CSCO-1007
`Cisco v. TQ Delta
`Page 1 of 34
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`

`
`PATENTS
`AWR—047
`
`Characterization of Transmission Lines Using Broadband Signals In A Multi—Carrier DSL System
`
`Enclosed are the following papers required to obtain a filing date under 37 C.F.R. §1.53(c):
`
`Sheets of Informal Drawings
`Pages of Specification, Drawings & Tables
`Claims
`
`The following papers, if indicated by an El, are also enclosed:
`
`A Declaration and Power of Attorney
`An Assignment of the invention
`An Information—Disclosure Statement, Form PTO—1449 and a copy of
`each cited reference
`
`A Small-Entity Declaration
`A Certificate of Express Mailing, Express Mail Label No. EE437022773US
`
`Basic Fee:
`
`$150
`
`A check in the amount of $150 is enclosed to cover the Filing Fee.
`
`Please address all communications and telephone calls to the undersigned.
`
`Respectfully submitted,
`
`Gail Leonick
`Aware, Inc.
`
`I
`
`'
`
`40 Middlesex Turnpike
`Bedfored mass. 01730
`
`Page 2 of 34
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`

`
`PATENT
`AWR—047
`
`UNITED STATES PROVISIONAL PATENT APPLICATION
`
`0f
`
`Murat Belge
`Michael A. Tzannes
`and
`Halil Padir
`
`for a
`
`Characterization of Transmission Lines Using Broadband Signals In A Multi-
`
`Carrier DSL System
`
`Page 3 of 34
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`Aware, Inc. Proprietary and Confidential Information
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`References Cited
`
`[1] Provisional patent by D. Krinsky and R. Pizzano, “ 1|/[ulticarrier Modulation System with
`Remote Transmission Mode”, serial no: 60/174,865, date filed: 1 /7/ 2000.
`
`[2] Provisional patent by M. Belge, “Estimation of the Loop Length and Bridged Tap Length
`of (1 Transmission Line”, serial no: 60/174,866, date filed: 1/7/2000.
`
`1 Background of the Invention
`
`Rapid developments in the computer industry and the availability of affordable hardware
`created the internet where any user having a communication link between his/her home
`and the computers in centralized locations can access publicly available information. Users
`of the internet are connected to the communication network through a link that includes
`a telephone line from the customer premises (CPE) to a telephone company central ofiice
`(CO). A computer user requesting data transfer from an internet server is faced with the
`limited bandwith of the connection between the his/her home and the central office. As
`more and more information is being created and stored in digital format, the demand from
`users to access large data files is increasing making it crucial to find new and faster ways of
`transferring data. One way of achieving faster data transmission is to increase the bandwith of
`the transmission line between users and the CO by replacing the current metallic conductors
`with fiber or using better quality metallic conductors with increased bandwith. But such an
`approach is costly and requires a substantial investment by the telephone companies.
`
`Recent developments in digital signal processing and telecommunications have resulted in the
`digital subscriber line (DSL) technology enabling a high speed data link over existing twisted
`pair telephone lines. Alhough a couple of different DSL systems had been proposed multi-
`carrier systems have quickly gained popularity and been standardized. Multi-carrier DSL
`systems operate on the principle of frequency division multiplexing where sepcrate frequency
`bands are used to transfer data from the CPE to the CO and vice versa. The portion of
`the bandwith allocated for transmitting data from the user’s computer to the CO is called
`the up-stream (US) channel and the portion of the bandwith allocated for passing data from
`the CO to the user’s computer is called the down—stream (DS) channel. Since in a typical
`internet session the amount of data being transmitted from the CO to the user’s computer is
`much larger than the amount of data transmitted from the user’s computer to the C0, the
`bandwith allocated for the DS channel is usually much larger than the bandwith allocated for
`the US channel (typical ratios are 4 to 1 or 8 to 1). The bandwith allocated to the US and DS
`channels are partitioned into a large number of sub-bands which are sufficiently narrow so as
`to allow the distortions introduced by the line to be described as an attenuation and a phase
`shift. These parameters can be measured in a training session prior to establishing the data
`link by sending and receiving a predefined signal on each subband. The amount of data that
`can be sent in a sub—band is limited by the signal to noise ratio (SNR) in that sub—band which
`is the signal strength described by the line attenuation divided by the noise power. Each of
`the sub-bands in the multi~carrier DSL system is used to transmit data that is consistent
`with the SNR on that sub—band and maximum allowable error bit rate. Multi-carrier DSL
`
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`system operating with the described principles are able to achieve data rates as high as ten
`million bits per second.
