dmt bit rate maximization with optimal time domain equalizer filter bank architecture
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
DMT Bit Rate Maximization DMT Bit Rate Maximization With Optimal Time Domain EqualizerWith Optimal Time Domain Equalizer
Filter Bank ArchitectureFilter 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
36th Asilomar IEEE Conference on Signals, Systems and Computers
Nov 3-6, 2002, Pacific Grove, CA
2MPEB Asilomar’02
P/S QAMdecoder
invert channel
=frequency
domainequalizer
Ser
ial-t
o-P
aral
lel (
S\P
)
QAMencoder
mirrordataand
N-IFFT
add Cyclic Prefix(
CP)
Digital-to-Analog
Converter +transmit
filter
N-FFTand
removemirrored
data
S/Premove
CP
TRANSMITTER
RECEIVER
N/2 subchannels N samples
N samplesN/2 subchannels
TEQtime
domain equalizer
receive filter
+Analog-to-
Digital Converter
channel
Basic Architecture: DMT Transceiver Basic Architecture: DMT Transceiver
Bits
00101
Par
alle
l-to-
Ser
ial (
P\S
)
noise
3MPEB Asilomar’02
DMT SymbolDMT Symbol
CP: Cyclic Prefix
N samplesv samples
CP CPs y m b o l ( i ) s y m b o l ( i+1)
copy copy
D/A + transmit filter
ADSL downstream upstream
CP 32 4 N 512 64
Inverse FFT
4MPEB Asilomar’02
ISI and ICI in DMTISI 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
5MPEB Asilomar’02
Channel Impairments and TEQ DesignChannel 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)
6MPEB Asilomar’02
Proposed TEQ Design MethodProposed 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
7MPEB Asilomar’02
Model SNR at Output of DemodulatorModel 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 – H is channel convolution matrix
– qk is 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
wGGGGHUqY echofextnextawgnisiHR kk
HwUqY circHDkk
isiU
circU
8MPEB Asilomar’02
Model SNR at Output of DemodulatorModel SNR at Output of Demodulator
• Proposed SNR model at the demodulator output
• After some algebra, we can rewrite the SNR model as
digDRHDR
DHDModel
)]()E[(
])E[()(SNR
kkkk
kkk YYYY
YYw
wBw
wAww
T
T
k
kk ~
~SNR Model
dig – Digital noise floor (depends on number of bits in DSP)
(*)H – Hermitian (conjugate transpose)
9MPEB Asilomar’02
• 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:
Model SNR at Output of DemodulatorModel SNR at Output of Demodulator
k k
k
k
kbwBw
wAwww
T
T
2
Model
2int log
SNR1log
DMT
*
ww
intoptint
DMTDMTmax bb
10MPEB Asilomar’02
• 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
Data Rate Optimal Time Domain Per-tone TEQ Filter Data Rate Optimal Time Domain Per-tone TEQ Filter Bank (TEQFB) AlgorithmBank (TEQFB) Algorithm
kkk
kkk
kkk
kkkk
kk wBw
wAw
wBw
wAww
wwT
T
T
T
2opt maxarglogmaxarg
kkkkkkkkk for λλfor λ satisfies optoptoptoptopt wBwAw
Ik kkk
kkkboptTopt
optTopt
2
optint logDMT
wBw
wAw
11MPEB Asilomar’02
Frequency Domain
Equalizer
Goertzel Filter Block
TEQ Filter Bank
TEQ Filter Bank ArchitectureTEQ Filter Bank Architecture
w1
w2
wN/2-1
G1
G2
GN/2-1
Received Signal x={x1,
…xN)
FEQ1
FEQ2
FEQN/2-1
y1
y2
yN/2-1
Y1
Y2
YN/2-1
12MPEB Asilomar’02
TEQFB Computational ComplexityTEQFB Computational Complexity
• Creating matrices Ak
and Bk ~ NO(M2N)
• Up to N/2 solutions of symmetric-definite problems– Using Rayleigh
quotient iteration
