Spectral Optimization and Joint Signaling Techniques for Communication in the Presence of Crosstalk. Rohit Gaikwad and Richard Baraniuk

Transcription

1 Spectral Optimization and Joint Signaling Techniques or Communication in the Presence o Crosstalk Rohit Gaikwad and Richard Baraniuk ECE Technical Report #9806 Rice University July

2 Spectral optimization and joint signaling techniques or communication in the presence o crosstalk Rohit Gaikwad and Richard Baraniuk Abstract We have invented a new modem technology or transmitting data on conventional telephone lines (twisted pairs) at high speeds. This discovery is timely, as new standards are being developed or this Digital Subscriber Line (DSL) technology at this very moment. The potential market or the new modem technology is massive, as the telephone service providers wish to oer Internet access to the masses using the current phone lines into the home. Key to the deployment o any new service is the distribution o power over requency, or new services must be designed to be robust to intererence that might be caused by other services that are carried by neighboring telephone lines. As well, new services cannot interere with existing services. We have made two discoveries. The irst is an optimization technique that provides the best possible distribution o power (over requency) or any new DSL service given the intererence rom other known services that are carried by neighboring telephone lines in the same cable. The second is a power distribution scheme that minimizes the intererence caused by the new DSL service into neighboring lines. This new modem technology can be applied to many channels besides the telephone channel (or example, coaxial cables, power lines, wireless channels, and telemetry cables used in geophysical well-logging tools). US Patents Pending Department o Electrical and Computer Engineering, Rice University, 6100 Main St., Houston, TX, RG Tel: (713) x3786, rohitg@rice.edu RB Tel: (713) , richb@rice.edu Fax: (713)

3 Contents 1 Background Twisted pairs Overview o services Crosstalk intererence NEXT and FEXT Notation or sel-next and sel-fext Capacity and perormance margin Problem Statement General statement Particular statement or DSLs HDSL2 service GDSL service VDSL2 service Previous Work Static PSD Masks and transmit spectra Joint signaling techniques Multitone modulation Summary o previous work New, Optimized Signaling Techniques Assumptions, Notation, and Background Intererence models and simulation conditions Signaling schemes Optimization: Intererence rom other services (DSIN-NEXT and DSIN-FEXT) Solution: EQPSD signaling Problem statement Additional assumption Solution Examples

4 4.5 Optimization: Intererence rom other services (DSIN-NEXT and DSIN-FEXT) plus sel-intererence (sel-next and low sel-fext) Solution: EQPSD and FDS signaling Sel-NEXT and sel-fext rejection using orthogonal signaling Problem statement Additional assumptions Signaling scheme Solution: One requency bin Solution: All requency bins Algorithm or optimizing the overall transmit spectrum Fast, suboptimal solution or the EQPSD to FDS switch-over bin Flow o the scheme Grouping o bins and wider subchannels Examples and results Spectral compatibility Optimization: Intererence rom other services (DSIN-NEXT and DSIN-FEXT) plus sel-intererence (sel-next and high sel-fext) Solution: EQPSD, FDS and multi-line FDS signaling Sel-FEXT and sel-next rejection using multi-line FDS Problem statement Additional assumptions Signaling scheme Solution using EQPSD and FDS signaling: All requency bins Switch to multi-line FDS: One requency bin Switch to multi-line FDS: All requency bins Special case: Perormance o lines Flow o the scheme Examples and results Joint signaling or lines diering in channel, noise and intererence characteristics Solution or lines: EQPSD and FDS signaling Solution or lines: EQPSD and FDS signaling Solution or lines: EQPSD and multi-line FDS signaling Optimizing under a PSD mask constraint: No sel-intererence

5 4.8.1 Problem statement Solution Examples Optimizing under a PSD mask constraint: With sel-intererence Problem statement Solution Algorithm or peak-constrained optimization o the transmit spectra Examples and results Bridged taps Optimal transmit spectra Suboptimal transmit spectra Examples and discussion Extensions More general signaling techniques More general intererer models Channel variations Broadband modulation schemes Linear power constraints in requency Summary o Contributions 90 Reerences 92 Glossary 94 Notation 96 5

6 List o Figures 1 Frequency response o a twisted pair telephone channel NEXT and FEXT between neighboring lines in a telephone cable. Tx s are transmitters and Rx s are receivers NEXT (DSIN-NEXT and sel-next), and FEXT (DSIN-FEXT and sel-fext) modeled as additive intererence sources. AGN denotes the additive Gaussian channel noise. DSOUT-NEXT and DSOUT-FEXT represent the intererence leaking out into other neighboring services Multicarrier or discrete multitone (DMT) modulation multiplexes the data onto multiple orthogonal carrier waveorms Channel sub-division into narrow bins (subchannels), each o width (Hz) Magnitude squared transer unction o the channel (CSA loop 6), sel-next intererers, and sel-fext intererers (see (1) (3)) Transmit spectra or dierent signaling schemes in a requency bin. EQPSD, FDS and multi-line FDS schemes (illustrated or lines, works or any number o lines) Model or combined additive intererence rom other services (DSIN-NEXT and DSIN- FEXT) plus channel noise (AGN) Flowchart o the optimal scheme to determine PSD mask using only EQPSD signaling Optimal transmit spectrum o HDSL2 (on CSA loop ) with HDSL DSIN-NEXT intererers and AGN o dbm/hz Optimal transmit spectrum o HDSL2 (on CSA loop ) with T1 DSIN-NEXT intererers and AGN o dbm/hz Upstream and downstream transmit spectra in a single requency bin ( EQPSD signaling and!" FDS signaling) #%$ is monotonic in the interval '&)(*,+-/ EQPSD and FDS signaling in a single requency bin Upstream and downstream transmit spectra showing regions employing EQPSD and FDS signaling. The bins ) employ EQPSD signaling and the bins 0 3'5,687;:<2+4 =. employ FDS signaling Flowchart o the optimal and suboptimal schemes to determine the transmit spectrum using EQPSD and FDS signaling Joint EQPSD-FDS signaling or a channel: discrete and contiguous transmit spectra. Top igures show the upstream and bottom igures show the downstream transmit spectra Optimal upstream transmit spectrum or CSA Loop (HDSL2 transmit spectrum with sel-next + sel-fext). EQPSD signaling takes place to the let o bin 9 (indicated by solid line); FDS signaling takes place to the right (indicated by dashed line)

