decimation filtering for complex sigma delta analog to digital conversion in a low-if receiver
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Decimation Filtering For Complex Sigma Delta Analog to Digital Conversion in A Low-IF Receiver. Anjana Ghosh SERC, Indian Institute of Science Bangalore February 2006. Presentation Outline. Fundamentals of Receiver Operation Salient features of ADC - PowerPoint PPT PresentationTRANSCRIPT
Decimation Filtering For Complex Sigma Delta Analog to Digital Conversion in A
Low-IF Receiver
Anjana GhoshSERC, Indian Institute of Science
BangaloreFebruary 2006
Presentation Outline
• Fundamentals of Receiver Operation• Salient features of ADC• Decimation Filtering for Low Pass ADC• Existing literature on decimation for
bandpass modulators• Proposed architecture
Receiver Architectures: A Heterodyne Receiver
if
Frequency Downconversion
High Frequency
Filter
cosct
LNA Low Pass Filter
A/D to Demodulator
Receiver Block Diagram
c -c 0 -
image signal
High Frequency Filter
c + if
c - if
-c -if
-c + if
0 -if if
LO Signal desired signal
Low IF Receiver
LO Signal
c -c DC
-
desired signal
image signal
c + if
c - if
-c -if
-c + if
if -if DC
-
RF
Stag
e
cosct
sinct
Analog to Digital Conversion
Digital Filtering, Baseband
Downconversion , Demodulation
X
Y
A
B
Frequency Downconversion
Receiver Block Diagram
ADC Sample rate : Effect on Analog Antialias Filter (AAF)
fN/2 -fN/2
fN/2 -fN/2 fOS/2 -fOS/2
AAF in Nyquist rate ADC
AAF in Oversampled ADC
Decimation Filter
Analog AAF
ADC Quantization Noise
fN/2 -fN/2
fos/2 -fos/2
fos/2 -fos/2
Nyquist Rate Converter
Oversampled Converter
Oversampled Lowpass Converter
0
0
0
Decimation Digital Filter for ADC • Purpose of decimation filters : Antialias
filtering followed by sample rate reduction • Multistage Decimation preferred to single
stage • Popular structure consists of a Cascaded
Integrator comb followed by one or two FIR stages
CIC Filter
• Moving Average Filter
• Z transform
11
011 )()(M
iM inxny
))1()1(1()(1 1
1
1
zz
MzH
M
)1(.sin
sin)(1 11
11
11 MfTjetTMTfM
fH
Order of the CIC Filter For A Low Pass ADC
• For a modulator of order l, a CIC of order l+1 is suitable for antialias filtering in the first stage of decimation
• This CIC can be used to reduce the sample rate to as low as 4 times the Nyquist sampling rate with negligible SNR degradation (<0.25dB). Further reduction in the sample rate using the CIC will degrade the SNR significantly.
CIC Structure (Second Order)
REG REG
REG -
REG -
fs1/M1 i/p o/p
1 1-z-1
1 1-z-1
1-z-M1
1-z-M
1
1 M1
2
fs1/M1
1 1-z-1
1 1-z-1
1-z-1
1-z-1
1 M1
2
fs1/M1
1-z-M1
M1 (1-z-1)
1-z-M1
M1 (1-z-1)
fs1/M1
1 M1
2
Efficient Polyphase Decomposition of Comb Filter
kM
i
izzH
1
01
1
)(
)()()1()1(1
11
1
zz
M
M
zH
kN
i
k
i
ikM
i
i iN
zzzzH
1
0
212
0
1
0
1)(1
k
i
MM
i
zzH
12log
0
22
1
1)(
E0(z)
E1(z)
P
P
E0(z)
E1(z)
2
2 z-1 z-1
E0(z)
E1(z)
2
2 z-1
y(n) x(n)
EP-1(z) P
z-1
Modified SINC
-
M1=4 CIC
Angle Rotation of Zeros
Zeros of Rotated Sinc Filter
Noise Transfer Function(NTF) and Signal Transfer Function(STF)
fos/2 -fos/2 Bandpass 0
NTF STF
fos/2 -fos/2
Complex Bandpass 0
NTF STF
fos/2 -fos/2 Lowpass 0
NTF STF
Complex Downconversion & Decimation
e-jot
I/P Complex low pass filter
Complex O/P
fos/2 -fos/2 Signal Before Downconversion 0
fos/2 -fos/2 Signal After Downconversion 0
fos/2 -fos/2 -fIF
fIF -fIF
0 Complex Sinusoidal
Downconverter Followed by Complex LPF
signal quantization noise
e-j0
t
-2fIF
Decimation structure for Band pass & Complex modulator
cos0T = 1,1/2,0,- 1/2,-1,…..
