ADSL System Enhancement with Multiuser Detection

Transcription

1 ADSL System Enhancement with Multiuser Detection A Thesis Presented to The Faculty of the Division of Graduate Studies By Liang C. Chu In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Electrical and Computer Engineering School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta Georgia July 2001

2 ACKNOWLEDGEMENTS There are a number of people that should be recognized for their help and assistance during my thesis work. First of all I want to express my sincere gratitude to my thesis advisor professor Martin A. Brooke, who has given me the opportunity to complete my Ph.D. study at school of Electrical and Computer Engineering in Georgia Institute of Technology. I really appreciate the time for his advising and it is very rewarding and inspiring to discuss questions with professor Brooke. I also want to thank professor Nikil Jayant and professor John Copeland, who have taken an active part in advising and guiding me in my research and education. Furthermore, I gratefully acknowledge professor Donald L. Schilling, who always encourages my study during these years, since I was studying in my Master s degree with him at the City College of New York, CUNY. Also, I would like to thank professor Russell M. Mersereau and professor Zhong L. Wang for their supporting to serve in my thesis committee, and all my colleagues at school of Electrical and Computer Engineering, Georgia Tech. Finally, and most importantly, I sincerely thank my wife, Dr. Jing Li, who help and support me in my graduate study at Georgia Tech during these years, and deeply love and care about me always. Also, I greatly thank my parents, Mr. Hsun C. Chu, Ms. Sai Y. Feng, and my bother, Dr. Liang T. Chu, for their continuing care and encouragement all the times in my life. I would like to show my great appreciation to my families for their constant help, support and encouragement. ii

3 ADSL System Enhancement with Multiuser Detection Approved: Dr. Martin A. Brooke, Chairman Dr. John A. Copeland Dr. Nikil Jayant Date Approved iii

4 Table of the Contents Chapter One: Introduction 1 Chapter Two: Background 5 2. Problem on the DSL Spectral Compatibility with Crosstalk Current Crosstalk Model and Distribution NEXT and FEXT Modeling Crosstalk Noise Distribution Spectral Compatibility between Asymmetric and Symmetric DSL Systems Symmetric DSL Systems Studies on Crosstalk Noise between ADSL and SDSL Current Deployment Plan and Proposed Enhancement 15 Chapter Three: DMT-ADSL Channel Modulation and Characteristics Multiuser Multitone Modulation System and ADSL Overview of Discrete Multitone Analysis of Discrete Multitone Channel Gap Analysis Margin of the DMT Performance Calculation Bit-loading and DMT-ADSL System 26 Chapter Four: Channel Model and Multiuser Transmission Twisted Wire Pairs Characteristics Electrical Characteristics of Twisted-pair Wires 33 iv

5 4.1.2 Telephone Channel Multiuser Transmission System Basic on Multiuser Detection Optimum Multiuser Detection Linear Multiuser Detection in AWGA Channel 42 Chapter Five: ADSL System Enhancement Multiuser Detection on DMT-ADSL System Theoretic Bounds on DMT-ADSL Channel Spectral Distribution on the Multiuser Channel Capacity Examples on Capacity Bound Analysis Joint Maximum-likelihood Sequence Estimation (JMLSE) DSL Co-channel Signal Model MLSE Receiver Design T/2-spaced MLSE Receiver Analyzing MLSE Receiver Structures Reduced Complexity Receiver Structures Joint MLSE for DMT-ADSL Receiver Preliminary Performance Studies 81 Chapter Six: Low Complexity Enhancement on ADSL Receiver Tone-zeroing Method Low Complexity Joint MLSE Multi-stage JVA Multi-stage JVA with Feedback 95 v

6 6.2.3 Practical Enhanced ADSL Receiver Example and Comparison 101 Chapter Seven: Performance Evaluations and Simulation Results on Enhanced ADSL Receivers Test Environment Test Channel Conditions Loop Characteristics Capacity Improvement Reach Improvement Disturber Scenarios Co-channel Transfer Functions Simulation Results 110 Chapter Eight: Conclusions 115 Chapter Nine: Recommendations 117 Reference 119 vi

7 LIST OF FIGURES Figure Page Near-end Crosstalk (NEXT) Far-end Crosstalk (FEXT) NEXT Power Sum Losses for 25 Pairs of PIC Cable Binder Group PSD of 2B1Q SDSL at 1168, 1552 and 2320 kbps Downstream ADSL Bit Rate with 1552 & 2320 kbps SDSL NEXT Basic Multitone Modulation Transmission Illustration of Frequency Bands for Multitone Transmission System DMT Bit-Loading Concept DMT-ADSL Frequency Spectrum Transmission Line Segment Basic Multiuser Transmission System ADSL Channel Model with k-l Crosstalk Signals TPC Attenuation Function with Difference Length Channel Attenuation and NEXT Coupling Characteristic Channel Capacity Single vs. Multiuser Channels Co-channel System Model Basic Receiver Structure Sophisticated Receiver Structure Carrier Recovery in the Noise-free AWGN Channel 78 vii

8 Joint ML Sequence Detection between Adjacent Pair BER for ADSL System with Single-user Detector and JMLSE ADSL System with SDSL Crosstalk on Single-user Detector and JMLSE Joint ML Crosstalk Signal Canceller with Tone Zeroing Margin on DMT-ADSL with Tone-zeroing Crosstalk Noise Cancellation Two-stage JVA (without Feedback Section) Single-user MLSE Computational Flow Structure Two-stage JVA (with Feedback Section) Desired Channel Performance with Three Methods Testing Loops Scatter Plot of Downstream ADSL Throughput with Mixed SDSL Crosstalk Rate-reach Curves for Test Loop # Rate-reach Curves for Test Loop # Rate-reach Curves for Test Loop # Channel Attenuation and NEXT Characteristic 118 viii