7 19 Optimal contiguous upstream and downstream transmit spectra or CSA Loop (HDSL2 transmit spectrum with sel-next + sel-fext). EQPSD signaling takes place to the let o bin Another set o optimal contiguous upstream and downstream transmit spectra or CSA Loop (HDSL2 transmit spectrum with sel-next + sel-fext). These spectra yield equal perormance margins (equal capacities) and equal average powers in both directions o transmission. EQPSD signaling takes place to the let o bin Transmit spectra o signaling line (> ), interering line (? ), and lumped channel noise (A ). FDS scheme (Case ) or interering line yields higher capacity or signaling line (> ) than other schemes like CDS (Case ) EQPSD and multi-line FDS signaling in requency bin or 3BC line case FDS and multi-line FDS signaling in requency bin or 3B< line case Upstream transmit spectrum o line employing EQPSD, FDS and multi-line FDS signaling schemes or 3 D line case. The bins '5,6FEG7IHKJL. employ EQPSD, 0 3'5,6FEG7HMJN: 2+43'EG7IHKJ/687HMJL. employ multi-line FDS, 0 3'EG7IHKJ/687HMJO:P2+43'7HMJ/6FEG7HMJQ. employ FDS, and 0 3'7HMJ/6FEG7HMJ:R2+4 =. employ multi-line FDS. The downstream spectrum o line (>TS U (WVYX ) is similar to >[Z U (WVYX except or putting power in the complimentary halves o FDS bins. The upstream spectra o o lines and are similar to >TZ U (WVYX except or putting power in complementary thirds o multi-line FDS bins. The downstream spectra or lines and are similar to > U Z (WVYX except or putting power in the complementary halves o the FDS bins and in the complementary thirds o multi-line FDS bins Practical observation number : Bins )56FEG7HMJQ. employ EQPSD, and bins 0 3'5,6FEG7IHKJ2: 2+4 =. employ multi-line FDS. There is no FDS spectral portion Practical observation number : Bins 'EG7HMJ/687HMJQ. employ EQPSD, bins 0 3'EG7HMJ/687HMJ: 2+43)7IHKJ/6FEG7HMJL. employ FDS, and bins0 3)7IHKJ/6FEG7HMJ:\2+4 =. employ multi-line FDS. There is no multi-line FDS spectral portion within the EQPSD region Upstream and downstream transmit spectra in a single requency bin (" EQPSD signaling and!] multi-line FDS signaling) EQPSD and multi-line FDS signaling in a single requency bin Flowchart o the optimal scheme to determine the transmit spectrum using EQPSD, FDS, and multi-line FDS signaling Dierent line characteristics: Upstream and downstream transmit spectra in a single requency bin (C EQPSD signaling and ^] FDS signaling) Dierent line characteristics: Upstream and downstream transmit spectra in a single requency bin (C EQPSD signaling and ^] multi-line FDS signaling) Optimal downstream transmit spectrum o HDSL2 (on CSA loop ) under an OPTIS downstream constraining PSD mask with HDSL DSIN-NEXT intererers and AGN o O dbm/hz. The o o line shows the peak-constrained optimal transmit spectrum and the line shows the constraining OPTIS PSD mask

8 33 Optimal upstream transmit spectrum or HDSL2 (on CSA loop ) under an OPTIS upstream constraining PSD mask with T1 DSIN-NEXT intererers and AGN o O dbm/hz. The o o line shows the peak-constrained optimal transmit spectrum and the line shows the constraining OPTIS PSD mask Optimal upstream and downstream transmit spectra or HDSL2 (on CSA loop ) under the OPTIS upstream and downstream constraining PSD masks with HDSL2 sel-next and sel-fext intererers and AGN o O dbm/hz. The o o lines show the peakconstrained optimal transmit spectra and the lines show the constraining OPTIS PSD masks Optimal upstream and downstream transmit spectra or HDSL2 (on CSA loop ) under the OPTIS upstream and downstream constraining PSD masks with _ HDSL2 sel-next and sel-fext intererers, _ T1 intererers, and AGN o O dbm/hz. The o o lines show the peak-constrained optimal transmit spectra and the lines show the constraining OPTIS PSD masks Optimal contiguous upstream and downstream transmit spectra or CSA Loop (having a non-monotonic channel transer unction due to bridged taps ) (HDSL2 transmit spectrum with sel-next + sel-fext). These spectra yield equal perormance margins (equal capacities) and equal average powers in both directions o transmission. Note that there is only one transition region rom EQPSD to FDS signaling The top igure shows the channel transer unction, sel-next, and sel-fext transer unctions or a short loop with bridged taps. GDSL service (note that sel-next is very low or this hypothetical service) is employed on this loop. The bottom igure shows the distributed EQPSD and FDS spectral regions or the upstream and downstream transmit spectra. A indicates EQPSD signaling, a indicates FDS, and a indicates EQPSD or FDS signaling. Note that in this case the non-monotonicity o the channel transer unction leads to several distributed signaling regions Alternative signaling scheme: In presence o high degrees o sel-next and sel-fext between group o lines and and lines and we employ multi-line FDS. There is EQPSD signaling within each group o lines ( and employ EQPSD as do and ) that have low sel-intererence