I /P Low pass filter Real O/P
-sin0T = 0,-1/2,-1,- 1/2,0,…..
Low pass filter
o=π/4
Complex O/P
cos0T
Re Low pass filter
sin0T
Low pass filter
-sin0T
cos0T
Im
Bandpass Complex
Existing Art : Downconversion of IF signal to Baseband followed by Standard Low Pass Decimation Digital Filter
New Decimation Filter Architecture : Motivation
• Accepted approach imposes restrictions on the choice of in order to take advantage of the optimization in the mixing process
• Compatability with the existing GPS engine
New Architecture : Block DiagramR
F St
age
cosct
sinct
Anti alias Filter and Complex Bandpass
ModulatorDigital
Baseband
X
Y
Digital Decimation
Filters
A
B
Low IF Receiver : Signal Spectrum
c-c 0 -
desired signal
image signal band
c-c 0 -
1/2
c-c 0 -
j/2
-j/2
RF
C (cosct)
S (sinct)
if-if 0 -
1/2A=IP*C
if-if0 -
j/2B=IP*S
-j/2
if-if 0 -
1IF
c + ifc - if-c -if -c + if
RF
Stag
e
cosct
sinct
A
B
Use of Complex Digital Filters
c-c 0 -
desired signal
image signal band
IP
if-if 0 -
1/2A=IP*cosct
if-if 0 - j/2B=IP*Sinct
-j/2
c + ifc - if-c -if -c + if
if-if0 -
P=X+jY
X=A* Y=B*
if-if 0 -Q=X-jY Noise Transfer
Function
Noise Transfer Function DF1 Transfer
Function
DF2 Transfer Function
if-if 0 -OP 1
RF
Stag
ecosct
sinct
A Anti alias Filter and Complex Sigma Delta Modulator
OPj-j
DF1 (Complex
Digital Filter)
X
Y
P
QDF2
(Complex Digital Filter)
Complex Digital Filters : Real Filters From Complex Filters
HDF1(z) = HRE(z) - j.HIM(z) ;HDF2(z) = HRE(z) + j.HIM(z) ;OP = P(z).HDF1(z) + Q(z).HDF2(z) ;
=>OP = [X(z) +j.Y(z)].[HRE(z) - j.HIM(z)] + [X(z)-j.Y(z)].[HRE(z) + j.HIM(z)]
=> OP= 2.[X(z). HRE(z) + Y(z). HIM(z)] Thus the Complex Digital Filtering can be accomplished by using two real filters corresponding to the real and imaginary parts of the transfer function of the individual complex filters.
if-if 0 -
if-if 0 -
DF1 Transfer Function
DF2 Transfer Function
Complex Digital Filters: Implementation
Real Filter Implementation of Digital Filtering, at Low IF.