9 LIST OF TABLES Table Page Worst-case Measurement for Telephone Channels Disturber Scenarios 109 ix

10 Summary In this thesis, a new approach on mitigating the cochannel interference (CCI), also called crosstalk, in the Asymmetric Digital Subscriber Line (ADSL) transmission system has been studied. This implementation ensures the spectral compatibility in the DMT- ADSL system together with other DSL services in a same binder cable. The major part of this thesis concerns a modified technique for high-speed communication over the ADSL telephone network. Discrete Multitone (DMT)-ADSL has been standardized in American National Standards Institute (ANSI) [1]. It offers bit rate up to 8 Mbps downstream and 1 Mbps upstream, depending on the deployment coverage ranges. A modified method based on multiuser detection is presented herein, which can mitigate the crosstalk interference in DMT-ADSL receiver. An important issue for ADSL is the problem with crosstalk, which is a major threat in ADSL receiver with other DSL services in a same binder. The performance on the mitigation of ADSL channel crosstalk impairment is the most important criteria for guaranteeing the Quality of Service (QoS) in an ADSL system. The essential issue of this thesis on optimizing the ADSL system transmission throughput is to modify its channel transceiver design. Treating an ADSL channel as a multiple-input and single-output (MISO) system with desired ADSL signal and cochannel interference signals is just like a multiuser communication channel model. Our modified ADSL multiuser detection can greatly outperform the currently deployed single-user receiver with either increasing transmission data rates, or extending deployment rages in impairment environments. Joint Maximum Likelihood Sequence Estimation (JMLSE) gives very good performance x

11 in our proposed model, but known as a computationally complex technique. The last part of this thesis deals with low complexity multiuser detection to balance the ADSL system performance and computational complexity with a reasonable VLSI capability, which can be implemented in a sub-optimum solution. With these approaches to the mitigation of ADSL impairments, the performance of the ADSL system is greatly enhanced; for example, the ADSL service can be either extended more than 2-kft from the current limit, or has more than 30% transmission data rate improvement, depending on the cost requirement. Under these circumstances, the capacity of the network is utilized to a near sub-optimum solution. [1]Asymmetric Digital Subscriber Line (ADSL) Metallic Interface, ANSI Standard T , ANSI, New York. xi

12 CHAPTER ONE INTRODUCTION This thesis deals with an enhancement approach on the DMT-ADSL twisted-pair wires communication system. Our implementation ensures the spectral compatibility between different DSL systems in a same binder cable. Therefore, the capacity of the DMT-ADSL telephone network to support fast Internet access can be better utilized than current solutions. Today, an increasing number of people use the telephone access network for digital data communication. Even if the speed of an analog modem has increased to 54 kbps, it is still frustratingly slow for the next generation fast Internet multimedia services. Highspeed access to Internet service with various kinds of multimedia content has become an emerging technology that is needed by all telecommunications end users. One of the best solutions is Digital Subscriber Lines (DSL) access, which is targeted for residential users, and has recently received much attention by many telephone companies. The architecture of DSL systems allows telephone companies to use existing twisted-pair infrastructures for their next-generation broadband access networks. The sheer inertia of the worldwide installed copper base means that it could take many years for access networks to migrate from copper to fiber. A combination of the existing copper 1

13 infrastructure and digital subscriber line transmission technologies means that a new era of universal broadband access can now begin at a fraction of the cost and in a fraction of the time required for optical access networks. Even with fiber optical network, the DSL technologies will still exist in the last-mile access transmission. Over the past ten years, DSL technologies have been developed and use larger parts of the available TCP bandwidth. Normally, xdsl use 1 to 15 MHz bandwidth. To be able to use this large bandwidth, the telephone lines interface in the center office (CO) and customer premise end (CPE) need to be exchanged when employing xdsl techniques. However, there is a serious threat to this vision of the future: a variety of impairments in the access systems. The reason is when trying to reach higher bit rates, there is no problem on the channel capacity of the twisted copper pair (TCP), but rather high frequency digital signal interfaces between the lines inside a same telephone binder. As we know that the telephone access networks were originally built for analog voice communication, carrying voice-band signals up to 4 khz in the frequency bandwidth and not for digital data communication. It is relatively simple to design transmission systems that work well in simulations and some specific laboratory tests, but more difficult to deliver useful capacity when subjected to the hostile environment of the real network. The uncontrolled deployment of such advanced transmission systems in multipair cables can result in server degradation due to cochannel interference. This interference is a linear coupling among multiple channels, also called crosstalk [1]. Even though this problem has been studied in the past [2], [3],[4], [5], solutions for real-world DSL services deployment are not currently available. Even low data rate implementation, such as ISDN service, can significantly pollute the copper network. The current DSL systems 2