9 List o Tables 1 Uncoded perormance margins (in db) or CSA No. : MONET-PAM vs. Optimal Uncoded perormance margins (in db) or CSA No. : Optimal vs. Suboptimal Spectral-compatibility margins: MONET-PAM vs. Optimal Uncoded perormance margins (in db) and channel capacities (in Mbps) using EQPSD, FDS and multi-line FDS or HDSL2 (CSA No. ) Uncoded perormance margins (in db) and channel capacities (in Mbps) using EQPSD, FDS and multi-line FDS or GDSL ( kt line) Uncoded perormance margins (in db) and channel capacities (in Mbps) using EQPSD, FDS and multi-line FDS or VDSL2 ( kt line) Uncoded perormance margins (in db) or CSA No. : OPTIS vs. Peak-constrained Optimal under OPTIS

10 1 Background 1.1 Twisted pairs Telephone service is provided to most businesses and homes via a pair o copper wires (a twisted pair ). A telephone cable contains many twisted pairs: ` twisted pairs are grouped in close proximity into binder groups, and several binder groups are packed together to orm a cable. The two terminations o a telephone cable are at the user (subscriber) end and at the telephone company (central oice, CO) end. We will use the terms twisted pair, line, and subscriber loop interchangeably in the sequel. Voice telephony uses only the irst 4 khz o bandwidth available on the lines. However, one can modulate data to over a MHz with signiicant bit rates. Only recently have schemes been developed to exploit the additional bandwidth o the telephone channel. A plot o the requency response o a typical telephone channel is given in Figure Overview o services In the past ew years, a number o services have begun to crowd the bandwidth o the telephone channel. Some o the important services are: POTS Plain Old Telephone Service. This is the basic telephone service carrying voice traic in the bdce khz bandwidth. Conventional analog modems also use the same bandwidth. ISDN Integrated Services Digital Network. This service allows end-to-end digital connectivity at bit rates o up to a, kbps (kilo-bits-per-second). T1 Transmission 1. This is a physical transmission standard or twisted pairs that uses Ie multiplexed channels (each at gie kbps) to give a total bit rate o ahiìee Mbps (Mega-bitsper-second). It uses costly repeaters. HDSL High bit-rate Digital Subscriber Line. This is a ull-duplex (two-way) T1-like (a,h1ìe,e Mbps) signal transmission service using only two twisted pairs and no repeaters. ADSL Asymmetric Digital Subscriber Line. Over one twisted pair, this service provides a high-speed (on the order o g Mbps) downstream (rom central oice (CO) to subscriber) channel to each user and a low-speed (on the order o g,ejb kbps) upstream (rom subscriber to the central oice) channel. This service preserves the POTS service over a single twisted pair. VDSL Very high bit-rate DSL. This yet-to-be-standardized service will provide a very high speed (on the order o ` Mbps) downstream channel to subscribers and a lower speed upstream channel to the central oice over a single twisted pair less than k to g kt long. Further, it will preserve the POTS service. 10

11 r o l n o p l 0 Channel attenuation (in db) s 30 n m Frequency ( in khz) q 1000 Figure 1: Frequency response o a twisted pair telephone channel. HDSL2 High bit-rate Digital Subscriber Line 2. This soon-to-be-standardized service will provide ull-duplex ahiìee Mbps signal transmission service in both directions (ull duplex) over a single twisted pair (tua kt long) without repeaters. GDSL General Digital Subscriber Line. This hypothetical service would (or illustration purposes) carry ` Mbps ull-duplex data rate over a single twisted pair (see Sections and ). VDSL2 Very high bit-rate DSL Line 2. This hypothetical service would (or illustration purposes) carry a vhe Mbps ull-duplex data rate over a single twisted pair less than k to g kt long (see Sections and ). Currently, all the above mentioned services have an ANSI standard except or VDSL, HDSL2, GDSL and VDSL2. We use a generic DSL (xdsl) service or all our analysis. For concreteness, we present results optimizing the HDSL2, GDSL, and VDSL2 services 1 in the ace o noise and intererence rom neighboring services. 1.3 Crosstalk intererence NEXT and FEXT Due to the close proximity o the lines within a binder, there is considerable amount o crosstalk intererence between dierent neighboring telephone lines. Physically, there are two types o intererence (see Figure 2): 1 The idea is general and can be applied to any communications channel that exhibits crosstalk intererence. 11

12 Tx 1 NEXT NEXT Rx1 Rx 2 Tx 2 FEXT Rx 3 Tx 3 Figure 2: NEXT and FEXT between neighboring lines in a telephone cable. Tx s are transmitters and Rx s are receivers. DSOUT-NEXT AGN sel-next sel-fext Tx Rx DSIN-NEXT DSIN-FEXT DSOUT-FEXT Figure 3: NEXT (DSIN-NEXT and sel-next), and FEXT (DSIN-FEXT and sel-fext) modeled as additive intererence sources. AGN denotes the additive Gaussian channel noise. DSOUT-NEXT and DSOUT- FEXT represent the intererence leaking out into other neighboring services. Near-end crosstalk (NEXT): Intererence between neighboring lines that arises when signals are transmitted in opposite directions. I the neighboring lines carry the same type o service then the intererence is called sel-next; otherwise, we will reer to it as dierent-service NEXT. Far-end crosstalk (FEXT): Intererence between neighboring lines that arises when signals are transmitted in the same direction. I the neighboring lines carry the same type o service then the intererence is called sel-fext; otherwise, we will reer to it as dierent-service FEXT. Figure 3 shows that crosstalk intererence can be modeled as additive intererence. Since neighboring lines may carry either the same or a dierent lavor o service, there are three categories o intererence (see Figure 3): 1. Sel-intererence (sel-next and sel-fext) between lines carrying the same service. 2. Intererence into a channel carrying service w rom other lines carrying services other than w (DSIN-NEXT and DSIN-FEXT). 3. Intererence rom a channel carrying service w into other lines carrying services other than w (DSOUT-NEXT and DSOUT-FEXT). Channel noise will be modeled as additive Gaussian noise (AGN). 12

