: Sub-Nyquist Sampling for TDR Sensors:

Size: px

Start display at page:

Download ": Sub-Nyquist Sampling for TDR Sensors:"

Marilyn Johnson
6 years ago
Views:

1 : Sub-Nyquist Sampling for TDR Sensors: Finite Rate of Innovation with Dithering Marc Ihle, Hochschule Karlsruhe, Germany

2 Who We are Bashar Ahmad Thomas Weber Marc Ihle : Marc Ihle ( ) 2

3 Presentation Outline : Introduction TDR Sensor : Problem Formulation : FRI and the Proposed Approach : Description of the System : Simulations : Conclusion : Marc Ihle ( ) 3

4 Time Domain Reflectometry Sensor (Guided Wave Radar Level Sensor) Aim: to measure liquid level in an industrial container by measuring ToF. Reflection coefficient: R = Z 1! Z 0 Z 1 + Z 0 a The processed signal (K pulses): K!1 x(t) = " a i p(t! t i ) i=0 a i : amplitude of the reflected pulse. t i : location of the reflected pulse. b c Gaussian pulses are typically used with given σ values. : Marc Ihle ( ) 4

TDR: An Example Sensing requirements: Requirement Measuring Range Inaccuracy Resolution Response Time Value 5 cm... 10 m < 5mm < 0.

5 TDR: An Example Sensing requirements: Requirement Measuring Range Inaccuracy Resolution Response Time Value 5 cm m < 5mm < 0.5 mm < 100 ms TDR-Level Sensor LFP Cubic; SICK AG è Maximum tolerated relative ToF measurement error is: s terror = = 33 ps c : Marc Ihle ( ) 5

6 Problem Formulation and Proposed Approach Classical Nyquist sampling demands collecting several Giga samples per second. Infeasible due to practical SWPaC limitations of miniature TDR sensors Alternative sub-nyquist techniques: t [ns] Equivalent Time Sampling: Bulky sensitive circuits (PLL) and long signal acquisition times. Compressed Sensing: Infinite time resolution and high SWPaC implementation. Finite Rate of Innovation: Can be easily integrated into existing TDR sensor architecture. FRI is an effective solution to the data acquisition problem in TDR sensors. FRI Limitation: Very sensitive to quantisation noise and high resolution ADCs cannot be used, e.g. due to TDR sensor practical limitations. Proposed Approach: FRI with dithering and averaging to combat quantisation noise. : Marc Ihle ( ) 6

7 System Description: Proposed Approach Implementation using FRI with Dithering and Averaging : Ensemble averaging of consecutive sequences shall improve the ADC resolution. : Averaging may lead to a slightly increased response time. : Marc Ihle ( ) 7

8 Description of the System Signals along the path : Marc Ihle ( ) 8

9 Description of the System Signals along the path t [ns] : Marc Ihle ( ) 9

10 Description of the System Signals along the path : Marc Ihle ( ) 10

11 Description of the System Signals along the path : Marc Ihle ( ) 11

12 Description of the System Signals along the path y(t) Output Sampling kernel Sampling points t [ns] : Marc Ihle ( ) 12

13 Description of the System Signals along the path Original signal without noise and estimated pulse positions Estimated pulse positions with Cadzow algorithm t [ns] : Marc Ihle ( ) 13

Data Acquisition Device ADC selection : Resolutions > 8bit are expensive for f s < 1ns. equivalent when using averaging thermal limitation -0.5bit/oct. aperture limitation: -1.0bit / oct.

14 Data Acquisition Device ADC selection : Resolutions > 8bit are expensive for f s < 1ns. equivalent when using averaging thermal limitation -0.5bit/oct. aperture limitation: -1.0bit / oct. Heisenberg limit : High-speed ADCs are mainly limited by the aperture jitter. : Averaging adjacent samples is not efficient; ensemble averaging however is. -0.5bit/oct. Graph taken from: Sigma-Delta Modulators: Tutorial Overview, Design Guide, and State-of-the-Art Survey ; IEEE Trans. on Circuits and Systems, Vol. 58, No. 1, Jan Limitations according: R. H. Walden: ADC Survey and Analysis, IEEE Journal on Selected Areas in Communications, Vol. 17, No. 4, April 1999 : Marc Ihle ( ) 14