Advantage: Number of Computations reduced from eight to two
RF Amp and Filter
90o
Antialias Filter and Complex Sigma Delta Modulator
cosct
sinct
realimaginary
IP
A
B
S
C
OP
HRE(z)
X
Y
HIM(z)
Decimation Filter : Requirements
• antialias filtering and reduction of the sample rate by 16
• attenuation of remaining out of band components in the signal
• generation of a real two sided signal centered around ±wif
Multistage Decimation Filter Structure
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
ADC Output FFT
AAF1: Fourth Order Comb
Passband (3-5MHz) droop = 0.33dB
Stopband Attenuation : 83.1dB
Aliasing Bands: 59MHz to 69MHz, 123MHz to 128MHz on either side
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
AAF2: 11 Tap HalfBand
Passband (3-5MHz) Ripple = 0.0027dB/-0.0054dB
Stopband Attenuation : 75.8 dB
Aliasing Bands: 27MHz to 32MHz on either side
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
Image Reject Filter
Passband (3-5MHz) Ripple = 0.0027dB/-0.0054dB
Stopband Attenuation : 75.8 dB
Aliasing Bands: 27MHz to 32MHz on either side
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
Image Reject Filter : Stopband
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
Image Reject Filter : Ripple, Phase Response
Passband Droop = 0.94dB Phase Response
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
Droop Correction filter
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
Net Transfer Function
COMPLEX FILTER
AAF1 4
AAF2 2
REAL PART
2 4fs 2fs 16fs
16fs
fs
fs
DROOP CORRECTION
FILTER
COMPLEX ADC MIXER
O/P AAF1
4 AAF2
2 IMAGINARY
PART 2
4fs 2fs
I Q
OP
Decimation Filter StructureSi
gma
Delta
M
odul
ator
4rth order Comb 11 tap Half Band
49 tap FIR
I
13 tap Image Reject4 2 2
O/P
256 M samples/s
4rth order Comb 11 tap Half Band 13 tap Image Reject4 2 2
Q
FFT of Silicon Data For A Single Tone Input
ADC O/P
Digital Filter O/P
Optimized Architecture : ScopeSi
gma
Delta
M
odul
ator
4rth order Comb 11 tap Half Band
49 tap FIR
I
13 tap Image Reject4 2 2
O/P
256 M samples/s
4rth order Comb 11 tap Half Band 13 tap Image Reject4 2 2
Q
Low Pass Complex Band Pass
Band PassLow Pass
Scope for optimization :Complex Bandpass?
Alternate Architecture : Block Diagram
-_
OP
HRE(z)
HIM(z)
HAAFRE
HAAFIM
HAAFIM
HAAFRE
Complex Sigma Delta ADC
X
Y
Alternate Architecture I:Decimate By 16
STAGE 1
STAGE 2
STAGE 3
Hc1R
(13 taps)
Hc1I (13 taps)
Hc1I (13 taps)
Hc1R (13 taps)
X
Y
Hc2R (5 taps)
Hc2I (5 taps)
Hc2I (5 taps)
Hc2R (5 taps)
4
4 Hc3R (5 taps)
Hc3I (5 taps)
Hc3I (5 taps)
Hc3R (5 taps)
2
2
2
2
OP_Q
OP_I - - -
484443214
)1()1(1161)(
zzzzzzH
Shifted 4th Order Comb : Stage 1
•13 tap , 15 bit coefficient quantization ; performs decimation by 4
•Passband = 3MHz to 5 MHz
•Aliasing bands = 67MHz to 69MHz, -59MHz to -61 MHz, -123MHz to -125MHz
Shifted 4th Order Comb :Stage 2
•5tap , 11 bit coefficient quantization;performs decimation by 2
•Passband = 3MHz to 5 MHz
•Aliasing bands = 35MHz to 37MHz, -27MHz to -29 MHz
Shifted 4th Order Comb :Stage 3
•5 tap, 11 bit coefficient quantization; Performs decimation by 2
•Passband = 3MHz to 5 MHz
•Aliasing bands = 19MHz to 21MHz, -11MHz to -13 MHz
Image Reject Filter
•5 tap, 15 bit coefficient quantization
•Passband = 3MHz to 5 MHz
•Aliasing bands = 19MHz to 21MHz, -11MHz to -13 MHz
Optimized Architecture