14 are modeled as single-user channel models and crosstalk is treated as white Gaussian noise [6]. This approach is usually conservative, as the true crosstalk signal distributions are bounded in amplitude. However, the Gaussian assumption reduces the attainable channel capacity, but hold for the case of current practical interests [6]. It is well known that the spectral compatibility has become a major issue for all DSL services, especially in the transmission of symmetric and asymmetric services in the same binder group [7], [8], [9], [10]. It is likely that as the DSL services reach significant penetration, their crosstalk between different services will become an important factor to the success of DSL services. The objective of this thesis research is to understand the spectral compatibility issues for various DSL variants [11], in order to determine a more accurate DMT-ADSL channel model and implement with digital signal processing techniques that realize the true broadband potential of the existing copper access network. Currently, a study [12] has demonstrated that crosstalk effects on VDSL might be mitigated; essentially, treated crosstalk is not exactly Gaussian. The drawback of this approach is computational complexity in realization. It is well known to us on accurate models for the case of a single type of crosstalk, where all crosstalk signals have the same power spectral density. The model is called the 1% worst-case crosstalk power-sum. It is described that no more than 1% of all pairs in all binders can receiver more crosstalk than this model [13]. However, crosstalk from multiple different types of DSL services is a relatively new area of study. In this thesis, we focus on a study of the DMT-ADSL system enhancement coupling with the SDSL services in a same binder cable. Our studies can apply to any cases of DSL application, where coexists asymmetric and symmetric services. A 3

15 proposed multiuser channel model has been derived, and the enhancement on the DMT- ADSL receiver is introduced to mitigate crosstalk from the SDSL services. Some important simplification algorithms, such as tone zeroing [14], and multi-stage joint maximum-likelihood detection for multiuser DMT-ADSL are derived, which can largely reduce the multiuser DMT-ADSL receiver complexity. Our proposed sub-optimal approach, multi-stage JMLSE with feedback section has a reasonable computational complexity, and also improves Signal-to-Noise-Ratio (SNR) about 8 db at a Bit-Error Rate (BER) of 10-7 in the DMT-ADSL channel. This enhancement gives us a core method on either increasing signal constellation sizes of each DMT sub-channel, or extending the deployment ranges with a fixed transmission rate, or compensating on a poor BER channel in achieving better throughput. In the following sections of this thesis, the origin of the spectral compatibility problem and its current solutions are covered; a new approach technique for mitigation on crosstalk interference is presented; and simulation procedures and results are addressed. Finally, discussions and conclusion of this thesis are presented. 4

16 CHAPTER TWO BACKGROUND 2. Problem of DSL Spectral Compatibility with Crosstalk Digital subscriber line technology provides transport of high-bit rate digital information over telephone lines. High-speed digital transmission via telephone lines requires advanced signal processing to overcome transmission impairments resulting from crosstalk noise from the signals present on the other wires in the same binder, radio noise, and impulse noise. Fortunately, amateur radio signals are narrowband and transmission methods attempt to notch the relatively few and narrow bands occupied by this noise, which avoids the noise rather than transmitting through it. Impulse noise is nonstationary crosstalk from temporary electromagnetic events in the vicinity of phone lines. The effects are temporary and typically at much lower frequencies. The channelcoding algorithm in ADSL overcomes this effect [15]. As increasing number of DSL services are deployed, the concern is that assumptions made in the design of modem equipment for one type of service will lead to errors in another type of modem equipment, which also share the cable. This is the crosstalk noise. Crosstalk can be the biggest noise impairment in a twisted pair and substantially reduces DSL performance when it cannot be circumvented. In this thesis, we focus on the ADSL receiver 5

17 enhancement design to mitigate the crosstalk from the other DSL services (mainly targeting on SDSL service). In general, this approach can be applied to any other DSL systems, such as VDSL, with their related channel characteristics. 2.1 Current Crosstalk Model and Distribution The primary impairment to sending digital information through the twisted-pair loop is crosstalk noise from similar digital services of adjacent loops. In the current situation, DSL transmission is treated as a single-user channel with crosstalk noise as loose Gaussian distribution [6]. The crosstalk noise can be categorized into two types. Crosstalk to a receiver from a neighboring transmitter is called near-end crosstalk (NEXT), as shown in Fig , and crosstalk to a receiver from a transmitter at the opposite end is called far-end crosstalk (FEXT), as shown in Fig

18 Same Binder Group NEXT Transmit Receive Fig : Near-end Crosstalk (NEXT) Same Binder Group Transmit FEXT Receive Fig : Far-end Crosstalk (FEXT) 7

19 2.1.1 NEXT and FEXT Modeling In the case of the NEXT model, it uses Unger s NEXT model [16], which states, as expected, 1% worst-case power sum crosstalk as a function of frequency [17]. NEXT is dependent on frequency as well as on the relative location of the pairs in the binder group. Thus, to find the crosstalk noise from a contributing circuit into another twisted pair in a 50-pair binder, the power spectral density (psd) on any line in the binder is modeled by S n N = ( ) 10 f S xtalk _ 49 cont ( f ), ( ) where N is the number of crosstalk-contributing circuits in the binder, S xtalk_cont is the psd of crosstalk-contributing circuits. FEXT is usually characterized in terms of 1% worst-power sum loss from all signals on other pairs in the binder group [17]. FEXT is less severe than NEXT because the FEXT noise is attenuated by traversing the full length of the cable. Measurement study on a number of pairwise coupling transfer functions in a 50-pair binder cable by C. Valenti [17] has been shown in Fig There are two interesting issues as shown in Fig First, it shows that the NEXT increases as f 1.5 with frequency, but with significant variation in coupling with frequency. 8

20 NEXT POWER SUM LOSS(dB) 1000 FT, 24 AWG PIC FREQUENCY(MHz) 1% Case Fig : NEXT Power Sum Losses for 25 Pairs of PIC Cable Binder Group Note: Power Sum Loss is expressed as 10 log 10 ( Power Sum Transfer Function ) 9