13 { Z Z S S Notation or sel-next and sel-fext Here is some notation to keep things clear in the sequel. Number the twisted pairs (lines) in the cable with index xzyc{9a 2h2h2hQ - ~}, and denote the direction o transmission with index =yc{ ƒ K}, with < upstream (to the central oice) and ] downstream (rom the central oice). All the twisted pairs in the cable bundle are assumed to carry the same service. Let be the complement direction o : P, R. Denote the transmitters and receivers on line x as: O ˆ : transmitter (Tx) on twisted pair x in direction. ˆ : receiver (Rx) on twisted pair x in direction. Ideally, O ˆ intends to transmit inormation only to d ˆ. In a real system, however, O leaks into the receivers Š and ˆ s signal Š. Using our notation, this sel-intererence corresponds to: Sel-NEXT: Crosstalk rom ˆ into Š or all 'Œ Px, yž{ ƒ K}. Sel-FEXT: Crosstalk rom ˆ into Š or all Œ Px, yž{ ƒ K}. In a ull-duplex xdsl service, each twisted pair x supports transmission and reception in both directions (using echo cancelers), so each line x has a ull set o transmitters and receivers: ˆ ˆ ˆ ˆ }. With perect echo cancellation, there is no crosstalk rom ˆ into ˆ. We will assume this or the balance o this document, although this crosstalk could be dealt with in a ashion similar to sel-next and sel-fext. 1.4 Capacity and perormance margin The Channel capacity is deined as the maximum number o bits per second that can be transmitted over a channel with an arbitrarily small bit error probability. The achievable rate $ or a channel is any transmission rate below or equal to capacity, i.e., $. Another channel perormance metric is perormance margin (or margin). It is deined (in db) as j x ' šabœ U žoÿon N O «ªv where is the received signal-to-noise ratio (SNR) andn is the minimum received SNR required to achieve a ixed bit error probability (BER) at a given transmission rate. The perormance margin o a channel or a ixed bit error probability measures the maximum degradation (rom noise and intererence) in achievable bit rate that a channel can sustain beore being unable to transmit at that bit rate or a ixed BER (see [12]). The higher the perormance margin o a channel at a given transmission rate and ixed BER, the more robust it is to noise and intererence, i.e., the better is its perormance. «ª 13

14 2 Problem Statement 2.1 General statement Given an arbitrary communications channel with: 1. Sel-intererence (sel-next and sel-fext) between users o service w, 2. Intererence rom users o dierent services with users o service w (DSIN-NEXT and DSIN-FEXT), 3. Intererence rom users o service w into users o dierent services (DSOUT-NEXT and DSOUT-FEXT), and 4. Other intererence (including noise), maximize the capacity o each user o service w margin) degradation o the other services. without signiicant perormance (capacity or Here services could reer to dierent possible signaling schemes. Users reer to the generic Tx-Rx pairs. 2.2 Particular statement or DSLs HDSL2 service As a special case o the general problem, we will look into a particular problem o subscriber loops. In particular, we can phrase our statement in the language o HDSL2 [2]. Here, the communication channel is the collection o twisted pairs in the telephone cable, intererence is caused by: 1. Sel-NEXT and sel-fext between neighboring HDSL2 lines (sel-next dominates over sel-fext [8]), 2. DSIN-NEXT and DSIN-FEXT rom T1, ISDN, HDSL and ADSL, 3. Intererence rom HDSL2 into other services, such as T1, ISDN, HDSL and ADSL, and 4. Channel noise, which we will model as AGN. We wish to maximize the capacity o the HDSL2 service in presence o other HDSL2, T1, ISDN, HDSL, ADSL, VDSL lines and even services not yet imagined while maintaining spectral compatibility with them. We will consider HDSL2 service in Sections 4.4 to 4.7. The HDSL2 service is intended to ill a key need or ast (1.544 Mbps) yet aordable ull duplex service over a single twisted pair. Eorts to deine the standard are being mounted by several companies and the T1E1 standards committee. The two key issues acing HDSL2 standards committee are: 14

15 Spectral optimization. All current proposed schemes or HDSL2 achieve the required data rates with satisactory margins only in complete isolation. However, due to the proximity o the lines in a cable, there is considerable DSIN-NEXT, DSIN-FEXT, sel-next and sel-fext intererence rom T1, ISDN, HDSL, ADSL and HDSL2 into HDSL2 this intererence reduces the capacity o the HDSL2 service. Simultaneously, there is considerable DSOUT-NEXT and DSOUT-FEXT intererence rom HDSL2 into T1, ISDN, HDSL and ADSL. This problem is known as spectral compatibility. The scheme ultimately adopted or HDSL2 must not interere overly with other DSL services like T1, ISDN, HDSL, and ADSL. Modulation scheme. At present no system has been developed that systematically optimizes the HDSL2 spectrum and reduces intererence eects both rom and into HDSL2. Further, a modulation scheme or HDSL2 has not been decided upon at this time GDSL service The GDSL service will enable very high bit-rate ull-duplex, symmetric traic over a single twisted pair. We assume that the lines carrying GDSL service have good shielding against sel- NEXT. In this case, intererence is caused by: 1. Sel-NEXT and sel-fext between neighboring GDSL lines (sel-fext dominates over sel-next), 2. DSIN-NEXT and DSIN-FEXT rom T1, ISDN, HDSL, HDSL2 and ADSL, 3. Intererence rom GDSL into other services, such as T1, ISDN, HDSL, HDSL2 and ADSL, and 4. Channel noise, which we will model as AGN. We wish to maximize the capacity o the GDSL service in presence o other GDSL, T1, ISDN, HDSL, ADSL, HDSL2 lines and even services not yet imagined while maintaining spectral compatibility with them. The spectral optimization issue is similar to the one discussed or HDSL2 case, and we need to ind an optimal transmit spectrum or GDSL. Further, a good modulation scheme needs to be selected VDSL2 service Optical iber lines having very high channel capacity and virtually no crosstalk will be installed in the uture up to the curb o each neighborhood (FTTC). The inal ew thousand eet up to the customer premises could be covered by twisted pairs. In such a scenario, high bit-rate asymmetrictraic services (like VDSL) and symmetric-traic services (like VDSL2 ) over short length twisted paris would become important. For illustration o such a potential uture service we propose a hypothetical VDSL2 service that would carry very high bit-rate symmetric traic over 15

