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: [A first arrival detection method] Date Submitted: [July, 2005] Source: [Yihong Qi, Huan-Bang Li, Shinsuke Hara, Ryuji Kohno, Company: National Institute of Information and Communications Technology ] Contact: Yihong Qi Voice:+81 46 847 5092, E-Mail: yhqi@nict.go.jp] Abstract: [A first arrival detection method is designed to detect weak first arrival signals] Purpose: [To present a first arrival detection method ] 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. A First-arrival Detection Approach Yihong Qi Huan-Bang Li, Shinsuke Haraand Ryuji Kohno National Institute of Information and Communications Technology (NICT)

3. Outline • A system model • Delay estimation for a single-path propagation • A first arrival detection method for a multipath environment • Simulation results • Conclusion

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

5. A Delay Estimation Algorithm

6. 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?

7. 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.

8. How to use the information? Formulate a maximum likelihood estimation. However, it is complicated: • One dimension iterative searching • Nonlinear autocorrelation function • Lots of samples (N) involved

9. How to simplify? 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

10. A simple solution where

11. 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.

12. A First-arrival Detection Method

13. Why the problem is difficult? The estimation performance would be degraded considerably when the energy of the first arriving component is not dominant among multipath components of a received signal.

14. Our Approach • A similar idea to the solution of near-far problem in multiuser detection. • An iterative scheme: In each iteration, the present strongest signal component is estimated, and is removed from sample data to be processed in the next iteration.

15. A graphic illustration h(t) There are three multipath components, and the second path is strongest. i=2 h(tn) i=3 i=1 h(t2) h(t1) t1 t2 tn t

16. A graphic illustration (cont’d) h(t) In the first iteration, n=1, we estimate the time delay and amplitude the strongest multipath. h(ti1+2) h(ti1+1) Using less samples is better to avoid the interference from other multipath components. t

17. Delay and Amplitude Estimation • Delay estimation can use the previous proposed method • Using less samples • Amplitude estimation, the ML estimation based on the delay estimate, known autocorrelation function and correlation samples.

18. A graphic illustration (cont’d) h(t) The strongest multipath is removed by using the delay estimate, amplitude estimate and the autocorrelation function. Removed t

19. A graphic illustration (cont’d) h(t) Since we are only interested on first arrival delay, samples with time instants later than the delay estimated just obtained is removed. n=1 Removed t

20. Robust to interference from other strong multipath components • Low computational complexity. • let the first arrival component be the M-th strongest component, the complexity is proportional to M. Advantages

21. Simulation Results

22. Notation • The conventional method: directly select the time instant corresponding to the largest sample. • Theoretical limit: assume a continuous correlation function is used. • Over-sampling ratio = sampling frequency/effective bandwidth. • E.g., A Gaussian waveform N(0,a^2) has the effective bandwidth 1/2a, a=1ns, effective bandwidth 500MHz.

23. Example 1: sampling frequency=420M

24. Example 2: sampling frequency=625M

25. Example 3: sampling frequency=1.25G

26. Concluding Remarks • A delay estimation method for mitigating the error due to digital sampling • A first arrival detection algorithm which is robust to weak first arriving signals