21 Second, at any given frequency, only few other pairs may contribute significantly to crosstalk, but over all frequencies, many wire lines contribute randomly. As a practical convenience, many telecommunication engineers who work on DSL, average the coupling over many pairs. They assume that the sum of many coupling functions is constant. Therefore, as shown in Eq. ( ), this constant has been determined by ANSI as N ( ) in a 50-pair binder Crosstalk Noise Distribution It has been widely used that in the time-domain, crosstalk noise at the DSL receivers is treated as a Gaussian distribution [6]. Obviously, this statement is not true for single crosstalk interference, because of the highly-frequency-dependent nature of the crosstalk. When summed over all frequencies from different contributors on different lines, the central limit theorem of statistics loosely applies to this statement. Practically, it has been validated that this does hold for the case of practical interest [6]. The drawback of such an analysis may strongly depend on the size error between a Gaussian distribution and its true distribution. When background thermal noise is small, this error can actually be large with respect to such noise. 2.2 Spectral Compatibility between Asymmetric and Symmetric DSL Systems Determining spectral compatibility between new and existing DSL services is a significant challenge. Recently, a number of studies have been conducted on spectral compatibility between DSL systems [18], [19], [20], [21]. Spectral compatibility has become a major issue for all DSL systems, especially with respect to transmission of 10

22 asymmetric and symmetric services in the same binder group. When DSL deployment reaches significant penetration, crosstalk between the various DSL services will become the dominant performance-limiting factor to QoS of DSL systems. The spectral compatibility of the ADSL service with the deployment of SDSL services is the main focus of this thesis Symmetric DSL Systems In 1996, ETSI has made the single-pair HDSL (early version of SDSL) in standard. This service transmits a full E1 payload on a single copper pair with a variable line rate up to 2320 kbps [22]. The technique that enables this superior performance of a singlepair SDSL service, uses the same 2B1Q modulation, (as in HDSL, and ISDN), but with a modified maximum likelihood detection on its receiver. There is no error correction coding in SDSL systems. SDSL transmits the same data rate in the upstream and downstream directions and same transmit PSD in the upstream and downstream directions. It is bi-directional and echo-canceled system. 2B1Q SDSL transmits a 4-level baseband pulse amplitude modulation signals. 2B1Q SDSL systems operating at different bit rates have different transmit PSDs. More detailed information about SDSL can be found in [22], [23], [24] Studies on Crosstalk Noise between ADSL and SDSL The spectral compatibility of high-rate SDSL services with the ADSL service in the same binder is studied herein. We focus on SDSL services interfere ADSL service, because of the following two reasons. First, The SDAL services are high in demand for 11

23 the future deployment and run on a single twisted pair telephone line together with ADSL service in a same binder. Second, the PSDs of SDSL services, shown in Fig , are overlapped in most areas with ADSL PSD, which is from DC to 1.104MHz. Spectral compatibility results are calculated for same-binder NEXT with the standard Unger 1% NEXT model. The maximum achievable bit-rate of T1.413 full-rate DMT ADSL in the presence of NEXT from SDSL systems was calculated. The DMT tones are separated by khz, and the received SNR of each tone was calculated. The maximum bit-rate that each tone can carry with a 6dB SNR margin was found and then summed across all tones to get the total achievable T1.413 bit rate. The average transmit power of downstream ADSL is -40 dbm/hz, and the average transmit power of upstream ADSL is -38 dbm/hz, within the passband. T1.413 ADSL is assumed to have trellis coding gain of 3dB and 2dB ripple, and is FDD with non-overlapping upstream and downstream spectra. Downstream T1.413 ADSL is assumed to transmit from 160 khz to 1104 khz, and upstream T1.413 ADSL transmits from 26 khz to 138 khz. The pilot tones carry no data. A maximum of 12 bits per Hz can be transmitted by any tone in the T1.413 simulations here, allowing a maximum constellation size of 4096 points. ADSL bit rates are rounded down to the nearest integer multiple of 32 kbps. Cyclic prefix redundancy (6.66%) and a minimal 32 kbps EOC redundancy was removed before presenting the bit rates here. Achievable downstream ADSL bit rates in the presence of SDSL crosstalk is obtained as a function of loop length and SDSL data transmission rates. The simulation studies have shown that high rate, such as 1552 and 2320 kbps SDSL NEXT, largely reduces the ADSL downstream transmission data rates below its required minimum target rate, which 12

24 is 6 Mbps (low bound) up to 9 kft and 1.5.Mbps (low bound) between 9 to 18 kft. The results are shown in Fig It is obvious that the higher the data rate of the SDSL transmission, the poorer the performance of the ADSL achievable rate. The degradation of the ADSL achievable rates can also be caused by the other DSL services in a same binder with the similar manner. Therefore, it is necessary for us to modify the ADSL system to suppressing crosstalk noise from the SDSL services (also to the other DSL services) to utilize its optimal capacity at reasonable cost. (Meanwhile, the preliminary enhancement studies on the SDSL systems can be found in [25], [26].) PSD (dbm/hz) , 1552 and 2320 kbps SDSL 1168 kbps 1552 kbps 2320 kbps Frequency (Hz) Fig : PSD of 2B1Q SDSL at 1168, 1552 and 2320 kbps 13

25 DMT-ADSL System with 24-SDSL Crosstalk Downstream Bit Rate in kbps kbps SDSL crosstalk 2320 kbps SDSL Crosstalk AWG Loop Length in kft Fig : Downstream ADSL Bit Rate with 1552 & 2320 kbps SDSL NEXT. 14

