Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs)

1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title: [Three ranging-related schemes] Date Submitted: [September, 2005] Source: [Yihong Qi, Huan-Bang Li, Masataka Umeda, Shinsuke Hara andRyuji Kohno, Company: National Institute of Information and Communications Technology ] Contact: Yihong Qi Voice:+81 46 847 5092, E-Mail: yhqi@nict.go.jp] Abstract: [Three ranging-related schemes are presented: 1. for the problem that the first arriving signals are often weak and NLOS, positioning using mulitpath delays will improve the accuracy. 2. a reduced dimensional approach is proposed for the bad GDOP problem. 3. a coherent delay estimation scheme is devised which works well with low sampling rate and feasible ADC implementation.] Purpose: [to discuss three ranging-related schemes ] Notice: This document has been prepared to assist the IEEE P802.15. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15.

2. Outline • Positioning using multipath delays (cf. first arrival detection) • Positioning in an ill-conditioned geometry (bad GDOP (geometric dilution of precision)) • A coherent delay estimation scheme with low sampling rate • Conclusions

3. Two Positioning Schemes

4. Current/conventional schemes • Ranging: first arrival detection • Positioning: based on multiple range estimates • triangulation • weighted least square (LS) methods

5. What are problems with the current schemes? Positioning accuracy will be degraded due to • Weak first arriving signals, e.g., 6dB lower than the strongest path. • NLOS first arriving signals • Bad GDOP (geometric dilution of precision)

6. Positioning using multipath delays

7. Motivation The second and later arriving signals also carry information on the position of interest. • cf. weak and/or NLOS first arriving signals  Positioning using both • Multipath delays • Their statistic information (e.g., mean, variance)

8. Two numerical examples based on analytical results For illustration purpose, some simplifying assumptions on multipath delays: • Exponential or equal gain models • The minimum delay resolution being the inverse of chip duration • Gaussian NLOS delay variables

9. Exponential gain with -6dB Exponential gain with -3dB Equal gain Numerical example 1 Positioning accuracy vs. num of multipath Observation: use of more strong multipaths can improve the positioning accuracy

10. Numerical example 2 Three types of system channels • For a fair comparison: • Using • fixed total energy; • relative accuracy improvement, compared with the conventional method using only the first arrivals 1 2 3

11. Numerical example 2 (cont’d) relative accuracy improvement vs. standard deviation of NLOS delays 100MHz Observation: using more multipaths is especially effective for accuracy improvement in wideband systems 5MHz 1MHz

12. A reduced-dimensional method for bad GDOP (geometric dilution of precision) cases

13. What is the bad GDOP? Good GDOP case: nodes are distributed evenly The error is small. The error is large. Mobile node Mobile node a2 a1 a3 a1 a2 a3 Bad GDOP case: all nodes are lined up

14. What is the problem? Two dimensional positioning estimation (x,y)vs. an essentially one-dimensional problem (y axis only) m a3 a1 a2 Bad dim: x Good dim: y

15. A reduced dimension approach • Find the good dim(s) • Perform a regular positioning in the good dimension • Estimate the coordinate in the bad dim(s) separately

16. A simulation result for 2-D bad GDOP Positioning accuracy vs. standard deviation of ranging errors Conventional method Reduced dimensional method Theoretical limit

17. Flashback • Positioning using multipath delays • For the problem of weak and/or NLOS first arriving signals • Con: increased computation complexity • A reduced-dimensional approach for positioning • For bad GDOP geometry

18. Coherent delay estimation with low sampling rate and feasible ADCimplementation

19. A basic system model Delay estimation/ First-arrival detection A delay estimate Correlator A/D A transmit signal

20. Two ways of implementing ADC easy to implement Difficult to implement code-correlator ADC LPF Matched to Gaussian pulse Spreading code BPF output code-correlator ADC LPF LO π/2

21. What is the problem? h(tn) h(tm+1) correlation function h(tm+Z-1) h(tm) tm+1 tm+2 tm+Z tn Given samples of a correlation function, how to estimate the time instant corresponding to the peak?

22. autocorrelation correlation tm+1 tm+2 tm+Z tn What is information we know? correlation function correlation = autocorrelation of s(t) +noise The expression is known. Statistics is known.

23. A natural way to use all information Formulate maximum likelihood estimation (ML). However, it is complicated: • One dimension iterative searching • Nonlinear autocorrelation function involved • Lots of samples (N) involved

24. Our approach: simplified MLE Intuition: samples near the peak are more important. h(tn) h(tm+1) h(tm+Z-1) h(tm) •  • Use less samples • Taylor expansion of autocorrelation function around the peak tm+1 tm+2 tm+Z tn

25. A simple solution where

26. A simple solution • An algebraic solution, no iterative search • Less than 4 samples in general • No nonlinear function any more • Independent of noise level • Optimal in the sense that the estimate is approaching to the theoretical lower limit as over-sampling is sufficiently large.

27. Simulation parameters • PRF=30.875MHz • Sampling rate fs (ADC)=494MHz (=16xPRF) • Ternary sequence with length of 31 • Gaussian Pulse with bandwidth 500MHz • AWGN Channel Conventional method: Pick up the largest sample Interpolation method: Not include the autocorrelation info.

28. Simulation result 1 ADC before Code Correlator Conventional method RMS Estimation Error [nsec] Interpolation Simplified ML ADC after Code Correlator Eb/N0 [dB]

29. Simulation result 2 Eb/N0=-3dB Conventional method Interpolation Simplified ML

30. Advantages • Working well at low sampling rate (less than signal bandwidth) • Feasible ADC implementation • Low computation complexity • Same level of complexity compared with conventional schemes • Independent of noise level Ongoing work: incorporating decay patterns for multipath scenarios

31. Conclusions • Positioning using multipath delays • A reduced dimensional approach for positioning in bad GDOP • A coherent delay estimation scheme with low sampling rate and feasible ADC implemetation