16 short distance loops on a single twisted pair. In the VDSL2 case, the intererence will be caused by: 1. Sel-NEXT and sel-fext between neighboring VDSL2 lines (both sel-next and sel- FEXT are dominant), 2. DSIN-NEXT and DSIN-FEXT rom T1, ISDN, HDSL, HDSL2, VDSL and ADSL, 3. Intererence rom VDSL2 into other services, such as T1, ISDN, HDSL, HDSL2, VDSL and ADSL, and 4. Channel noise, which we will model as AGN. Again, we wish to maximize the capacity o VDSL2 in presence o all the other intererers. To achieve this we need to ind optimal transmit spectra and a good modulation scheme. 3 Previous Work Here we discuss prior work pertaining to HDSL2 service. 3.1 Static PSD Masks and transmit spectra The distribution o signal energy over requency is known as the power spectral density (PSD). A PSD mask deines the maximum allowable PSD or a service in presence o any intererence combination. The transmit spectrum or a service reers to the PSD o the transmitted signal. Attempts have been made by several groups to come up with PSD masks or HDSL2 that are robust to both sel-intererence and intererence rom other lines. One way o evaluating channel perormance is by ixing the bit rate and measuring the perormance margins [12]: The higher the perormance margin or a given disturber combination, the more robust the HDSL2 service to that intererence. The term crosstalk here implies sel-intererence plus intererence rom other lines. To the best o our knowledge, no one has optimized the PSD o HDSL2 lines in presence o crosstalk and AGN. The signiicant contributions in this area, MONET-PAM and OPTIS, [1, 2, 4, 5] suggest a static asymmetrical (in input power) PSD mask in order to attempt to suppress dierent intererers. The PSD masks suggested in [1, 2, 4, 5] have a dierent mask or each direction o transmission. Furthermore, the techniques in [1, 4] use dierent upstream and downstream average powers or signal transmission. However, the mask is static, implying it does not change or diering combinations o intererers. Optis [5] is currently the perormance standard or HDSL2 service. The transmit spectrum always lies below a constraining PSD mask (when imposed). Speciying a constraining PSD mask only limits the peak transmit spectrum. We do PSDs (transmit spectra) and not masks in this document unless stated otherwise. In Section 4.11 we indicate ideas to get PSD masks. 16

17 S Z 3.2 Joint signaling techniques Sel-NEXT is the dominant sel-intererence component in symmetric-data-rate, ull-duplex, longlength line xdsl service (e.g., HDSL2). One simple way o completely suppressing sel-next is to use orthogonal signaling (or example, time division signaling (TDS), requency division signaling (FDS), or code division signaling (CDS)). In TDS, we assign dierent dierent services to dierent time slots. In FDS, we separate in requency the services that could interere with each other. In CDS, a unique code or signature identiies each direction o transmission. Further, in CDS each transmit spectrum occupies the entire available bandwidth or all o the time. CDS is similar to code-division multiple access (CDMA), but here instead o multiple access we separate the upstream and downstream transmit spectra using dierent codes. The choice o orthogonal signaling scheme depends on the intent. We will see that FDS is in a sense optimal under an average power constraint (see Section ). To eliminate sel-next using FDS, we would orce the upstream transmitters { ˆ x a 2h_h2h_ - š} and the downstream transmitters { ˆ x a 2h2h2hL - ~} to use disjoint requency bands. The upstream and downstream transmissions are orthogonal and hence can be easily separated by the corresponding receivers. Since in a typical system FDS cuts the bandwidth available to each transmitter to a± the overall channel bandwidth, we have an engineering tradeo: FDS eliminates sel-next and thereore increases system capacity; however, FDS also reduces the bandwidth available to each transmitter/receiver pair and thereore decreases system capacity. When sel- NEXT is not severe enough to warrant FDS, both upstream and downstream transmitters occupy the entire bandwidth. In this case, the upstream and downstream directions have the same transmit spectrum; we reer to this as equal PSD (EQPSD) signaling. On a typical telephone channel, the severity o sel-next varies with requency. Thereore, to maximize capacity, we may wish to switch between FDS and EQPSD depending on the severity o sel-next. Such a joint signaling strategy or optimizing the perormance in the presence o sel-next and white AGN was introduced in [3]. The scheme in [3] is optimized, but only or an over simpliied scenario (and thereore not useul in practice). In particular, [3] does not address sel-fext and intererence rom other lines as considered in this work. Further, [3] does not address spectral compatibility issue. All other schemes or joint signaling employ adhoc techniques or intererence suppression [1, 2, 4, 5]. 3.3 Multitone modulation Multicarrier or discrete multitone (DMT) modulation [6] can be readily used to implement a communication system using a wide variety o PSDs. Multitone modulation modulates data over multiple carriers and adjusts the bit rate carried over each carrier according to the signal to noise ratio (SNR) or that carrier so as to achieve equal bit error probability (BER) or each carrier (see Figure 4). Orthogonal FDS signaling is easily implemented using the DMT: we simply assign transmit- 17