26 2.2.3 Current Deployment Plan and Proposed Enhancement For the telephone companies deploying the ADSL and SDSL services in their loops, they use a so-called loop plan, which is basically testing and estimating of their deployment loops with limitation on the coverage and numbers of the customer subscribers. Therefore, the ADSL achievable rates degradation resulting from the crosstalk can be loosely controlled with various DSL services in the same binder groups. The drawbacks of this method are inconvenience for deployment management; limit on the transmission data rate; not rejecting out-of-band signal (crosstalk) by receivers, and trading off the loop coverage and subscriber numbers. Our studies on the crosstalk characteristics show that the crosstalk channel characteristics change very slowly over the time and can be modeled as static. Moreover, the type of crosstalk on each line, say on ADSL service line, does not change, as there are fixed DSL services in the same binder from the CO to CPE sides. Therefore, mitigating the crosstalk between DSL systems, we use a technique to enhance the ADSL receiver that filters the crosstalk noise. Without loss generality, this approach can be applied to the other DSL systems as well. 15

27 CHAPTER THREE DMT-ADSL CHANNEL MODULATION AND CHARACTERISTICS 3. Discrete Multitone Modulation System and ADSL Discrete Multitone (DMT) is a common form of multicarrier modulation. It has been introduced by IBM [27] to take advantage of digital signal processing and the FFT. It was later refined to a very high-performance form [28], [29]. That later form is used in the most recent multicarrier voiceband modems, such as ADSL [30]. DMT is a method to approximate the channel complex filters by simpler operations, which are to exploit the knowledge of the channel information matrices, tend to discrete Fourier transforms (DFT) algorithm [31]. It is similar to orthogonal frequency division multiplexing (OFDM), which is widely used in wireless communications systems. A DMT system transmits data in parallel over narrowband channels. The subchannels carry a different number of bits, depending on their SNR. A DMT system transmits data using a twodimensional QAM on each channel. DMT-ADSL has been standardized by ANSI [15]. Herein, we only focus our study in DMT-ADSL. We are going to have an overview on DMT system first, before landing on the details of the DMT-ADSL system. 16

28 3.1 Overview of Discrete Multitone The principle of multitone transmission is by using two or more coordinated passband (like QAM) signals to carry a single bit stream over the communication channel. The passband signal are independently demodulated in the receiver and then remultiplexed into the original bit stream. The motivation for multitone is that if the bandwidth of each the sub-channel (tone) is sufficiently narrow, then no ISI occurs on any sub-channel. The individual passband signals may carry data equally or unequally. Usually, the passband signals with largest channel output SNR carry a proportionately larger fraction of the digital information. Fig shows the simplest multitone system to understand. N QAM (or like) modulators, along with possibly one DC/baseband PAM modulator, transmit N+1 subsymbol components X, n = 0, 1,, N, where N = N / 2 and N is assumed to be n even number. X 0 and X N are real one-dimensional subsymbols while X n, n = 1, 2,, N-1 can be two-dimensional complex subsymbols. Each subsymbol represents one of b 2 n messages that can be transmitted on sub-channel n. The carrier frequencies for the corresponding sub-channels are f n = n T, where T is the symbol period. The baseband- 1 t equivalent basis functions are ϕ n = sinc( ), n. The entire transmitted signal can T T be viewed as N+1 independent transmission sub-channels as indicated by the frequency band of Fig

29 X 0 ϕ ( t 0 ) j 2πf1t e j 2πf1t e ϕ ( ) 0 t Y 0 X 1 ϕ 1 ( t)... + j 2 f N 1t e π real part n(t) + h(t) + phase split + j 2πf N 1t e ϕ ( ) 1 t... Y 1 X N-1 X N ϕ ( t N 1 ) ϕ N (t) + + j f Nt e 2π N = 2N Y = H X + N n n n n + e + j 2πf Nt ϕ ( ) N 1 t ϕ ( N t) Y N Y N-1 Fig Basic Multitone Modulation Transmission 18

30 X ( f ) Input... X 0 X 1 X 2 X N-1 X N H ( f ) Y n H n X n Y ( f ) Output... Y 0 Y 1 Y2 Y N-1 Fig : Illustration of Frequency Bands for Multitone Transmission System 19

31 The multitone-modulated signal is transmitted over an ISI/AWGN channel with the corresponding demodulator structure also shown in Fig First quadrature decoupling with a phase splitter and then baseband demodulating with a matchedfilter/sampler combination separately demodulates each sub-channel. With this particular ideal choice of basis functions, the channel output basis function ϕ ( ) is an p, n t orthonormal basis set. Each sub-channel may have ISI, bit as N, this ISI vanishes. Thus, symbol-by-symbol detection independently applied to each sub-channel implements an overall maximum-likelihood (ML) detector. No equalizer (nor Viterbi detector) is necessary to implement the maximum-likelihood detector with large N. Therefore, ML detection is more easily achieved with multitone modulation on an ISI channel than it is on a single QAM or PAM signal, the latter of which would require sequence detection with the Viterbi algorithm for a large number of states. Equalization is also unnecessary if the bandwidth of each tone is sufficiently narrow to make the ISI on that sub-channel negligible. Multitone modulation typically uses a value for N that ensures that the pulse response of the ISI channel appears almost constant at H ( n / T ) H = n H ( f ) for f n / T < 1/ 2T. In practice, this means that the symbol period T greatly exceeds the length of the channel pulse response. The scaled matched filters simply become the bandpass filters ϕ ϕ j(2π / T ) nt p, n ( t) = n ( t) = 1/ T sinc( t / T ) e and the sampled outputs become Y H X + N (3.1.1) n n n n 20