`
`Although the multi—carrier DSL systems are promising because they offer a cost effective way
`of opening current telephone lines to high speed data transmission traflic, there are important
`problems in the installation and maintenance phases of DSL deployment that prevents rapid
`wide spread deployment. Existing telephone lines were initially installed for voice only
`transmission which can be done by using only a small bandwith. Multi—carrier DSL system
`require utilizing a bandwith much larger than that required by the voice transmission. At high
`frequencies line conditions that don’t afiect the voice transmission become important factors
`limiting the digital data transmission rate. For example, the line attenuation is related to the
`loop length. The strength of the signals sent from either CO or user’s computer decreases with
`distance. Small open circuited twisted pairs, called bridged taps (BT), connected in shunt
`with working twisted pairs, while not effecting voice transmission, cause periodic dips in the
`attenuation function of the line at certain sub-bands and hence degrade the performance of
`the DSL service. Telephone lines are usually bundled as 25 or 50 twisted pairs in a cable.
`Close proximity of the twisted pairs in the cable causes the signals generated by varioms DSL
`services carried by a specific telephone line to be picked up by the remaining telephone lines
`in the bundle. These signals are perceived as additive noise components because they are
`unpredictable and meaningless for all but one of the telephone lines carrying the service. The
`interference entering the telephone lines through some coupling path with other telephone
`lines are called crosstalk. There may be other sources of noise in a telephone line which are
`caused by the reception of electromagmetic (EM) waves transmitted by various sources such
`as AM stations or electrical devices such as hair dryers, dimmer switches, alarm systems etc.
`The most detrimental of these EM sources are generally AM stations. Since no two telephone
`lines are the same and the availibility and the quality of a DSL link depend on the conditions
`of the line as described above, it is very important to be able to qualify telephone lines for
`DSL service and maintain the link once the service is established. It is a challenge to ease the
`installation and maintenance issues. To decrease the cost associated with service qualification
`and maintenance, it is preferrable to qualify and maintain telephone lines remotely without
`sending a technician to the customer premises.
`
`It is the object of the present invention to provide a system for the qualification, maintenance
`and monitoring of telephone lines for DSL service by taking advantage of the DSL tranccivers
`in the CO and the CPE sites.
`
`2
`
`Summary of the Invention
`
`Establishing a digital data link between the computer in user’s home and the servers
`connected to the backbone of the central office requires DSL tranceivers handling the data
`transmission with the basic principles outlined in the previous section. Each of the tranceivers
`at either side of the link,
`the CO and the CPE, are called modems. The CO and the
`CPE modems consist of some analog harware to perform analog signal transmission and
`reception and a digital section which consists of a digital signal processing (DSP) chip and
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`an application specific integrated circuit (ASIC) handling sophisticated signal processing
`operations. Because of the high data rate associated with the DSL service, the DSP chip must
`complete the necessary processing and manipulation on digital data in short time intervals.
`That is the DSP chips used in the CO and the CPE modems must be, by definition, very
`powerful. The present invention takes advantage of the vast computational capacity of the
`DSL modems and the presence at the two sides of the transmission line to characterize the
`transmission line. The DSL modems operate as a modem in their usual state but they can
`be put in a different mode where they can be used as test and measurement devices.
`
`The most important issues faced during the installation and maintenance is finding out the
`physical structure and the conditions of the line so that the a decision can be made regarding
`the suitability of the loop for DSL service and necessary steps can be taken to improve the
`telephone line so that the service providers can offer better DSL service to their customers.
`For example, if a bridged tap causing a substantial data rate reduction is found the telephone
`company may send a technician to remove it.
`In general the following information is very
`useful for characterizing the transmission line
`
`a the loop length
`
`0 the detection of the bridged taps and the estimation of their lengths and locations
`
`0 the detection of interferers on the line.
`
`the installation the link must be monitored in order to ensure service quality.
`After
`This requires determining changes in the transmission environment which can be again
`accomplished by using the signal processing capabilities of the DSL modem.