18 ² ³ ² 0 Channel attenuation ( H() in db) µ Subchannels Frequency ( in khz) Carrier Freqs Figure 4: Multicarrier or discrete multitone (DMT) modulation multiplexes the data onto multiple orthogonal carrier waveorms. ter/receiver pairs to distinct sets o carriers. Note, however, that multitone modulation is deinitely not the only modulation scheme that can be used to implement (optimal) transmit spectra. We can just as well use other techniques, such as CAP, QAM, multi-level PAM, etc. 3.4 Summary o previous work The current state o the art o DSL technology in general and HDSL2 in particular can be described as ollows: Ad hoc schemes (sometimes reerred to as optimized ) have been developed that attempt to deal with sel-intererence and DSIN-NEXT and DSIN-FEXT as well as spectral compatibility o the designed service with other services. However, these schemes by no means optimize the capacity o the services considered. An optimal signaling scheme has been developed in [3] or the case o sel-next only. The development o [3] does not address crosstalk rom other sources, such as DSIN-NEXT and DSIN-FEXT, or sel-fext. The development o [3] also does not address spectral compatibility o the designed service with respect to other services. 4 New, Optimized Signaling Techniques The proposed techniques combine a number o ideas into one signaling system that optimizes its perormance given many dierent possible combinations o intererers. These ideas include: 18

19 1. Given expressions or the crosstalk rom other services (DSIN-NEXT and DSIN-FEXT) into an xdsl channel and channel noise (AGN), our scheme computes the optimal distribution o power across requency that maximizes the capacity (see Section 4.4). This distribution uses the same transmit spectrum (EQPSD signaling) in both upstream and downstream directions. 2. Given expressions or the sel-next and sel-fext crosstalk in an xdsl channel along with intererence rom other services (DSIN-NEXT and DSIN-FEXT) and channel noise (AGN), our scheme computes the optimal distribution o power across requency that maximizes the capacity. This distribution involves equal PSD (EQPSD) signaling in requency bands with low sel-intererence, orthogonal signaling (FDS) in requency bands where sel- NEXT dominates other intererence sources (Section 4.5), and orthogonal signaling (multiline FDS introduced in Section 4.3) in requency bands where sel-fext is high (Section 4.6). 3. Given dierent channel, noise, and intererence characteristics between lines, our scheme chooses the optimal signaling strategy (EQPSD, FDS or multi-line FDS) in each requency bin (see Section 4.7) to maximize the channel capacity. 4. Given an additional peak-power constraint in requency, our scheme computes the optimal transmit spectra that maximize the capacity and choose the optimal joint signaling strategy (EQPSD, FDS and multi-line FDS) or a given channel, noise and intererence characteristics (see Sections 4.8 and 4.9). 5. We present optimal and near-optimal signaling strategies in case o non-monotonic channel, sel-next and sel-fext transer unctions (see Section 4.10 on bridged taps). We will present the above ideas in the ollowing sections in the context o a generic xdsl line carrying symmetric-data rate services like HDSL2, GDSL, and VDSL2 services. Note that the techniques developed here can be applied to a more general communications channel with intererence characteristics characterized by sel-intererence and dierent-service intererence models. Further, we can extend this work to apply to channels that support asymmetric data rates (dierent in each direction), or e.g., ADSL, and VDSL. We can ollow a similar approach o binning in requency and then analyzing the signaling strategy in each bin. In the asymmetrical data-rate case, the ratio o the average power between upstream and downstream directions needs to be known. We will present background material and our assumptions in Section 4.1. In Section 4.2 we give details about the intererence models and the simulation conditions. Section 4.3 looks at the various signaling schemes we will employ. We will present the optimal transmit spectrum using EQPSD signaling in Section 4.4 in the presence o only dierent-service intererence and AGN. Sections 4.5 and 4.6 detail the new signaling strategies to obtain an optimal and/or suboptimal transmit spectrum in the presence o sel-intererence, dierent-service intererence and AGN. Section 4.7 derives some results applicable when neighboring lines vary in channel, noise and intererence characteristics. Sections 4.8, and 4.9 present optimal transmit spectra under additional peak-power constraint in requency. We present optimal and near-optimal signaling schemes or non-monotonic channel, sel-next, and sel-fext transer unctions in Section Finally, Section 4.11 presents several new ideas, extending the results presented here. 19

20 ¹ à 6 b b b c c c Ã Ã Ã È È È ¾ ¾ ¾ Note: All the transmit spectra are optimal (i.e., yield the maximum possible bit rates or perormance margins) given the assumptions in Section 4.1 (see Sections 4.4.2, 4.5.3, and or additional assumptions) and that one o the speciic joint signaling strategies is employed over the channel (see Sections 4.4, 4.5, and 4.6). 4.1 Assumptions, Notation, and Background We present background material and some o the standard assumptions made or simulations. These assumptions apply throughout the document unless noted otherwise. 1. Channel noise can be modeled as additive Gaussian noise (AGN) [13]. 2. Intererence rom other services (DSIN-NEXT and DSIN-FEXT) can be modeled as additive colored Gaussian noise [13]. 3. We assume the channel can be characterized as a LTI (linear time invariant) system. We divide the transmission bandwidth o the channel into narrow requency bins o width (Hz) each and we assume that the channel, noise and the crosstalk characteristics vary slowly enough with requency that they can be approximated to be constant over each bin (For a given degree o approximation, the aster these characteristics vary, the more narrow the bins must be. By letting the number o bins º¼» ½, we can approximate any requency characteristic with arbitrary precision). 2 channel transer unction [10] ¾ ÁÀG ÃTľ 6 sel-next transer unction ¾«ÌË ÃTľ [8] 6 and sel-fext transer unction ¾ ÐÏN Ã[ľ [9] ÆÅ ÆÅÍ ÊÅ!Ñ We use the ollowing notation or line x on the ˆ Ç È ˆÎÇ È ˆ Ç È ¾«Ã i otherwise ¾ à i otherwise ¾Òà i otherwiseh ÊÉ 6 ÊÉ 6 ÊÉ 6 È are the center requencies (see Figures 5 and 6) o the º Here subchannels (bins) with index ÓDyu{9a, 2h2h2hQ ƒºž}. We will employ these assumptions in Sections 4.5.4, 4.6.6, and The DSIN-NEXT and DSIN-FEXT transer unctions are also assumed to vary slowly enough that they can be similarly approximated by a constant value in each requency bin. Note that the concept o dividing a transer unction in requency bins is very general and can include nonuniorm bins o varying widths or all bins o arbitrary width (i.e., the bins need not be necessarily narrow). 2 We divide the channel into narrow requency bins (or subchannels) or our analysis only. This does not necessarily mean that we need to use DMT as the modulation scheme. 20 (1) (2) (3)