Single TEQ Real MACs Words/Sym
TEQ Mfs 2M
FFT 2Nlog2Nfsym 4N
FEQ 2Nfsym 2N
TEQFB Real MACs Words/Sym
TEQ FB N/2Mfs M(1+N/2)
Goertzel FB N(fs+fsym) 4N
FEQ 2Nfsym 2N
PTE Real MACs Words/Sym
FFT 2Nlog2Nfsym 4N+2Combiner 2NMfsym (M+1)N
MM
Miter
NR 412
322
3
N= 512, =32, M 2, fs= 2.204 MHz, fsym=4 kHz
Initialization Data Transmission
13MPEB Asilomar’02
• 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 DesignData Rate Maximization Single TEQ Design
k
kbw
wModel
2int
SNR1log
DMT
k
kbw
wModel
2
SNR1log
14MPEB Asilomar’02
• 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
Data Rate Maximization Single TEQ DesignData Rate Maximization Single TEQ Design
15MPEB Asilomar’02
• Measurement of the SNR in subchannel k– S = 1000 symbols
– Every subchannel in a symbol loaded with a random 2-bit constellation point Xk
i, passed through the channel, TEQ block and FEQ block (where applicable) to obtain Yk
i
• Bit rate reported is then
Simulation ResultsSimulation Results
1
0
21
2log10SNR S
i
ik
ik
k
YXS
256
72
SNR1log
k
kb
16MPEB Asilomar’02
Effect of TEQ Size on Bit RateEffect of TEQ Size on Bit Rate
Data rates achieved for different number of TEQ taps, MN = 512, = 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
17MPEB Asilomar’02
Effect of Transmission Delay on Bit RateEffect of Transmission Delay on Bit Rate
Data rates achieved as a function of for CSA loop 1.N = 512, = 32, input power = 23.93 dBm, AWGN power = -140 dBm/Hz,
and NEXT modeled as 49 disturbers. Accuracy of bit rate: 60 kbps.
18MPEB Asilomar’02
• 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
Simulation ResultsSimulation Results
%100*),,(
),,(
31
1),(
32
2TEQFB
TEQFB
opt
opt
M
Alg
MCSAb
MCSAbAlgCSARowAvg
8
1
),(8
1)(
CSA
AlgCSARowAvgAlgAvg
19MPEB Asilomar’02
TEQ Design Methods - ComparisonTEQ Design Methods - Comparison
CSA loop
LS PTENew TEQ
Min-ISI MBR MSSNRMMSE-
UECMMSE-
UTC
1 99.5% 99.6% 97.5% 97.3% 95.0% 86.3% 84.4%
2 99.5% 99.6% 97.3% 97.0% 96.5% 87.2% 85.8%
3 99.6% 99.5% 97.3% 97.8% 97.0% 83.9% 83.0%
4 99.1% 99.3% 98.2% 98.1% 95.4% 81.9% 81.5%
5 99.5% 99.6% 97.2% 97.7% 97.1% 88.6% 88.9%
6 99.4% 99.5% 98.3% 97.7% 96.4% 82.7% 79.8%
7 99.6% 98.8% 96.3% 96.3% 96.7% 75.75% 78.4%
8 99.2% 98.7% 97.5% 97.4% 97.5% 82.6% 83.6%
Avg. 99.4% 99.3% 97.5% 97.4% 96.4% 83.6% 83.2%
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
20MPEB Asilomar’02
TEQFB Data RatesTEQFB Data Rates
Highest data rates in Mbps achieved by TEQFB for TEQ lengths 2-32, input power = 23.93 dBm
CSA loop TEQFB
1 11.417 Mbps
2 12.680 Mbps
3 10.995 Mbps
4 11.288 Mbps
5 11.470 Mbps
6 10.861 Mbps
7 10.752 Mbps
8 9.615 Mbps
Backup SlidesBackup Slides
Milos Milosevic
Lucio F. C. Pessoa
Brian L. Evans
Ross Baldick
22MPEB Asilomar’02
Bit/symbol for a 2-tap TEQBit/symbol for a 2-tap TEQ
23MPEB Asilomar’02
Bit/symbol for a 3-tap TEQBit/symbol for a 3-tap TEQ
24MPEB Asilomar’02
CSA LoopsCSA 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”.
25MPEB Asilomar’02
Selected Previous TEQ Design MethodsSelected 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]
26MPEB Asilomar’02
• 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}
Goertzel FiltersGoertzel Filters
N
kNGj
N
kNGNGY
nGnGN
knynG
kkkk
kkkk
2sin1
2cos1
212
cos2