`
`In the present invention the CO and the CPE modems are used as test points and the test
`process consists of collecting specific data sets during modem training, postprocessing the
`data to ease the use and interpretation and finally extracting plain English results regarding
`the line conditions. In modern training the objective is to do measurements and determine
`the parameters of the transmission line so as to allow restoration of the original signals
`transmitted by the CPE and the CO modems. These signals are distorted by the transmission
`line through attenuation and phase shift and further degraded by the noise. The CO and CPE
`modems go through a pre-defined and standardized set of states to learn the parameters of
`the entire communication system. They transmit and receive signals known to each modem.
`These signals help characterize the transmission line but the CO and the CPE modems do
`not use these signals for anything other than improving the signal transmission and reception.
`The current invention requires adding a data collection software to either the CO or the CPE
`or preferably to both so that some of the data sets already used in the modem training can be
`collected with improved accuracy and can be saved for further analysis. The data collection
`software also allows some new data sets to be obtained.
`
`Because the CO and the CPE modems operate by frequency division multiplexing principle,
`the data collected at the CPE and CO modems are different in the sense that the CPE modem
`transmits in the US channel and receives in the DS channel and the CO modem transmits in
`
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`CPE Transmit
`00 Receive
`
`CO Transmit
`CPE Receive
`
`Frequency
`
`Figure 1: US and DS channel allocation for a typical ADSL multi—carrier DSL system.
`
`the DS channel and receives in the US channel. Therefore the bandwith of the data collected
`at the CPE is limited to the bandwith of the DS channel and similiarly the bandwith of the
`data collected at the CO is limited to the bandwith of the US channel. As an example, the
`bandwith allocation for an ADSL system is illustrated in Figure 1. To summarize, as a result
`of the modem training we have the following:
`
`0 US data collected and saved in the CO modem.
`
`0 DS data collected and saved at the CPE modem.
`
`Note that the test process as mentioned above makes use of the standard modem training
`and therefore relies on the existence of both the CO and the CPE modem. We call such a
`test process a double-ended test.
`
`In a double ended test, the DS data collected at the CPE can be transferred to the CO site to
`be analyzed by service technicians. This requires the ability to establish a special diagnostic
`link between the CO and the CPE for passing the diagnostic data even if the standard DSL
`link fails. This can be accomplished, for example, by the method that was described in
`reference
`In the case a diagnostic link cannot be established only local data (US data at
`the CO test point and DS data at the CPE test point) is available for further analysis.
`
`The telephone company may want to perform a
`
`single-ended test from either the CO or
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`the CPE site to pre—qualify customer lines for DSL service. Also, a computer manufacturer
`who installs DSI. modems into its computers may want to perform a single-ended test so
`that the customer can determine what kind of DSL service to order. In these cases We can
`continue using the signal processing cababilities of the DSL modem in a different fashion. In
`a double-ended test, one of the modems acts as a signal generator and the other Works as
`a signal receiver. In the single-ended testing the same DSL modem acts both as the signal
`generator and signal receiver for characterizing the customer line.
`
`The objective of the present invention is to to analyze the data collected as a result of a single
`or double-ended test process and characterize the transmission environment by plain English
`interpretation results such as loop length, bridged tap lengths, interferer types etc., that can
`be easily understood by unskilled technicians and at the same time producing graphs for the
`visual inspection of the line conditions. Specifically, the present invention embodies
`
`1. a method for using DSL signal processing engine to characterize transmission lines.
`
`2. a method for tracking changing line conditions.
`
`3. a method for compensating the effects of analog front end
`CPE modems to better characterize the transmission line.
`
`of the CO and the
`
`. a method and algorithm for estimating the loop length and detecting bridged taps and
`estimating their lengths from DS data (the current presentation of this algorithm is an
`improved version of the method given in reference
`
`. a method and algorithm for estimating the loop length and detecting the bridged taps
`and estimating their lengths from US data.
`
`. a method an algorithm for estimating the loop length and detecting the bridged taps
`and estimating the location and the lengths of the detected bridged taps using single-
`ended testing.
`
`. a method and algorithm for detecting crosstalk interferers on the line and estimating
`the power level of the detected disturbers.
`
`. a method and algorithm for detecting EM disturbers such as AM stations or amateur
`radio stations and estimating their frequencies and power levels.