21 Ô Ù Ø Ø 0 Channel attenuation (in db) Bins Center Frequencies Frequency ( in khz) Figure 5: Channel sub-division into Õ narrow bins (subchannels), each o width (Hz) Magnitude squared requency response H () N Û2 H i,k X F i,k i,k H Ú () C Û2 H () F Û2 Channel sel NEXT sel FEXT k Frequency (khz) Figure 6: Magnitude squared transer unction o the channel (CSA loop 6), ÜÝ sel-next intererers, and ÜÝ sel-fext intererers (see (1) (3)). 21

22 4. Echo cancellation is good enough that we can ignore crosstalk rom ÞOß à into á à ß. We can relax this assumption in some cases where spectral regions employ FDS signaling (see Sections 4.5, 4.6, 4.7, 4.9, and 4.10). 5. All sources o DSIN-NEXT can be lumped into one PSD âäãtåæ çtè and all sources o DSIN- FEXT can be lumped into one PSD âäã[égæ çtè. 6. All sources o sel-next can be added to orm one overall sel-next source. 7. All sources o sel-fext can be added to orm one overall sel-fext source. 8. Spectral optimization is done under the average input power constraint, i.e., the average input power is limited to êìë í î (Watts). 9. The PSDs o the upstream and downstream transmission directions can be written using the notation introduced in Section There are ï interering lines carrying the same service with index ð ñžò9ó,ô2õ2õ2õlô-ï~ö. Denote the direction o transmission with index ñ"òìôùmö, with = upstream (to CO) and ù = downstream (rom CO). Denote the upstream and downstream PSDs on line ð as: ãú à æüçtè : PSD on twisted pair ð in upstream direction. ãgý à æüçtè : PSD on twisted pair ð in downstream direction ù. Further, we denote the upstream and downstream PSD on line ð in a generic requency bin (or subchannel) þ as: úà æüçtè : PSD on twisted pair ð in upstream direction. àý æüçtè : PSD on twisted pair ð in downstream direction ù. Note: When we reer to àß æüçtè we mean PSD on twisted pair ð in a generic bin, demodulated to baseband (çžñ "ô ) or ease o notation. When we reer to ßæüçTè we mean PSD on a generic twisted pair in a generic bin, demodulated to baseband (ç ñ "ô ) or ease o notation. 10. We assume a monotone decreasing channel transer unction. However, in case the channel transer unction is non-monotonic (e.g., in the case o bridged taps on the line), our optimization techniques can be applied in each individual bin independently. This scenario makes the power distribution problem more diicult however (see Section 4.10). 11. We assume we desire equal channel capacities in upstream and downstream directions (except when the channel, noise, and intererence characteristics between lines vary as in Section 4.7). 22

23 4.2 Intererence models and simulation conditions The intererence models or dierent services have been obtained rom Annex B o T ([9], the ADSL standard), with exceptions as in T1E1.4/ [7]. The NEXT coupling model is 2-piece Unger model as in T1E1.4/ [8]. BER was ixed at ó. Our optimal case results were simulated using Discrete Multitone Technology (DMT) and were compared with that o MONET-PAM [1]. MONET-PAM uses Decision Feedback Equalizers (DFE) [20] in the receivers along with multi-level pulse amplitude modulation (PAM) scheme. The margin calculations or DFE margins were done per T1E1.4/97-180R1 [11], Section võkõ õvõ óõ ó. AGN o power ó dbm/hz was assumed in both cases. MONET-PAM uses PAM with bits/symbol and a baud rate o baud = vó õ ksymbols/s. The actual upstream and downstream power spectra can be obtained rom [1]. MONET-PAM spectra is linearly interpolated rom /3 Hz sampled data. The PAM line-transormer hp corner, that is, the start requency is assumed to be at ó khz. A!! Hz rectangular-rule integration is carried out to compute margins. The required DFE SNR margin or ó BER is!võ db. To implement our optimal signaling scheme, we used DMT with start requency ó khz and sampling requency o ó MHz. This gives us a bandwidth o! khz and! carriers with carrier spacing o khz. No cyclic preix (used to combat intersymbol intererence (ISI)) was assumed, so the DMT symbol rate is same as the carrier spacing equal to khz. However, the scheme can easily be implemented by accounting or an appropriate cyclic preix. The addition o cyclic preix lowers the symbol rate and hence lowers the transmission rate. No limit was imposed on the maximum number o bits per carrier (this is oten done or simulations). Even with a ó bits/carrier limit, the results should not change very much, as some o the test runs show. 4.3 Signaling schemes The joint signaling techniques used in the overall optimized signaling schemes use one o the basic signaling schemes (see Figure 7) in dierent requency bins depending on the crosstalk and noise combination in those bins. Figure 7 illustrates the three signaling schemes: EQPSD, FDS and multi-line FDS (in the case o three lines). 3 The Figure shows in requency bin þ the PSDs or each case (recall the notation introduced in Section 4.1, Item 9): " When crosstalk and noise are not signiicant in a requency bin, EQPSD signaling is preerred as it achieves higher bit rate than the other two orthogonal signaling schemes (see Section 4.5.5). In EQPSD signaling, the upstream and downstream PSDs are the same ( úà æüçtè$# àý æ ç[è ). " When sel-next is high and sel-fext is low in a bin and there are a large number o neighboring lines carrying the same service together, FDS signaling yields the highest bit rates by eliminating sel-next (we prove this in Section 4.5.5). In FDS signaling, each requency bin is urther divided into two halves, with all the upstream PSDs being same or 3 The signaling schemes EQPSD, FDS, and multi-line FDS work in general or % lines. 23