32 The accuracy of this approximation becomes increasing exact as N. Fig illustrates the scaling of H n at the channel output on each of the sub-channels. Each subchannel scales the input X n by the pulse-response gain H n. Each sub-channel in the multitone system carriers b n bits per symbol. The total number of bits carried by the multitone system is then b = N b n n= 0 (3.1.2) and the corresponding data rate is then R = b T = N R n n= 0 (3.1.3) where Rn bn / T. Thus, the aggregate data rate R is divided, possibly unequally, among the sub-channels. With sufficiently larger N, an optimum ML detector is easily implemented as N+1 simple symbol-by-symbol detectors. This detector need not search all combinations of b m = 2 possible transmit symbols. Each sub-channel is symbol-by-symbol detected. The reason for this ML detector is so easily constructed is because of the choice of the basis function: multitone basis functions are generically well suited to transmission over ISI channels. 21

33 3.2. Analysis of Discrete Multitone The multitone transmission system is construed as N subchannels (tones). The most importance is performance analysis and optimization of performance for the entire set of subchannels Channel Gap Analysis The probability of error for a multicarrier system is the average of the probabilities of error on each sub-channel. We assume that the probability of subsymbol error to be equal on all sub-channels and to be equal to P e / 2 = We also assume that the gap Γ, is a constant value for all the sub-channels, which is defined for any coded QAM system as Γ = γ ( db) ( ) m γ c where γ m is the margin and γ c is the coding gain. We derive for an individual i th sub-channel that having 2 2 d H i d i 3Γ = = ( ) 4 4δ 2 min, i 2 δ i 2 i 22

34 For any sub-channel, we have SNRi b i = log 2 (1 + ) ( ) Γ as the maximum number of bits per symbol that can be carried on that sub-channel with margin γ m and coding gain γ c. The quantity SNR i is computed by SNR i 2 H i ε i = ( ) 2δ 2 i in this thesis, we assume that ε i = ε, a constant value on the sub-channels used and zero on else. This is called on/off energy distribution. In practice, a better solution on the energy distribution, which is called water-pouring can be found in [32]. Moreover, in a DMT system, the sub-channels carry a different number of bits, depending on their respective SNR i, this is referred to as a bit-loading algorithm. Several techniques on how to perform bit-loading in a DMT system has been studied [33], [34], [35], [36] and [59] Margin of the DMT The total number of bits that is transported in one symbol is the sum of the number of bits on each of the sub-channels, that is N N SNRi b = b = log (1 + ) ( ) i 2 i= 1 i= 1 Γ 23

35 Therefore, the data rate is b R = ( ) T Eq. ( ) can also be derived as N SNR b = log [ (1 + i )] ( ) 2 i= 1 Γ We can define an average SNR as 1 N SNR N SNR = Γ{[ (1 + i )] 1} ( ) Γ i= 1 Therefore, Eq.( ) can be written as SNR b = N log 2 (1 + ) ( ) Γ From Eq. ( ), it permits direct computation of a margin for a multicarrier system with fixed data rate and probability of error. Normally, the -1 term in Eq. ( ) can be ignored, and the average SNR becomes the geometric average N N SNR [ ( SNR i )] ( ) i

36 The definition of margin, γ m, for transmission on an AWGN subchannel with a given SNR, a given number of bits per dimension b, and a given coding-scheme/target-p e with gap Γ is the amount by which the SNR can be reduced and still maintain a probability of error at or below that target P e [37]. We may compute the margin of the DMT with Eq. ( ) as SNR γ = [ 10log10( ) + γ 9.8 db ( ) m b c ] N Performance Calculation The procedure to analyze the multicarrier system is summarized in [37] as: 1. From the power budget, compute a preliminary subsymbol energy allocation PT according to ε = ε i =. N 2. Compute the sub-channel SNR s according to SNR i 2 ε H = ( ) δ i 2 i 3. Compute the number of bits that can be transmitted on each sub-channel with given margin and given error correction code SNRi b i = log 2 (1 + ) ( ) Γ 25

37 4. For those sub-channels with b < 0. 5, reset ε = 0 and reallocate their energy to i the other sub-channels equally. Then, we need re-compute b i. 5. Compute b by summing the b i, and then compute the maximum data rate R = b/t. i A margin can be computed using any number of used sub-channels. For data rates considerably below theoretical optimums, the number of used sub-channels often decreases with respect to the bandwidth used for the maximum data rate. The bandwidth with the best margin is used for a target rate, which is lower than maximum data rate Bit-loading and DMT-ADSL System In this subsection, we review the concept on the DMT-ADSL system characteristics. Fig , illustrates the concept of the bit-loading algorithm in the DMT-ADSL system. Bit-loading is a technique that is used for multicarrier systems (DMT in this thesis) operating on a stationary channel [33]. A stationary channel makes it possible to measure the SNR on each subchannel and assign individual numbers of transmitted bits. A subchannel with high SNR transmitted more bits than a subchannel with low SNR. Fig shows a schematic picture of SNR and how the numbers of bits on each subchannel vary accordingly. When performing bit loading, one usually optimizes for either high data rate, or low average transmitting energy, or low error probability. Typically two of these are kept in constant, and the third parameter is the goal for the optimization. The parameter is optimized depending on the system, its environment, and its application. 26

