Loading in 5 sec....

DMT Bit Rate Maximization With Optimal Time Domain Equalizer Filter Bank ArchitecturePowerPoint Presentation

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

Download Presentation

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

Loading in 2 Seconds...

- 91 Views
- Uploaded on
- Presentation posted in: General

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

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

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

v samples

N samples

s y m b o l ( i+1)

CP

CP

s y m b o l ( i )

copy

copy

DMT SymbolInverse FFT

D/A + transmit filter

CP: Cyclic Prefix

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

- 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

- 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

- 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 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 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

- 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

G (TEQFB) Algorithm1

w1

FEQ1

G2

w2

FEQ2

GN/2-1

wN/2-1

FEQN/2-1

TEQ Filter Bank Architecturey1

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) Algorithm

- 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 (TEQFB) Algorithm

- 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 Design (TEQFB) Algorithm

- 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 (TEQFB) Algorithm

- 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 (TEQFB) Algorithm

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 (TEQFB) Algorithm

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 Results (TEQFB) Algorithm

- 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 (TEQFB) Algorithm

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) Algorithm

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

Bit/symbol for a 2-tap TEQ (TEQFB) Algorithm

Bit/symbol for a 3-tap TEQ (TEQFB) Algorithm

CSA Loops (TEQFB) Algorithm

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 (TEQFB) Algorithm

- 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 (TEQFB) Algorithm

- 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}