AAF & Decimation
ImageReject
Complex AAF
Stage1 4
X
Y
Droop correction (48 taps)
IRR (5 taps)
IRIM (5 taps)
OP
Complex AAF
Stage2 2
Complex AAF
Stage3 2
Complex Sigma Delta ADC
Multiplier less polyphase implementation
CSD coded; multiplier less polyphase implementation
Comparison of Transfer Function : Original Architecture and Architecture I
Comparison of Transfer Function : Original Architecture and Architecture I
Comparison of Image Rejection
Comparison of Passband Ripple
STAGE 1
STAGE 2
STAGE 3
4th
order Comb
(13 taps)
4rth order Comb
(13 taps)
X
Y
Hc2R (5 taps)
Hc2I (5 taps)
Hc2I (5 taps)
Hc2R (5 taps)
4
4 Hc3R (5 taps)
Hc3I (5 taps)
Hc3I (5 taps)
Hc3R (5 taps)
2
2
2
2
OP_Q
OP_I - -
Optimized Architecture II
Low Pass COMB Shifted COMB
Decimation Filter Stages in Architecture II
Comparison of the Three Architectures
Design Parameter Original Architecture Alternate Architecture I Alternate Architecture II
Stage 1 AAFFilter TypeNumber of tapsCoefficient QuantizationData QuantizationArea
Real Filter4th order comb13Ideal101160
Complex Filter4th order shifted comb13 15 bits16 bits3409.5
Real Filter4th order comb13Ideal 10 bits971.75
Stage2 AAFFilter TypeNumber of Taps Coefficient QuantizationData QuantizationArea
Real FilterHalfband1115 bits13 bits3154.5
Complex Filter4th order shifted comb511 bits16 bits4460.75
Complex Filter4th order shifted comb511 bits15 bits3147.75
Stage 3 AAFFilter TypeNumber of Taps Coefficient QuantizationData QuantizationArea
None Complex Filter4th order shifted comb511bits15 bits4657.75
Complex Filter4th order shifted comb511 bits15 bits4437.25
Image RejectFilter TypeNumber of TapsCoefficient QuantizationData Quantization Area
Complex FilterShifted Modified Comb1315 bits14 bits11702
Complex FilterShifted Modified Comb515 bits14 bits2208.5
Complex FilterShifted Modified Comb515 bits14 bits2209.25
Total area 16037.25 14736.5 10766
Summary
• Architecture and design of decimation digital filtering of the output of a complex ∆ modulator for low IF receivers is proposed.
• Two optimized implementations with variations of the same basic architecture are proposed
Reference• REFERENCES• James C Candy and Gabor C Temes, ”Oversampling Methods for A/D and D/A Conversion”, • Eugene B Hogenauer, “An Economical Class of Digital Filters for Decimation and Interpolation”, IEEE Transactions on Acoustics,Speech And Signal Processing, Vol ASSP
29,No 2, April 1981• Brian Paul Brandt, “Oversampled Analog to Digital Conversion”, Doctoral Thesis, Stanford University, Electrical Engineering Department, Stanford, California, October 1991• Letizia Lo Presti,” Efficient Modified-Sinc Filters For Sigma Delta A/D Converters”,IEEE Transaction on Circuits and Systems-II:Analog and Digital Signal Processing,Vol 47,No
11,November 2000• Richard Schreier and W Martin Snelgrove,”Decimation For Bandpass Sigma Delta Analog to Digital Conversion”, IEEE International Symposium on Circuits and Systems,1990, 1-
3 May, Pages 1801-1804 Vol 3• Stephen Andrew Jantzi, “Quadrature Bandpass Delta Sigma Modulation for Digital Radio”, PhD Thesis, Dept of Electrical and Computer Engineering,University of Toronto• Ashok Swaminathan,”A Single-IF Receiver Architecture Using a Complex Sigma-Delta Modulator”, ME thesis, Dept of Electronics, Ottawa-Carleton Institute for Electrical
