Decimation Filtering For Complex Sigma Delta Analog to Digital Conversion in A Low-IF Receiver

1. 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

2. 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

3. Receiver Architectures: A Heterodyne Receiver if

4. Low IF Receiver Frequency Downconversion Digital Filtering, Baseband Downconversion , Demodulation A cosct X RF Stage Analog to Digital Conversion B sinct Y Receiver Block Diagram

5. ADC Sample rate : Effect on Analog Antialias Filter (AAF)

6. ADC Quantization Noise

7. 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

8. CIC Filter • Moving Average Filter • Z transform

9. 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.

10. CIC Structure (Second Order)

11. Efficient Polyphase Decomposition of Comb Filter

12. Modified SINC

13. Noise Transfer Function(NTF) and Signal Transfer Function(STF)

14. Complex Downconversion & Decimation

15. Decimation structure for Band pass & Complex S D modulator Bandpass S D Complex S D Existing Art : Downconversion of IF signal to Baseband followed by Standard Low Pass Decimation Digital Filter

16. 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

17. New Architecture : Block Diagram A X cosct Anti alias Filter and Complex Bandpass Modulator Digital Decimation Filters RF Stage Digital Baseband sinct B Y

18. Low IF Receiver : Signal Spectrum A cosct RF Stage sinct B desired signal image signal band RF  - c - if c + if c -c -if -c -c + if 0 1/2 C (cosct) -  c -c 0 j/2 S (sinct) c  - -c 0 -j/2 1/2 A=IP*C  - if -if 0 j/2 B=IP*S  - if 0 -if -j/2 1 IF  - if -if 0

19. Use of Complex Digital Filters A X Anti alias Filter and Complex Sigma Delta Modulator P DF1 (Complex Digital Filter) cosct RF Stage j OP sinct -j Y DF2 (Complex Digital Filter) Q desired signal image signal band IP -  c -c -if -c c - if -c + if c + if 0 1/2 A=IP*cosct -  if -if 0 B=IP*Sinct j/2 -  if -if 0 -j/2 Noise Transfer Function DF1 Transfer Function X=A* Y=B* P=X+jY  - 0 if -if DF2 Transfer Function Noise Transfer Function Q=X-jY  - if -if 0 OP 1  - if -if 0

20. Complex Digital Filters : Real Filters From Complex Filters DF1 Transfer Function • 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)] -  if -if 0 DF2 Transfer Function  - if -if 0 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.

21. Complex Digital Filters: Implementation A HRE(z) cosct C Antialias Filter and Complex Sigma Delta Modulator X RF Amp and Filter real IP OP imaginary 90o Y sinct S B HIM(z) Real Filter Implementation of Digital Filtering, at Low IF. Advantage: Number of Computations reduced from eight to two

22. 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

23. Multistage Decimation Filter Structure

24. ADC Output FFT

25. 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

26. 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

27. Image Reject Filter Passband (3-5MHz) Ripple = 0.0027dB/-0.0054dB Stopband Attenuation : 75.8 dB Aliasing Bands: 27MHz to 32MHz on either side

28. Image Reject Filter : Stopband

29. Image Reject Filter : Ripple, Phase Response Passband Droop = 0.94dB Phase Response

30. Droop Correction filter

31. Net Transfer Function

32. 256 M samples/s 11 tap Half Band 13 tap Image Reject 4rth order Comb 2 4 2 Sigma Delta Modulator I 49 tap FIR O/P 11 tap Half Band 13 tap Image Reject 4rth order Comb Q 4 2 2 Decimation Filter Structure

33. FFT of Silicon Data For A Single Tone Input

34. 256 M samples/s 11 tap Half Band 13 tap Image Reject 4rth order Comb 2 4 2 Sigma Delta Modulator I 49 tap FIR O/P 11 tap Half Band 13 tap Image Reject 4rth order Comb Q 4 2 2 Optimized Architecture : Scope Low Pass Low Pass Complex Band Pass Band Pass Scope for optimization :Complex Bandpass?

35. Alternate Architecture : Block Diagram

36. Alternate Architecture I:Decimate By 16

37. 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

38. 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

39. 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

40. Image Reject Filter • 5 tap, 15 bit coefficient quantization • Passband = 3MHz to 5 MHz • Aliasing bands = 19MHz to 21MHz, -11MHz to -13 MHz

41. Optimized Architecture Multiplier less polyphase implementation CSD coded; multiplier less polyphase implementation

42. Comparison of Transfer Function : Original Architecture and Architecture I

43. Comparison of Transfer Function : Original Architecture and Architecture I Comparison of Image Rejection Comparison of Passband Ripple

44. Optimized Architecture II Shifted COMB Low Pass COMB

45. Decimation Filter Stages in Architecture II

46. Comparison of the Three Architectures

47. 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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