decimation filtering for complex sigma delta analog to digital conversion in a low-if receiver

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

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