Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory
-
Upload
brielle-griffin -
Category
Documents
-
view
25 -
download
0
description
Transcript of Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory
![Page 1: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/1.jpg)
1ESPL
Wordlength Optimization withComplexity-and-Distortion Measure andIts Application to Broadband Wireless
Demodulator Design
Kyungtae Han and Brian L. Evans
Embedded Signal Processing LaboratoryWireless Networking and Communications Group
The University of Texas at Austin
![Page 2: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/2.jpg)
2ESPL
Fixed-Point Design
• Digital signal processing algorithms– Often developed in floating point
– Later mapped into fixed point for digital hardware realization
• Fixed-point digital hardware– Lower area
– Lower power
– Lower per unit production cost
Idea
Floating-Point Algorithm
Quantization
Fixed-Point Algorithm
Code Generation
Target System
Algorithm
Level
Implem
entationL
evel
Range Estimation
Introduction
![Page 3: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/3.jpg)
3ESPL
Fixed-Point Design
• Float-to-fixed point conversion required to target– ASIC and fixed-point digital signal processor core
– FPGA and fixed-point microprocessor core
• All variables have to be annotated manually– Avoid overflow
– Minimize quantization effects
– Find optimum wordlength
• Manual process supported by simulation– Time-consuming
– Error prone
Introduction
![Page 4: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/4.jpg)
4ESPL
Optimum Wordlength
• Longer wordlength– May improve application
performance– Increases hardware cost
• Shorter wordlength– May increase quantization errors
and overflows– Reduces hardware cost
• Optimum wordlength– Maximize application performance
or minimize quantization error– Minimize hardware cost
Wordlength (w)
Cost c(w)Distortion d(w)[1/performance]
Optimumwordlength
Background
![Page 5: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/5.jpg)
5ESPL
Wordlength Optimization
• Express wordlengths in digital system as vector
• Wordlength range for kth wordlength
• Cost function c
),,,,( 210 nwwww w
nkwww kkk ,...,1
RI nc :
n
kkk
n wcc1
)()(, wIw
Background
![Page 6: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/6.jpg)
6ESPL
Wordlength Optimization
• Application performance function p
• Wordlength optimization problem
• Iterative update equation
• Good choice of update direction can reduce number of iterations to find optimum wordlength
reqPp )(w
},)(|)({min wwPpc reqI n
wwww
)()()1( hhh ww
Background
![Page 7: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/7.jpg)
7ESPL
Sequential Search [K. Han et al. 2001]
• Greedy search based on sensitivity information (gradient)
• Example– Minimum wordlengths {2,2}
– Direction of sequential search
– Optimum wordlengths {5,5}
– 12 iterations
• Advantage: Fewer trials• Disadvantage: Could miss global optimum point
jjj sww
1
wopt
wb
w1
w2
dw1
dw2
5
5
Search Methods
![Page 8: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/8.jpg)
8ESPL
Measures for Optimum Wordlength
• Complexity measure method [W.Sung and K.Kum 1995]
– Minimize complexity c(w) subject to constraint on distortion d(w)
– Update direction uses complexity sensitivity information• Distortion measure [K. Han et al. 2001]
– Minimize distortion d(w) subject to constraint on complexity c(w)
– Update direction uses distortion sensitivity information
?w0w1
wn
…
Complexity
w
wc
)( ?
w0w1
wn
…
Distortion
w
wd
)(
Measures
![Page 9: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/9.jpg)
9ESPL
• Combine complexity measure with distortion measure by weighting factor (0≤α≤1)
• Tradeoffs between measuresby changing weighting factor
• Update direction uses both sources of sensitivity information
Complexity-and-Distortion Measure
)()1()()( www dcf
)]()1()([ ww dc
},)(,)(|)({min wwCcDdf reqI n
wwwww
Update direction
Objective function
Optimization problem
?w0w1
wn…
α
Complexity
Distortion
Measures
![Page 10: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/10.jpg)
10ESPL
Broadband Wireless Access(IEEE 802.16a) Demodulator
w0: Input wordlength of orthogonal frequency division multiplex (OFDM) demodulator which performs a fast Fourier transform (FFT)w1: Input wordlength of equalizerw2: Input wordlength of channel estimatorw3: Output wordlength of channel estimator
EncoderOFDM
Modulator
WirelessChannelModel
OFDMDemodulator
ChannelEstimator
DecoderBit error
ratetester
DataSource
ChannelEqualizer
w0w1
w2w3
Case Study
![Page 11: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/11.jpg)
11ESPL
Simulations
• Assumptions– Internal wordlengths of blocks have bee
n decided
– Complexity increases linearly as wordlength increases
• Required application performance– Bit error rate of 1.5 x 10-3 (without error
correcting codes)
• Simulation tool– LabVIEW 7.0
Case Study
Input Weight
FFT 1024
Equalizer
(right)
1
Estimator 128
Equalizer (upper)
2
![Page 12: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/12.jpg)
12ESPL
Minimum Wordlengths
• Change one wordlength variable while keeping other variables at high precision{1,16,16,16},{2,16,16,16},...{16,1,16,16},{16,2,16,16},...……{16,16,16,15},{16,16,16,16}
• Minimum wordlength vector is {5,4,4,4}
Case Study
![Page 13: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/13.jpg)
13ESPL
Number of Trials
