). 25

29 Bibliography [Ded06] [Bin00] [Sjö00] [Cio02] [Cio00] [Bel00] H. Dedieu, K. Jacobsen, P. Golden: Fundamentals of DSL Technology, Auerbach Publications, 2006 J. Bingham: ADSL, VDSL, and Multicarrier Modulation, John Wiley and Sons, Inc., New York, USA, 2000 F. Sjöberg: A VDSL Tutorial, Forschungsbericht, Institut für Systemtechnik, Technische Universität Lulea, 2000 J. Cioffi, P. Silverman, M. Sorbara, T. Starr: DSL Advances, Prentice Hall, 2002 J. Cioffi, P. Silverman, T. Starr: xdsl Eine Einführung, Addison-Wesley, München, Deutschland, 2000 J.C. Bellamy: Digital Telephony, John Wiley and Sons, Inc., New York, USA, 2000 [06] Very high speed digital subscriber line transceivers 2 (VDSL2), ITU Standard, G.993.2,