Submission Title: [Three ranging-related schemes] 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 and 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: [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. TG4a

Three Ranging-related Schemes Yihong Qi, Huan-bang Li, Masataka Umeda, Shinsuke Hara and Ryuji Kohno NICT, JAPAN TG4a

Outline Positioning using multipath delays (cf. the current first arrival detection) Positioning in an ill-conditioned geometry (the bad GDOP problem) A coherent delay estimation scheme with low sampling rate Conclusions TG4a

Two Positioning Schemes TG4a

Current/conventional schemes Ranging: first arrival detection with LOS (line-of-sight) assumption Positioning: based on multiple ranging estimates triangulation weighted least square (LS) methods TG4a

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) TG4a

Positioning using multipath delays TG4a

Motivation An NLOS delay estimate: dtotal = d0 (real distance) + lnlos (NLOS induced path length error) + n (estimation error) The second and later arriving signals also carry information on the distance of interest. An NLOS delay estimate TG4a

Analytical results Positioning accuracy is improved by using Multipath delay estimates It is sufficient to adopt those strong multipaths. Statistic information of lnlos (e.g., mean, variance) No accuracy improvement without incorporating the statistic information. E.g., the maximum a priori (MAP) estimator TG4a

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 the chip duration The NLOS induced path length error being independent Gaussian variables TG4a

Numerical example 1 Positioning error vs. num of multipath Equal gain Exponential gain with -6dB Exponential gain with -3dB Observation: use of more strong multipaths can improve the positioning accuracy TG4a

Numerical example 2 1 2 3 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 2 3 TG4a

Numerical example 2 (cont’d) relative accuracy improvement vs. standard deviation of NLOS induced error 100MHz Observation: using more multipaths is especially effective for accuracy improvement in wideband systems 5MHz 1MHz TG4a

Flashback Positioning using multipath delays Sufficient to use the strong multipath Good for wideband systems Tradeoff: accuracy improvement computation complexity TG4a

A reduced-dimensional method for the bad GDOP problem TG4a

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 Good GDOP case: nodes are distributed evenly Bad GDOP case: all nodes are lined up TG4a

What is the core 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 TG4a

A reduced dimension approach Find the good dim(s) Perform a regular positioning in the good dimension Estimate the coordinate(s) in the bad dim(s) separately TG4a

A simulation result for 2-D bad GDOP Positioning error vs. standard deviation of ranging errors Conventional method Reduced dimensional method Theoretical limit TG4a

Flashback Positioning using multipath delays For the problem of weak and/or NLOS first arriving signals Con: increased computation complexity A reduced-dimensional approach to the bad GDOP positioning TG4a

Coherent delay estimation with low sampling rate and feasible ADC implementation TG4a

A Review of 406r0 Two issues Main part: Delay estimation with mitigation of sampling induced errors Extension: a first arrival detection scheme based on the sequential cancellation principle TG4a

First-arrival detection A basic system model Delay estimation/ First-arrival detection Correlator A/D A delay estimate A transmit signal TG4a

Two ways of implementing ADC easy to implement Difficult to implement code- correlator LPF ADC Matched to Gaussian pulse BPF Spreading code output code- correlator LPF ADC LO π/2 TG4a

What is the problem? h(tn) correlation function h(tm+1) 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? TG4a

What is information we know? correlation function tm+1 tn tm+2 tm+Z correlation autocorrelation correlation = autocorrelation of s(t) +noise The expression is known. Statistics is known. TG4a

A natural way to organize all information Formulate maximum likelihood estimation (ML). However, it is complicated: One dimension iterative searching Nonlinear autocorrelation function involved Lots of samples (N) involved TG4a

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 TG4a

A simple solution where TG4a

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. TG4a

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. TG4a

Simulation result 1 ADC before Code Correlator Conventional method RMS Estimation Error [nsec] Interpolation Simplified ML ADC after Code Correlator Eb/N0 [dB] TG4a

Simulation result 2 Eb/N0=-3dB Conventional method Interpolation Simplified ML TG4a

Advantages Working well at low sampling rate (less than twice of the signal bandwidth) Feasible ADC implementation Low computation complexity Same level of complexity compared with conventional schemes Independent of noise level TG4a

Some questions from 406r0 Performance in a multipath environment (ongoing work) Relate to the decay pattern of the multipaths in a cluster, specifically, its bandwidth vs. the bandwidth of the UWB signal Accommodate the multipath information by modifying Signal autocorrelation function Noise statistics Fix point calculation of ADC The quantization error being approximated by a random variable of uniform distribution Noise statistics is modified to incorporate such errors Similar performance is observed TG4a

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 implementation TG4a