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36 th Asilomar IEEE Conference on Signals, Systems and Computers Nov 3-6, 2002, Pacific Grove, CA. DMT Bit Rate Maximization With Optimal Time Domain Equalizer Filter Bank Architecture. * M. Milo š evi ć, **L. F. C. Pessoa, *B. L. Evans and *R. Baldick.

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DMT Bit Rate Maximization With Optimal Time Domain Equalizer Filter Bank Architecture

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Dmt bit rate maximization with optimal time domain equalizer filter bank architecture

36th Asilomar IEEE Conference on Signals, Systems and Computers

Nov 3-6, 2002, Pacific Grove, CA

DMT Bit Rate Maximization With Optimal Time Domain EqualizerFilter Bank Architecture

*M. Milošević, **L. F. C. Pessoa, *B. L. Evans and *R. Baldick

*Electrical and Computer Engineering Department

The University of Texas at Austin

**Motorola, Inc, NCSG/SPS

Austin, TX


Basic architecture dmt transceiver

Basic Architecture: DMT Transceiver

N/2 subchannels

N samples

Serial-to-Parallel (S\P)

QAM

encoder

mirror

data

and

N-IFFT

add

Cyclic Prefix(CP)

Digital-to-Analog Converter +

transmit filter

Parallel-to-Serial (P\S)

Bits

00101

TRANSMITTER

channel

noise

RECEIVER

N/2 subchannels

N samples

receive filter

+

Analog-to-Digital Converter

P/S

TEQ

time domain equalizer

QAM

decoder

N-FFT

and

remove

mirrored

data

S/P

remove

CP

invert channel

=

frequency

domain

equalizer


Dmt symbol

v samples

N samples

s y m b o l ( i+1)

CP

CP

s y m b o l ( i )

copy

copy

DMT Symbol

Inverse FFT

D/A + transmit filter

CP: Cyclic Prefix


Isi and ici in dmt

ISI and ICI in DMT

  • Channel is longer than cyclic prefix (CP)+1

    • Adjacent symbols interfere (ISI)

    • Subchannel are no longer orthogonal (ICI)

  • TEQ mitigates the problem by shortening the channel

    • No symbol at demodulator contains contributions of other symbols

    • Cyclic prefix converts linear convolution into circular

    • Symbol  channel  FFT(symbol) x FFT(channel)

    • Division by the FFT(channel) can undo linear time-invariant frequency distortion in the channel


Channel impairments and teq design

Channel Impairments and TEQ Design

  • Conventional ADSL TEQ design

    • Mitigate inter-symbol interference at the TEQ output

  • Proposed ADSL TEQ design - Maximize data rate

    • Inter-symbol interference at the output of the demodulator (FFT)

    • Near-end crosstalk (NEXT)

    • Design with respect to digital noise floor (DNF)

    • White noise in the channel (colored by TEQ)

  • Other impairments present in an ADSL system

    • Impulse noise

    • Near-end echo

    • Far-end echo (of concern in voice-band communication)

    • Phase and frequency content distortion (compensated by FEQ)


Proposed teq design method

Proposed TEQ Design Method

  • Maximize bit rate at the demodulator (FFT) output instead of TEQ output

  • Incorporate more sources of distortion into design framework

  • Expected contributions

    • Model SNR at output of the FFT demodulator

    • Data Rate Optimal Time Domain Per-Tone TEQ Filter Bank Algorithm (TEQFB)

    • Data Rate Maximization Single TEQ Design

  • Results


Model snr at output of demodulator

Model SNR at Output of Demodulator

  • Desired signal in kth frequency bin at FFT output is DFT of circular convolution of channel and symbol

    • is desired symbol circulant convolution matrix for delay D

    • H is channel convolution matrix

    • qkis kth column vector of N DFT matrix

  • Received signal in kth frequency bin at FFT output

    • is actual convolution matrix (includes contributions from previous, current, and next symbol)

    • G(*) is convolution matrix of sources of noise or interference


Model snr at output of demodulator1

Model SNR at Output of Demodulator

  • Proposed SNR model at the demodulator output

  • After some algebra, we can rewrite the SNR model as

  • adig – Digital noise floor (depends on number of bits in DSP)

  • (*)H – Hermitian (conjugate transpose)


Model snr at output of demodulator2

Model SNR at Output of Demodulator

  • Bits per symbol as a nonlinear function of equalizer taps.

    • Multimodal for more than two-tap w.

    • Nonlinear due to log and .

    • Requires integer maximization.

    • Ak and Bk are Hermitian symmetric.