38 In a multi-system environment, where there are several DSL systems transmitting in the same binder, the problem is complicated, since this kind of system experience crosstalk. The level of crosstalk is proportional to the transmitting power in the systems, as shown in Eq.( ). It is therefore desirable to have an equal transmission power in all systems, to obtain equal distribution. In a multi-system environment, the average transmitting power is usually fixed, and the optimization is for either high data rate or low BER. There are several techniques for bit loading in DMT systems and some of these are described [33], [38], [39], [40]. As mentioned earlier, there are several parameters that one can optimize for. Most algorithms optimize for high data rate or low BER. Given a certain data rate and energy constraint, the algorithm to achieve minimal BER is to assign one bit at a time to the subchannels. The algorithm calculates the energy cost to send one bit more on each subchannel. The subchannel with smallest energy cost then assigned the bit. This procedure is repeated until a desired bit rate is obtained. In [38], it has shown that complexity of this algorithm is proportional to the number of subchannels and the number of bits transmitted in a DMT frame. It also suggests a suboptimal algorithm of low complexity. An algorithm that maintains an equal bit-error probability over all subchannels, given a data rate and an energy constraint, is presented in [39]. A suboptimal way of performing bit loading to achieve a high data rate, while maintaining a constant BER across all subchannels is shown in [40]. In this algorithm, the bit-loading are calculated by 27

39 b 3Ek g kγ d = log 2 ( + 1) log 2 2Kδ k 2 k C ( ) where b k is the number of bits carried on subcarrier k, E k is the average symbol transmission energy, g k is the channel attenuation, and δ 2 k is the noise variance. The coding gain is denoted γ d and the constellation expansion factor, due to coding is denoted C. To obtain a desired symbol error rate of P e, the design constant K is chosen to K P 1 e 2 = [ Q ( )] ( ) N e where N e is the number of nearest neighbors. Expression Eq. ( ) can be viewed as the union bound for a QAM constellation, with some modification for coding, where K is the SNR required obtaining an error 3Ek g kγ probability P e. The channel SNR, 2 2Kδ k d, is divided by the SNR required to transmit one bit. The number of bits needed in the coding, log 2 C is subtracted to get the number of bits carried by subchannel k. Finally, to handle the situation where the numbers of transmitting systems vary one can either do the bit loading for a worst case or employ adaptive bit loading. In [38], it has presented such an adaptive algorithm, which called bit-swap algorithm, designed for the case when a fixed data rate is specified. For detailed information on the bit-loading for DMT-ADSL system, it can be found in [41], [42]. 28

40 The ANSI T1.413 and ITU g.dmt ADSL system are standardized in the DMT system [15]. The standards of the characteristic of the DMT-ADSL system are addressed in the rest of the section. Bits/channel Attenuation AM Crosstalk Frequency Frequency Frequency Fig : DMT Bit-Loading Concept. 29

41 As shown in Fig , the DMT-ADSL system has two traffic channels. One is downstream transmission, which signals from CO to CPEs side; the revised traffic is called upstream transmission. They occupy different bandwidths. In a downstream transmission, the system employs a sampling rate of MHz, a block size of 512 (FFT) with conjugate symmetry, meaning 256 tones (subchannels) from 0 to 1.104MHz. The actual downstream symbol rate is 4 khz and the width of a tone is khz. The average downstream psd is 40 dbm/hz. The upstream transmission employs a sampling rate of 276 khz, a block size 64, with conjugate symmetry, meaning 32 tones from 0 to 138 khz. The symbol rate for the upstream transmission is 4 khz and the width of the tone remains khz. The average upstream psd is 38 dbm/hz. The detailed state of the DMT-ADSL system can be found in [15], [43]. 30

42 # of Bits 14 Upstream Channel Downstream Channel POTS Frequency in khz Fig : DMT-ADSL Frequency Spectrum 31

43 CHAPTER FOUR CHANNEL MODEL AND MULTIUSER TRANSMISSION The investigation of crosstalk testing results [17], in Fig. 3, shows that the crosstalk coupling function generally increases as f 1.5 with frequency, but with significant (about 10 to 20 db) variation in coupling with frequency. At any given frequency, only a few other pairs may contribute significantly to crosstalk. Over all frequencies range, many lines contribute crosstalk affect. Plus, the crosstalk psd is significantly high than the background psd of AWGN. Otherwise, the crosstalk would not dominate the effect on DSLs. With these conditions, we propose multiuser detection [44] for the DMT-ADSL receiver that significantly outperforms the single-user detection, which treats crosstalk as a Gaussian distribution. In the following section 4 and 5, we derive the twisted-pair channel model and introduce the multiuser transmission systems. 4.1 Twisted Wire Pairs Characteristics Twisted wire pairs are the dominating cable type in telephone access networks that are built for point-to-point two-way communication. The copper wire pair does not change its physical behavior significantly with time and is considered a stationary channel [55]. This makes it possible to use a technique called bit loading [33], as shown in section for DMT transmission system, which also makes good use of the 32

44 spectrally shaped channel. Since DMT with bit loading makes efficient use of available bandwidth, it has become a good candidate for DSL systems. The characteristics of the wire pair channel have been studied in number of the papers [45], [55], [11]. In this thesis, twisted pair cable transfer function is derived from lab measurements using an HP 89410A spectrum analyzer. The transfer function can be modeled as H att 10 ( d, f ) = 10 e RCf d (4.1.1) where d is the cable length, att is the maximum attenuation, and RC is the cable constant. The corresponding impulse response is given by h( d, t) = 10 0 att 10 2 RCd RC e 3 4π t 4t t > 0 (4.1.2) t < 0 This model is often used when DSL systems are analyzed [54], [46]. As DSL services carry on the telephone network, we discuss the characteristics of the telephone channel in the following subsection Electrical Characteristics of Twisted-pair Wires The details of twisted-pair wire line electrical characteristics can be found in [47] and [48]. According to standard transmission line theory, a wire line can be thought of as a succession of many small sections of the kind shown in Fig The inductance and 33