24 ' ' & & & & ' ' & & & ' & ' EQPSD u u d d s (), s (), s (), s (), u d s () 3 s () 2a 3 2a a a 0 W 0 2 W W 2 W FDS u u d d s (), s (), s (), s (), u s () 2a u s () 2a 3 3 a a u s (), 1 d 1 0 s () 0 W 2 W W 2 W u s (), 2 d 2 s () multi-line FDS u 3 s (), d 3 s () 3a 3a 3a 2a 2a 2a a a a W 3 W 3 2W 3 2W 3 W Figure 7: Transmit spectra or dierent signaling schemes in a requency bin (. EQPSD, FDS and multiline FDS schemes (illustrated or Ü lines, works or any number o lines). 24

25 # DSOUT-NEXT AGN Tx Rx DSIN-NEXT DSIN-FEXT DSOUT-FEXT Figure 8: Model or combined additive intererence rom other services (DSIN-NEXT and DSIN-FEXT) plus channel noise (AGN). all the lines and all the downstream PSDs being same or all the lines ( úà æ çtè*) àý æ çtè ). This type o orthogonal signaling completely eliminates sel-next but does not combat sel-fext. " In requency bins where sel-fext is high, using FDS is not suicient since sel-fext still exists. In this case, doing multi-line FDS eliminates sel-fext as well as sel-next and this achieves the highest bit rates when there are ony a ew lines and sel-fext is high and dominant over sel-next (we prove this in Section 4.6). In multi-line FDS signaling each line gets a separate requency slot (,+2ï or ï lines carrying the same service) in each bin and the upstream and downstream PSDs or each line are the same ( àß æ çtè-). ß æ ç[è0/21 3 ð ôz ñ"òìôùmö ). We will see in uture sections the exact relationships that allow us to determine which scheme is optimal given an intererence and noise combination. 4.4 Optimization: Intererence rom other services (DSIN-NEXT and DSIN- FEXT) Solution: EQPSD signaling In this scenario, each xdsl line experiences no sel-intererence (Figure 8 with neither sel-next nor sel-fext). There is only DSIN-NEXT and DSIN-FEXT rom other neighboring services such as T1, ADSL, HDSL, etc., in addition to AGN. The solution is well known, but will be useul later in the development o the subsequent novel (Sections 4.5, 4.6, 4.7, and 4.11) signaling schemes Problem statement Maximize the capacity o an xdsl line in the presence o AGN and intererence (DSIN-NEXT and DSIN-FEXT) rom other services under two constraints: 1. The average xdsl input power in one direction o transmission must be limited to êìë í î (Watts). 2. Equal capacity in both directions (upstream and downstream) or xdsl. Do this by designing the distribution o energy over requency (the transmit spectrum) o the xdsl transmission. 25

26 4 4 ß ß ß Additional assumption We add the ollowing assumption to the ones in Section 4.1 or this case: óvõ Both directions (upstream and downstream) o transmission experience the same channel noise (AGN) and dierent service intererence (DSIN-NEXT and DSIN-FEXT) Solution Consider a line (line ó ) carrying xdsl service. Line ó experiences intererence rom other neighboring services (DSIN-NEXT and DSIN-FEXT) and channel noise 4 NEXT or sel-fext (see Figure 8). æüçtè (AGN) but no sel- The DSIN-NEXT and DSIN-FEXT intererence can be modeled as colored Gaussian noise or calculating capacity [13]. Recall that âäãtåæ çtè is the PSD o the combined DSIN-NEXT and let âäã[égæ çtè is the PSD o the combined DSIN-FEXT. Let ã ú æüçtè and ãgýæ çtè denote the PSDs o line ó upstream ( ) direction and downstream (ù ) direction transmitted signals respectively. Further, let 5 ú and 5\ý denote the upstream and downstream direction capacities o line ó respectively. Let 687 æ ç[è denote the channel transer unction o line ó. The twisted pair channel is treated as a Gaussian channel with colored Gaussian noise. In this case the channel capacity (in bps) is given by [14] and 5 ú #:9<;>=?@ABDC 5 ý #V9W;>=?XAB C EGF 687 æüçtè M ã ú æ çtè H IKJLM0N ópo Q Q æ ç[èroâäãtåæ çtèsoâäã[é æüçtèut EGF 687 æüçtè M ã ý æüçtè H IYJ!LM0N ópo Q Q æ çtè èzoâ ãtå æüçtèroâäã[égæ çtèt The supremum is taken over all possible ã ú æ çtè and ãgýiæ çtè satisying ã ú æ çtè\[] /Tç ôcã ý æ ç[è\[] /TçYô and the average power constraints or the two directions E F H ã ú æüçtè ù4ç_^ ê ë í îiôp`ba>cd ù4ç (4) ù4ç õ (5) E F H ã ý æ çtè ù4ç_^ êìë í îiõ (6) It is suicient to ind the optimal ãúvæ çtè which gives 5;ú, since setting ã ý æüçtè$#uãúvæ çtèe/tçyô gives the capacity 5 ý #5;ú as seen rom (4) and (5). Thus, the optimal upstream and downstream channel capacities are equal (5 ú #g5 ý ). The optimal power distribution in this case is obtained by the classical water-illing technique [16]. The optimal ã ú æüçtè is given by å>o AB CqpsrR?tuAB CKpsrR?Uv>AB C w xzy AB C w { ã hjiwk ú æüçtè$#mlgn J} ç ñ~ (7) J! >ƒu}w 9 ƒ ô with a Lagrange multiplier and ~ the spectral region where ãúvæ ç[è [ˆ. We vary the value o such n that ã hji<k ú æ çtè satisies with equality the average power constraint in (6). The equality is n 26