`
`. a method and algorithm for estimating the data rate reduction caused by the presence
`of various interferers on the line.
`
`. a method and algorithm for prequalification of a telephone line where the maximum
`data rate that can be supported by the telephone line is estimated by single-ended
`testing.
`
`. a method and algorithm for obtaining visually displayable data from the raw data
`collected in the CO and CPE modems.
`
`. a method for displaying the results in plain English for unskilled technicians.
`
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`CO/CPE
`
`Data Collection
`
`CPE
`
`Data Collection
`
`Local Data (Raw)
`
`Remote Data (Raw)
`
`Interpretation
`Parameters
`
`Postprocessing
`+
`
`Interpretation
`
`Processed Data for
`
`V‘5“3l D’9F’l3V
`
`Figure 2: Various functional blocks of the present invention.
`
`Although the above description disscusses the use of ADSL for this application, it is clear
`that any form of DSL (including VDSL, SDSL, HDSL, HDSL2) could also be used. It should
`also be noted that the methods and algorithms listed above are applicable to both discrete
`multietone (DMT) and discrete wavelet n1u1ti—tone (DVVMT) DSL systems.
`
`3 Detailed Description of the Invention
`
`invention, from a functional point of view,
`The present
`illustrated in Figure 2:
`
`involves three primary steps as
`
`1. Data collection,
`
`2. Postprocessing,
`
`3. Interpretation.
`
`The data collection process is always implemented in the DSL modem and responsible for
`producing the raw data for postprocessing and interpretation. The postprocessing part is
`designed to ease the use and interpretation of the raw data.
`Its responsibilities include
`calibration, filter compensation, estimation of remote SNR tables from bits and gains tables,
`and data rate conversion. Detailed descriptions of each of these processes and sample software
`are provided in Appendices in section A.
`
`Interpretation part of the present invention is responsible for analyzing the postprocessed
`data and extracting plain English, easily understandable results about the line conditions.
`
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`We have a number of different interpretation routines
`
`9 Loop Length/Bridged-Tap Length Estimation (Appendix B.1): Estimates the
`loop length and tries to determine the presence of the bridged tap on the transmission
`line‘ If a bridged tap is detected, its lengh is also estimated. The algorithm operates by
`comparing a model of the transfer function of the line, which is parametrized in terms
`of the loop length and the bridged tap lengths and locations, to the actual measured
`transfer function of the line. We have three different algorithms to estimate the physical
`structure of the loop depending on which data set is being used (US, DS or single-ended
`time domain reflectometry data set). These three algorithms are described in detail in
`Appendix B.1.1 - B.1.3.
`
`Interferer Detection (Appendix B.2): Performs the task of identifying crosstalk
`and EM disturbers on the line by analyzing the measured power spectrum of the noise.
`We have two different algorithms for identifying crosstalk sources (Appendix B.2.1) and
`detecting EM sources (Appendix B.2.2).
`
`Data Rate Reduction Estimation (Appendix B.3): Estimates the data rate
`reduction caused by the presence of the disturbers on the transmission line.
`
`Data Rate Estimation (Appendix B.4): Estimates the maximum data rate that
`the transmission line can support by performing a single—ended test. It combines the
`results of single-ended TDR test and the measurement of the power spectrum of the
`noise on the line to estimate a rough SNR profile for US and DS channels and estimates
`the data rate based on these SNR tables.
`
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`Appendix
`
`A Post processing
`
`Postprocessing routines perform Various simple tasks such as converting raw data from one
`format to the other, scaling the data, and compensating for the analog and digital filters
`in the receive path. Below We outline the basic postprocessing routines.
`their functional
`specifications and implementational details.
`
`A.1 Calibration
`
`Processes the raw data in fixed point format (ION, Reverb, TDR) so that the data appears
`the same way as it would if measured by a standard test equipment. The calibration routine
`takes the raw data array, PGA setting used to collect the data and the gain scaling (if there
`is any) and outputs the calibrated data. Below we provide a C—like pseudo-code for the
`calibration routine. Note that calibration function in the actual implementation may slightly
`Vary depending on the raw data being used.
`
`First we explain the conventions used in pseudo-code implementation. Below, int16 represents
`a 16-bit integer number. Outputs of a function is listed in square brackets. All inputs and
`outputs are described in the comments section immidiately after function declaration.