45 capacitance of the line section are given in L and C per unit length, and the line dissipation losses are R 1 ohms per unit length down the line and R 2 ohms per unit length across the line. For any sections, the characteristic impendence, defined as the ratio of voltage to current, is R1 + jωl Z 0 = and ω = 2πf ( ) R + jωl 2 + I L dy R 1 dy V R 2 dy C dy _ dy Fig : Transmission Line Segment Another wire line parameter, called propagation constant is defined as γ = R + jωl)( R + jω ) ( ) ( 1 2 C 34

46 If a voltage V ( jω) or a current I ( jω) enters the telephone line, it can be decayed along the line as V ( jω) exp( γy) or I ( jω) exp( γy). In particular, amplitudes decay as ( y) e α, where α is the real part of γ, called the attenuation constant. Normally, it is expressed as 20α y log10 e (db/length) ( ) The wave velocity along the line is ω / β, where β is the imaginary part of γ. We need stress that all these parameters depend on the frequency. In particular R is approximately f, because of the skin effect in conductors Telephone Channel The telephone is an analog medium with a certain character, roughly speaking as a linear channel with a voice passband of 300 to 3300 Hz initially. There are many kinds of actual physical telephone channels, due to several telephone network connections in the world. In fact, it is necessary to define the telephone channel statistically, because no fixed definition is practical. Extensive studies of the telephone network have been made in different parts of the world. In North America, the telephone channel has been studied in [49], and [50]. In Table , we summarize some of its main conclusions. 35

47 Table Worst-case Measurement for Telephone Channels Attenuation, end to end, at 1 khz SNR, with special weighting Frequency offset Peak-to-peak phase jitter, Hz Phase jumps greater than 20 o Noise impulses, 4 db below mean signal or 27 db 20 db 3 Hz 13 o 1/per minute 4/per minute higher Delay 50 ms Different wire line definitions need be pointed out here for a better understanding on the telephone loops. The term on leased line refers to a connection that is permanently allocated to a customer, rather than dialed at each use. A connection is entirely within a local switching area, called central office, has a much better behavior than a toll wire line, called a local loop. In a local loop, sometimes, there are a simple wire pair and have quite a wide bandwidth. The sources of noise in the telephone channel are digital quantization noise, thermal noise in detectors, crosstalk between adjacent lines, impulse, etc. Both thermal and quantization noise can be viewed as a Gaussian noise. Therefore, the telephone channel is normally treated as a Gaussian channel. 36

48 4.2 Multiuser Transmission System The fundamental limit of multiuser detection is to mitigate the interference among different modulated signals, called crosstalk. We focus our study in telephone cables Basic on Multiuser Detection The basic model for a multiuser channel and transmission system is shown in Fig , where L different data symbols, x l, l = 1, 2,,L, share a channel with joint probability distribution p Y. The channel input can be considered to be one large vector X X of dimension L N x = N x, l and the output vector is of dimension N. The set of users l= 1 can be viewed as a single user with a larger signal set and a corresponding larger number of possible messages to be transmitted. Optimum detection of the entire set will be addressed in the late of this section. However, a receiver observing Y may not desire all the messages, and likely is attempting to attempting to detect messages from one user. In the most general form, the multiuser channel is described by the conditional probability distribution p X. Normally, many channels fit in the linear AWGN model, Y that is Y = H X + N ( ) where N is a vector of uncorrelated additive Gaussian noise values that each have variance N o 2 per dimension. 37

49 X x 1 x 2 x L... multiuser channel p Y X Y Fig : Basic Multiuser Transmission System Optimum Multiuser Detection The optimum detector for a multiuser channel is a generalization form of the optimum single-user channel detector. The set of all possible multiuser channel inputs will be denoted C X, and contain M = C possible distinct N-dimensional symbols, X which may be a large number that typically grows exponentially with L, the number of users. C X is a signal constellation, equivalently a code, for the set of all users. The details of the optimum multiuser detection have been addressed in [52], and [51]. We review some topics related to our research works. 38

50 Theorem (Optimum Multiuser Detection) The Probability of multiuser symbol error is minimum when the detector selects X ˆ C to maximize X p X and is Y known as the maximum a posteriori multiuser detector. When all possible multipleuser input symbol values are equally likely, this optimum detector simplifies to maximization of the conditional probability p X over the choice for Y Xˆ C X, and is called the maximum likelihood multiuser detector [51]. The probability of error for such a system reflects the likelihood that any of the users may been incorrectly detected P e M = Pc = 1 i=1 1 P p ( ) c / i i where P c/i is the probability that the i th possible multiuser message set is correctly received. The users are often modeled as being independent in their choice of transmit message so that L P = P ( X X l) ( ) l= 1 A MAP decoder simplifies to a ML decoder, when each of the users is distributed uniformly and independently. 39

51 The ML decoder for the AWGN channel has a probability of error that is d min P e N eq( ) 2δ ( ) where the number of nearest neighbors, N e, now includes all mutiuser-symbol values in the calculation and similarly the minimum distance is over the entire set of all multiuser symbol values. The co-channel interference in multiuser channel is defined in the following [51]. Definition (Co-channel Interference Free Channel) A co-channel interference free multiuser channel (IFC) has a conditional probability distribution that satisfies L p Y = p ( ) X l= 1 yl / xl This is the channel probability distribution factor into independent terms for each of the users. When the channel is not IFC, it is called co-channel interference (CCI) channel. With this definition, a lemma trivially follows 40