  • Unconstrained optimization problem:


Data rate optimal time domain per tone teq filter bank teqfb algorithm

Data Rate Optimal Time Domain Per-tone TEQ Filter Bank (TEQFB) Algorithm

  • Per channel maximization: find optimal TEQ for every k subchannel in the set of used subchannels I

  • Generalized eigenvalue problem

  • Bank of optimal TEQ filters


Teq filter bank architecture

G1

w1

FEQ1

G2

w2

FEQ2

GN/2-1

wN/2-1

FEQN/2-1

TEQ Filter Bank Architecture

y1

Y1

TEQ Filter Bank

Goertzel Filter Block

Frequency Domain Equalizer

y2

Y2

Received Signal x={x1,…xN)

yN/2-1

YN/2-1


Teqfb computational complexity

TEQFB Computational Complexity

  • Creating matrices Ak and Bk ~ NO(M2N)

  • Up to N/2 solutions of symmetric-definite problems

    • Using Rayleigh quotient iteration

Initialization

Data Transmission

N= 512, n=32, M 2, fs= 2.204 MHz, fsym=4 kHz


Data rate maximization single teq design

Data Rate Maximization Single TEQ Design

  • Find a single TEQ that performs as well as the optimal TEQ filter bank.

    • Solution may not exist, may be unique, or may not be unique.

    • Maximizing b(w) more tractable than maximizing bDMTint(w).

    • b(w) is still non-linear, multimodal with sharp peaks.


Data rate maximization single teq design1

Data Rate Maximization Single TEQ Design

  • Find a root of gradient of b(w) corresponding to a local maximum closest to the initial point

    • Parameterize problem to make it easier to find desired root.

    • Use non-linear programming

    • Find a good initial guess at the vector of equalizer taps w – one choice is the best performing TEQ FIR in TEQFB.

    • No guarantee of optimality

    • Simulation results are good compared to methods we looked at


Simulation results

Simulation Results

  • Measurement of the SNR in subchannel k

    • S = 1000 symbols

    • Every subchannel in a symbol loaded with a random 2-bit constellation point Xki, passed through the channel, TEQ block and FEQ block (where applicable) to obtain Yki

  • Bit rate reported is then


Effect of teq size on bit rate

Effect of TEQ Size on Bit Rate

Data rates achieved for different number of TEQ taps, MN = 512, n= 32, input power = 23.93 dBm, AWGN power = -140 dBm/Hz, and NEXT modeled as 49 disturbers. Accuracy of bit rate: 60 kbps.

(a) CSA loop 2

(b) CSA loop 7


Effect of transmission delay on bit rate

Effect of Transmission Delay on Bit Rate

Data rates achieved as a function of D for CSA loop 1.N = 512, n= 32, input power = 23.93 dBm, AWGN power = -140 dBm/Hz, and NEXT modeled as 49 disturbers. Accuracy of bit rate: 60 kbps.


Simulation results1

Simulation Results

  • We evaluate TEQFB, proposed single TEQ, MBR, Min-ISI, LS PTE, MMSE-UTC and MMSE-UEC for CSA loops 1-8

  • Results presented in a table

    • Each row entry

    • Final row entry


Teq design methods comparison

TEQ Design Methods - Comparison

CSA – carrier serving area, MBR – Maximum Bit Rate, Min-ISI – Minimum InterSymbol Interference TEQ Design, LS PTE – Least-squares Per-Tone Equalizer, MMSE – Minimum Mean Square Error, UTC – Unit Tap Constraint, UEC – Unit Energy Constraint


Teqfb data rates

TEQFB Data Rates

Highest data rates in Mbps achieved by TEQFB for TEQ lengths 2-32, input power = 23.93 dBm


Backup slides

Backup Slides

Milos Milosevic

Lucio F. C. Pessoa

Brian L. Evans

Ross Baldick


Bit symbol for a 2 tap teq

Bit/symbol for a 2-tap TEQ


Bit symbol for a 3 tap teq

Bit/symbol for a 3-tap TEQ


Csa loops

CSA Loops

Configuration of eight standard carrier serving loops (CSA). Numbers represent length in feet/ gauge. Vertical lines represent bridge taps.

From Guner, Evans and Kiaei, “Equalization For DMT To Maximize bit Rate”.


Selected previous teq design methods

Selected Previous TEQ Design Methods

  • Minimize mean squared error

    • Minimize mean squared error (MMSE) method[Chow & Cioffi, 1992]

    • Geometric SNR method[Al-Dhahir & Cioffi, 1996]

  • Minimize energy outside of shortened channel response

    • Maximum Shortening SNR method[Melsa, Younce & Rohrs, 1996]

    • Divide-and-Conquer methods – Equalization achieved via a cascade of two tap filters[Lu, Evans & Clark, 2000]

    • Minimum ISI method - Near-maximum bit rate at TEQ output[Arslan, Evans & Kiaei, 2001]

    • Maximum Bit Rate (MBR) - Maximize bit rate at TEQ output [Arslan, Evans & Kiaei, 2001]

  • Per-tone equalization

    • Frequency domain per-tone equalizer [Acker, Leus, Moonen, van der Wiel & Pollet, 2001]


Goertzel filters

Goertzel Filters

  • Used to calculate single DFT point

  • Denote with yk(n) as the signal emanating from TEQ making up TEQFB

  • Then, the corresponding single point DFT Yk is:

    where Gk (-1) = Gk (-2) = 0 and n={0,1,…,N}


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