`
`Pseudo—C ode:
`
`int16 Gscale )
`
`[float CalData] = Ca.librate( int16 RawData[], int N, float PGA,
`// Inputs:
`// RawData[] ' array containing the raw data
`// N = number of elements in array RawData[]
`// PGA = PGA setting used to collect data
`// Gscale = Scaling applied to the elements of RawData[]
`//
`
`// Output:
`// CalData = Output array containing the calibrated data.
`{
`
`for (i=0;
`{
`
`i < N;
`
`i++)
`
`Ca1Data[i] = 10*1oglO( RawData[i] * 2"GScale ) - PGA;
`
`} r
`
`}
`
`eturn CalData ;
`
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`A.2 Filter Compensation
`
`Removes the effects of AFB filters from the measured data. The filter compensation routine
`takes the calibrated data and the device specific frequency domain response of the AFE filters
`and outputs the filter compensated data.
`
`Pseudo-Code:
`
`[complex CompData] = FilterCompensate( complex CalData[], complex CompFilter[],
`int N)
`
`// Inputs:
`// CalData[] = array containing the calibrated data in dB.
`// CompFilter = device specific frequency domain filter function in dB.
`// N = number of elements in array CalData[]
`//
`// Output:
`// CompData — array containing filter compensated, calibrated data.
`{
`
`for (i=0;
`{
`
`i < N;
`
`i++)
`
`CompensatedData[i] = Calibrated.Data[i] - Filter[i];
`
`return CompData;
`
`}
`
`A.3 Filter Compensation for Reverb Collected in Showtime
`
`In service monitoring, CPE and CO modems collect the reverb signal received in sync frame.
`Since TDQ and FDQ are normally in operation in showtime, the received reverb signal is
`affected by the TDQ and FDQ filters. It is possible to remove the effects of TDQ and FDQ
`filters by doing a trivial frequency domain deconvolution.
`
`Pseudo-Code:
`
`[float CompData] = FilterCompensate(complex CalData[] , Complex TDQ [] ,
`complex FDQ [] ,
`int N)
`
`// Inputs:
`calibrated data array (in dB).
`// CalData
`// TDQ = array containing TDQ filter coefficients.
`// FDQ = array containing FDQ filter coefficients (in dB).
`// N = number of elements in array CalData[].
`
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`//
`// Output:
`// CompData = compensated data in dB.
`{
`
`FFT( TDQ, N );
`TDQ =
`for (i=0; i < N;
`i++)
`{
`
`//FFT of TDQ coeffs in dB.
`
`TDQ[i] = 10*lOg10( TDQ[i] );
`
`i++)
`
`} /
`
`/ Deconvolution
`for (i=0;
`i < N;
`‘E
`
`CompData[il = CalData[i] — FDQ[i] - TDQ[i];
`
`eturn CompData;
`
`} r
`
`}
`
`A.4 SNR Medley from Bits and Gains Table
`
`In twoeended provisioning, if CO or CPE is not cpable of establishing a diagnostic link, we
`only have the local US or DS data. However, a crude representation of the SNR table of
`the far end modem can be obtained through a standard link. According to the G.dmt and
`G.lite specs, each modern has to send a bits and gains table to the other side which indicates
`the number of bits assigned to each tone and corresponding fine gain. Since bit allocation is
`directy related to the SNR, a reverse transformation from bits and gains table to the SNR
`table is possible. However, the reverse transformation is not perfect. SNR’s below 10 dB and
`above 55 dB cannot be observed.
`
`Pseudo-Code:
`
`[float SNR] = SNRFromBits&Gains( int16 Bits[],
`// Input:
`// Bits = Far end bitloading table.
`// Gains = Far end fine gains table.
`// N = number of elements in Bits [] and Gains [] arrays.
`//
`
`int16 Gains[],
`
`int N)
`
`// Ouput:
`// SNR = Estimated far end SNR table.
`{
`
`11.31, 14.32, 19.11
`float SNRRequired[] = {0.0,
`21.31, 24.46, 27.54, 30.59,
`
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`33.61, 36.63, 39.65, 42.66,
`45.67, 48.68, 51.69, 54.70};
`
`for (i=0;
`{
`
`i < N;
`
`i++)
`
`SNR[i] = SNRRequired( Bits [1]
`
`) - Gains [i];
`
`return SNR ;
`
`}
`
`A.5 Rate Conversion
`
`Converts the data rates in units of 32,000 kilo bits per second (Kbps) to the actual rate in
`Kbps.