• Start at {5,4,4,4} wordlength• Next wordlength combinatio
n for complexity measure (α = 1.0)
{5,4,4,4},
{5,5,4,4}, …
• Increase wordlength one-by-one until satisfying required application performance
Case Study
![Page 14: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/14.jpg)
14ESPL
Complexity and Number of Iterations
• Each iteration computes complexity & distortion measures
• Distortion measure: high cost, low iterations
• Complexity-distortion: medium cost, fewer iterations
• Complexity measure: low cost, more iterations• Full search: low cost, more iterations
Method α w Complexity Iterations
Distortion Only
Complexity-Distortion
Complexity Only
Full Search
0
0.5
1
n/a
{10,9,4,10}
{7,10,4,6}
{7,7,4,6}
{7,7,4,6}
10781
7702
7699
7699
16
15
69
210
Case Study
![Page 15: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/15.jpg)
15ESPL
Conclusion
• Summary– Fixed-point conversion requires wordlength optimization
– Develop complexity-and-distortion measure
– Complexity-and-distortion method finds optimal solution in one-third the time that full search takes for case study
• Future extensions for wordlength optimization– Automate selection of wordlength range
– Combine simulation-based and analytical approaches
– Employ genetic algorithms
![Page 16: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/16.jpg)
16ESPL
Fixed-Point Representation
• Fixed point type– Wordlength
– Integer wordlength
• Quantization modes– Round
– Truncation
• Overflow modes– Saturation
– Saturation to zero
– Wrap-around
S X X X X X
Wordlength
Integer wordlength
SystemC formatwww.systemc.org
Introduction
X X X X X
Wordlength
Integer wordlength = 2Back
![Page 17: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/17.jpg)
17ESPL
Full Search [W. Sung and K. Kum 1995]
• Exhaustive search of all possible wordlengths
• Advantages– Does not miss optimum points – Simple algorithm
• Disadvantage– Many trials (=experiments)
• Distance• Expected number of iterations
wb
wopt
w1
w2
dw1
dw2
21
24
22
23
5
5
Direction of full search:minimum wordlengths {2,2}
optimum wordlengths = {5,5}d = 6
trials = 24!
)1)(2)...(1()(
N
dddNddE N
FS
Ndwdwdwd ...21
Search Methods
Back
![Page 18: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/18.jpg)
18ESPL
FFT Cost
1024
256log2
256Cost 2FFT
• N Tap FFT cost
• 256 Tap FFT cost
NN
2FFT log2
Cost
Back
![Page 19: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/19.jpg)
19ESPL
• Uses complexity sensitivity information as direction to search for optimum wordlength
• Advantage: minimizes complexity• Disadvantage: demands large number of iterations
Complexity Measure [W.Sung and K.Kum 1995]
)()( ww cf
)(wc
},)(|)({min max wwDdfnI
wwww
Update direction
Objective function
Optimization problem
Measures
Back
![Page 20: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/20.jpg)
20ESPL
• Applies the application performance information to search for the optimum wordlengths
• Advantage: Fewer number of iterations• Disadvantage: Not guaranteed to yield optimum
wordlength for complexity
Distortion Measure [K. Han et al. 2001]
)()( ww df
)(wd
},)(,)(|)({min maxmax wwCcDdfnI
wwwww
Update direction
Objective function
Optimization problem
Measures
Back
![Page 21: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/21.jpg)
21ESPL
Broadband Wireless Access Demodulator Simulation
Case Study
![Page 22: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/22.jpg)
22ESPL
Top-Level Simulation
Case Study
Back
![Page 23: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/23.jpg)
23ESPL
Tools for Fixed-Point Simulation
• gFix (Seoul National University) – Using C++, operator overloading
• Simulink (Mathworks)– Fixed-point block set 4.0
• SPW (Cadence)– Hardware design system
• CoCentric (Synopsys)– Fixed-point designer
gFix a(12,1);gFix b(12,1);gFix c(13,2);c = a + b;
float a;float b;float c;c = a + b;
Introduction
Wordlengths determined manuallyWordlength optimization tool needed
![Page 24: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/24.jpg)
24ESPL
Wordlength Optimization Methods
• Analytical approach– Quantization error model
– Overestimates signal wordlength
– For feedback systems, instability and limit cycles can occur
– Difficult to develop analytical quantization error model of adaptive or non-linear systems
• Simulation-based approach– Wordlengths chosen while observing error criteria
– Repeated until wordlengths converge
– Long simulation time
Background
![Page 25: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/25.jpg)
25ESPL
Optimum Wordlength Search Methods
• Full search [W. Sung and K. Kum 1995]
• Min + b bit search [W. Sung and K. Kum 1995]
• Max – b bit search [M. Cantin et al. 2002]
• Hybrid search [M. Cantin et al. 2002]
• Sequential search [K. Han et al. 2001]
• Preplanned search [K. Han et al. 2001]
• Branch and bound search [H. Choi and W.P.Burleson 1994]
• Simulated annealing search [P.D. Fiore and L. Lee 1999]
Search Methods
![Page 26: Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory](https://reader030.fdocuments.us/reader030/viewer/2022032606/56812e8f550346895d94322e/html5/thumbnails/26.jpg)
26ESPL
Procedure
1. Range estimation– Find maximum and minimum values for each
2. Find minimum wordlengths– Defines starting wordlength values to use
3. Iterative search– Increase/decrease wordlengths one-by-one until meeting
specification using one of the measures
Case Study