15 Monte Carlo Simulations Set Up Signal Model: : K = 5 Gaussian Pulses with σ = 200 ps, each. : Period of the pulse sequence is 50 ns. : Two dynamic ranges are examined: 0 db and 26 db. Pulse sequence with 0 db dynamic range: FRI: : Sum of Sincs (SoS) sampling kernel is used. : Cadzow plus total least squares are applied. : FRI minimum sampling rate is 220 MHz. Dithering: : Uniform distributed dither is used. : Maximum dithering amplitude is ±Q/2. Pulse sequence with 26 db dynamic range: t [ns] Assessment: : Maximum error and RMS error are used to assess the results accuracy. : In practise the maximum error is more important. : Marc Ihle ( ) 15

16 Simulations Effect of ADC Resolution (0 db dynamic range) random guess Max. Error without dithering RMSE Error without dithering Max. Error with dithering RMSE Error with dithering : Errors of more than 10 ns correspond to random guesses. t (ps) 10 3 : ADC resolution of at least 10 bits is needed Simulation parameters: sampling rate: f s = 440 MHz oversampling: β = 2 averaging: 250 times ADC Resolution in Bit : Marc Ihle ( ) 16

17 Simulations Effect of ADC Resolution t [ns] (26 db dynamic range) : 26 db dynamic range causes the RMSE time resolution to decrease by a factor of 2 to 3. : random guesses occur with ADC resolutions of up to 10 bits. : maximum error notably increases by 5.5. t (ps) random guess Max. Error without dithering RMSE Error without dithering Max. Error with dithering RMSE Error with dithering 5.5 Simulation parameters: sampling rate: f s = 440 MHz oversampling: β = 2 averaging: 250 times ADC Resolution in Bit 2.0 : Marc Ihle ( ) 17

18 Simulations Effect of Averaging t [ns] : Averaging 125 estimates enhances the RMSE time resolution by factor of 200. : A further increase of the number of averages to 2000 enhances the RMSE time resolution again by at least a factor of 2. Simulation parameters: sampling rate: f s = 440 MHz dynamic range: 26 db ADC resolution: 6 bits t (ps) random guess 3.0 Max. error: Dithering, no averaging Max. error: Dithering, 125 averages Max. error: Dithering, 250 averages Max. error: Dithering, 2000 averages RMS error: Dithering, no averaging RMS error: Dithering, 125 averages RMS error: Dithering, 250 averages RMS error: Dithering, 2000 averages / Oversampling factor 2.0 : Marc Ihle ( ) 18

19 Simulations Effect of Oversampling t [ns] : Oversampling by a factor of 4 enhances the RMSE time resolution by factor of random guess Max. error: Dithering, no averaging Max. error: Dithering, 125 averages Max. error: Dithering, 250 averages Max. error: Dithering, 2000 averages RMS error: Dithering, no averaging RMS error: Dithering, 125 averages RMS error: Dithering, 250 averages RMS error: Dithering, 2000 averages : An oversampling factor exceeding 12 gives a further improvement by a factor of 4. t (ps) Factor 4 Simulation parameters: sampling rate: f s = 440 MHz dynamic range: 26 db ADC resolution: 6 bits Oversampling factor : Marc Ihle ( ) 19

20 Conclusion and Outlook Conclusions: : TDR using FRI is a promising method in respect to efficient hardware implementation. : However: TDR using FRI is very sensitive to quantisation noise. : Dithering and Averaging leads to significant performance improvements. : Improvements are not yet sufficient for highly demanding TDR requirements (<33 ps error). Outlook: : Further reduction of the ToF estimation error is needed. : Evaluation of the minimum ToF estimation error bound (Cramer-Rao bound) pending. : Marc Ihle ( ) 20

21 Thank you for your attention.

Data Conversion Techniques (DAT115)

Data Conversion Techniques (DAT115) Hand in Report Second Order Sigma Delta Modulator with Interleaving Scheme Group 14N Remzi Yagiz Mungan, Christoffer Holmström [ 1 20 ] Contents 1. Task Description...