`
`Psendo—Code:
`
`ProcessR.ate( int16 R.awRate )
`
`[int Rate]
`// Input:
`// Rawfiate
`// Output:
`// Rate = Rate in Kbps.
`{
`
`raw data rate.
`
`return Rawftate * 32,000;
`
`B Interpretation
`
`Interpretation software is responsible for extracting plain-English results from the postpro-
`cessed data. In the following sections, we provide theoretical background on the interpretation
`algorithms, give computational and memory requirements and elaborate on implementational
`details.
`
`B.1 Loop Characterization: Loop Length Estimation and Bridged Tap
`Detection/ Length- Estimation
`
`The loop characterization algorithms employ a model based approach to estimate the length
`of the loop and the lengths of upto two bridged taps. Specifically, our channel diaracterization
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`13
`
`algorithm compares the measured channel impulse response to the channel impulse response
`of a loop model consisting of a single-gauge wire and containing upto two bridged taps. The
`loop length and the bridged tap lengths are the parameters of the theoretical channel impulse
`response. The algorithm changes the parameters of the theoretical model and evaluates the
`error between the measured channel impulse response and the theoretical channel impulse
`response. The loop length/bridged tap lengths that minimize the error function are declared
`as the estimated values. The presence of a bridged tap is declared only if the bridged tap
`length is greater than a hundred feet.
`
`There are two separate algorithms which perform loop characterization from downstream
`(DS) and upstream (US) data. During modem initialization, data collection software collects
`the reverb signal by averaging K consecutive frames (K 2 64). The received reverb signal
`obtained in this way is an estimate of the impulse response of the entire channel including
`the fiont end responses of the transmitting and receiving modems. The frequency domain
`received reverb signal is obtained in the following way:
`
`R
`
`FFT
`
`1 K
`: ——
`)
`(
`N (WW)
`$0‘) K kg
`. ,N, is the samples of
`where f is a dummy variable denoting frequency and r:1:(n), n 2 1,. .
`the time—domain received reverb signal within a frame with N being the number of samples
`contained in a single frame. The equation in (1) may contain a slight abuse of notation
`because in reality the frequency variable f is not continuous but rather discrete and for this
`reason the channel impulse response is available only at a set of discrete frequencies, called
`tones, which are multiples of A f = 4312.5Hz:
`
`1
`
`f,:iAf, i:1,...,N/2
`
`(2)
`
`The reverb signal is transmitted only over a portion of the entire ADSL spectrum. The
`reverb signal is available at 224 (96 in G.Lite) tones from f32 = 3?Af to f255 = 255Af in DS
`channel and at 26 tones from f5 = 6Af to far = 31Af in US channel. The DS reverb signal is
`collected at CPE and US reverb signal is collected at C0. V’Vhile there is no difference in the
`data collecttion process for US or DS reverb signal, the characteristics of these two data sets
`are quite different. First of all the DS reverb data contains significantly more information.
`There are more samples of the frequency domain reverb signal available in DS direction and
`these samples cover an extended range in frequency domain where the effects of bridged taps
`on impulse response can be easily detected. There is one crucial difference between US and
`DS data sets which prevents using the same interpretation algorithm for both.
`In the DS
`channel, the matching of the front and impedance to the loop impedance tends to be better
`than the US channel. This makes it possible to use a simplified channel model for DS channel.
`Unfortunately, impedance matching in the US channel is not as good as in DS channel and a
`more complicated channel impulse response must be used. Because of the said complications
`in channel modeling and the lack of sufficient data samples, the US channel characterization
`algorithm is limited in terms of estimation accuracy and the number of bridged taps that can
`be detected. Currently, channel characterization software is capable of detecting upto two
`bridged taps from DS data and one bridged tap from US data.
`
`Below we give theoretical details leading to the derivation of the frequency domain channel
`impulse response of our model and explain channel characterization from DS and US data in
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`
`14
`
`detail. Both DS and US interpretation algorithms employ the same least squares minimization
`concept where the square of the error norm between the actual and the theoretical channel
`impulse responses is minimized but difi'er in the theoretical channel impulse response used.