Engineering, Carleton University,Ottawa,Canada• Stephen A Jantzi, Kenneth W Martin, Adel S Sedra, “Quadrature Bandpass DS Modulation For Digital Radio”, IEEE Journal Of Solid State Circuits, Vol 32,No 12, December 1997• Asad A Abidi, “Direct Conversion Radio Transceivers For Digital Communications”, IEEE Journal Of Solid State Circuits, Vol 30,No12,December 1995• Jan Crols, Michiel S J Steyaert, ”Low-IF Topologies For High Performance Analog Front Ends of Fully Integrated Receivers”, IEEE Transactions on Circuits And Systems-II:
Analog And Digital Signal Processing, Vol 45,No3,March1998• Hong-Kui Yang, W Martin Snelgrove, “High Speed Polyphase CIC Decimation Filters”, IEEE International Symposium on Circuits and Systems, 1996• Yonghong Gao, Lihong Jia, Hannu Tenhunen, “A Partial-Polyphase VLSI Architecture For Very High Speed CIC Decimation Filters”, Twelfth Annual IEEE International ASIC/SOC
Conference, 1999• Hassan Aboushady,Yannick Dumonteix, Marie Minverte Louėrat, Habib Mehrez, “Efficient Polyphase Decomposition of Comb Decimation Filters in Analog to Digital
Converters “,IEEE Transactions on Circuits And Systems-II: Analog And Digital Signal Processing, Vol 48,No10,October 2001• Youngbeom Jang, Sejung Yang, ”NonRecursive Cascaded Integrator Comb Decimation Filters With Integer Multiple Factors”, 44th IEEE Midwest Symposium on Circuits and
Systems, Volume: 1 , 14-17 Aug. 2001• Yonghong Gao, Lihong Jia, Hannu Tenhunen, ”A Fifth Order Comb Decimation Filter For Multi-standard Transceiver Applications”, IEEE International Symposium on Circuits and
Systems, May 28-31,2000,Geneva , Switzerland• Brian A White, Mohamed I Elmasry, “Low Power Design of Decimation Filters For A Digital IF Receiver”, IEEE Transactions On Very Large Scale Integration (VLSI) Systems, Vol
8,No3, June 2000• Yonghong Gao, Lihong Jia, Hannu Tenhunen, ”An Improved Architecture and Implementation of Cascaded Integrator Comb Decimation Filters”,IEEE Pacific Rim Conference on
Communications, Computers and Signal Processing, 1999 • Farbod Behbahani,Yoji Kishigami, John Leete, Asad A Abidi,”CMOS Mixers And Polyphase Filters For Large Image Rejection”, IEEE Journal of Solid State Circuits, Vol 36. No 6,
June 2001• James F Kaiser, Richard W Hamming, “Sharpening the Response of A Symmetric Nonrecursive Filter by Multiple Use of the Same Filter”, IEEE Transactions on Acoustics,
Speech, And Signal Processing, Vol ASSP 25, No 5, October 1977• Matthias Henker, Tim Hentschel, Gerhard Fettweis, “Time Variant CIC Filters For Sample Rate Conversion With Arbitrary Rational Factors”, The 6th IEEE International
Conference on Electronics, Circuits and Systems, Volume: 1 , 5-8 Sept. 1999• Ken Martin, “ Complex Signal Processing is Not Complex”, Conference on European Solid-State Circuits, 2003, 16-18 Sept• James C Candy, “Decimation for Sigma Delta Modulation”, IEEE Transactions On Communications, Volume COM 34,No1,January 1986• Alan V Oppenheim , Ronald W Schafer, ”Discrete Time Signal Processing”, Prentice Hall Signal Processing Series• Ghosh Anjana, BG Chandrashekar , Venkatraman Srinivasan and Nandy S K, “Decimation For Complex Sigma Delta Analog to Digital Conversion In A Low-IF GPS
Receiver”,10th International Symposium On Integrated Circuits, Devices & Systems”, September 2004