`
`B.1.1
`
`Loop Characterization from DS Data
`
`A two-wire loop is chracterized by its characteristic impedance, ZQ(w) = 1/ , and its
`propagation constant, 7(f) = «(R +jwL)(G +jwC), where w = 27rf and R, L, G and C
`are the frequency dependent constants of the loop. For a perfectly terminated loop (or for a
`very long loop) with length d, and two bridged taps of lengths b1 and b2, the transfer function
`of the loop, H(d, b1, ()2, f), is given by
`
`H(d’ b1’ b2’
`
`3-d*r(f)
`— [2 + tanh(b1'y)][2 + tanh(b27)]
`
`ln logarithmic scale
`
`10% lH(d,b1,b2,f)| = rd“/(fl *10g[2 + t3Hh(bi7)l -10gl2 + taI1h(b27)l
`
`(3)
`
`(4)
`
`Note the linear dependence of the loop loss to the length of the cable. The actual transfer
`function of the loop can be measured during modem initialization as explained in section .
`Then we try to match the measured transfer function of the loop with that of a loop of length
`d with two bridged taps as given in
`In other words we try to find d, b1, and b2 which
`minimizes the following least squares error criterion:
`1:
`
`drgirg Z 1H<d, bl7b21f‘A) — R/w(;2>|§
`1 1: 2 l:1f
`
`(5)
`
`where R:c(fz) is the received reverb signal sampled at
`and the last tones R:L'(f1) is available.
`
`f1 = 2A f and if and 1'; are the first
`
`An example of the operation of the algorithm is illustrated in Figure 3. Here we display
`the measured received reverb signal R$( f) and the theoretical model H (d, bhbg, f) which
`was obtained by finding the model parameters d,b1, bg that best match the data. The loop
`consisted of 26 awg 6000 ft wire with a 26 awg 1300 ft bridged tap close to CPE. Model
`parameters best matching the observed data were found to be d = 6000 ft, b1 = 1300 ft and
`b2 : 0 ft.
`
`It is obvious from the
`Memory Requirements and Computational Complexity:
`problem statement in (5) that the interpretation algorithm basically does a search over the
`Variables d, b1 and b2 and finds the ones minimizing the cost function given below:
`
`E<d,b1,b2> = ‘:3 1H<d, b1,b2,fz) — Rx(i2)I§-
`z'=zf
`
`£6)
`
`Unfortunately, the cost function E ((1, b1, b2) is a nonlinear function of d, 291 and b2 and contains
`many local minima. Therefore many well known optimization algorithms such as Gauss-
`Newton cannot be used since these algorithms cannot cope with multiple local minima and
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`Page 16 of 34
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`I
`
`I
`
`".__ —H(d,b 1,1?)
`Fix(f)
`
`I
`120
`
`_.a
`140
`Tone
`
`1 80
`
`1 80
`
`200
`
`220
`
`Figure 3: Observed (dashed line) received reverb signal Rx (f) versus the theoretical channel
`model [solid line) H (d, bl, b2, f) as functions of frequency for a 6000 ft loop with a single 1300
`ft bridged tap.
`
`In our case we definitely want
`they converge to a local minimum of the cost function.
`the global minimum of E(d, bl, ()2). For this reason, we decided to use a brute-force global
`minimization algorithm where we sample the cost function at the points (d”,b‘{, E), dp =
`pAD, b'11=qAbl and bg =1'Abg withp= 1,...,P, q : 1,...,Q and 1" = 1,...,R. We then
`choose the parameters (dp ,b‘1’., bg) which results in the minimum cost among the sampled
`values. This requires evaluating the cost function at P X Q X R locations.
`
`In order to be able to compute the theoretical transfer function of the loop, H (d, bl, b2, f),
`we need to store the frequency dependent propagation constant ’7‘( f) for a number of wires of
`different gauges. In the current implementation, we only use 24awg and 26awg wires which
`require 4 X N locations to store the real and the imaginary parts of 7(f) for N ADSL tones.
`We also need to store the AFE compensation curves which takes up N locations in memory.
`Depending on where we implement the algorithm, We can either compute the loop transfer
`function directly from (4) (as it would have been the case if the algorithm were implemented
`on a PC or workstation) or we may have to store log[2 + tanh( bl'7)] terms in regular intervals
`as required by our sampling procedure for (dP,bq,b§). For example, we