1. July 2002
Project: IEEE P Working Group for Wireless Personal Area Networks (WPANs)
Submission Title: [UWB Propagation Phenomena]
Date Submitted: [4 July, 2002; r1: 7 July, 2002]
Source: [Kai Siwiak]
Company [Time Domain Corporation]
Address [7057 Old Madison Pike, Huntsville, AL 35806]
Voice [ ]
[ ]
Re: [Response to the Call for Contributions on UWB Channel Models (IEEE P /208r1-SG3a).]
Abstract: [This contribution exposes a behavior of UWB signals in multipath which is relevant to propagation laws in multipath and hence for models intended for evaluating UWB physical layer submissions for a high-rate extension to IEEE ]
Purpose: [A connection is shown between measured multipath delay spread and the propagation law. this leads to a theory for the connection and to a generalized propagation law model that offers a better understanding of UWB multipath channels model which can be used to compare different UWB PHYs.]
Notice: This document has been prepared to assist the IEEE P 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 P
Time Domain Corporation

2. UWB Propagation Phenomena
July 2002
UWB Propagation Phenomena
Kai Siwiak
Time Domain Corporation
7 July, 2002: IEEE /301r2
Time Domain Corporation

3. July 2002
Overview
High resolution UWB propagation measurements reveal a close connection between propagation law and multipath
A theory based on measurements leads to a generalized multipath propagation law model
Result has implications on receiving signals, RAKE gain and understanding of the UWB channel and channel models
Time Domain Corporation

4. UWB Propagation Measurements
July 2002
UWB Propagation Measurements
A set of UWB propagation measurements [1] were carried out using a UWB pulse transmitter and a UWB scanning receiver
The data were processed using the CLEAN algorithm [2] to extract:
‘Strongest pulse power density’ vs. distance
‘Total power density’ vs. distance
RMS delay spread vs. distance
Time Domain Corporation

5. Strongest pulse vs. Distance
July 2002
Strongest pulse vs. Distance
The indoor UWB measurements [1] reveal that the “strongest pulse power density” propagates approximately as 30 log(d), distance d is meters
-40
-30
-20
-10 1 10
100
Distance, m
Power, strongest pulse, dB .
Time Domain Corporation

6. Indoor Channel Impulse Response
July 2002
Indoor Channel Impulse Response
Channel pulses (left) are processed with CLEAN algorithm to obtain CIRs (right). The “total power density” represented by the CIR can then be reported
Source: Yano [1]
Time Domain Corporation

7. Total Power Density vs. Distance
July 2002
Total Power Density vs. Distance
The same measurements [1] reveal that the “total power density” propagates approximately as 20 log(d), distance d is meters, and with smaller variance
-40
-30
-20
-10 1 10
100
Distance, m
Total power, dB .
Time Domain Corporation

8. RMS Delay Spread vs. Distance
July 2002
RMS Delay Spread vs. Distance
The same measurements [1] further reveal that the rms delay spread varies approximately as t0d, distance d is in meters, and here t0=3 nano seconds 20 40 60 80 10 30
Distance, m
Delay spread, ns
Time Domain Corporation

9. July 2002
Initial Assumptions
A simple ‘Gedankenexperiment’ leads us to conclude that in a lossless 3-d environment of copolarized scatterers, total power propagates with inverse square of distance
P(d) = Ptx/4pd2
We further assert that the multipath power delay profile is exponentially distributed [3]
S = e-t/trms/trms
Time Domain Corporation

10. July 2002
Dissipative Losses
There are additional dissipative losses of the form e-2ad which will increase the rate of signal attenuation beyond free space loss
Dissipative lass basis for a very simple UWB propagation law [5] which modeled successive wall reflections as homogeneous attenuation
Here, however a nepers/m, is actual dissipative I2R loss constant for total power propagation
Time Domain Corporation

11. Model Parameters Rays or pulses arrive at uniform rate 1/t0
July 2002
Model Parameters
Rays or pulses arrive at uniform rate 1/t0
For this measurements set, trms=t0d
The fractional power density associated with strongest ray P1 is P1 t0 e
-t/trms ó ô õ dt =
= 1-exp(-t0/trms) 1
trms
Time Domain Corporation

12. P1(d) = [Ptx/4pd2][1- exp(-t0/trms)]e-2ad
July 2002
Propagation Law
Pulses propagate as
P1(d) = [Ptx/4pd2][1- exp(-t0/trms)]e-2ad
where trms=t0d
The value of t0/t0 establishes the transition between free space and higher order power law
When t0/t0d is small (increasing d) we use the approximation
ex = 1+ x
Time Domain Corporation

13. Deriving Higher Order Power Law
July 2002
Deriving Higher Order Power Law
Substituting
P1(d) = [Ptx/4pd2][t0/t0d]e-2ad
... and we have the theoretical basis for inverse 3rd power propagation law in multipath scattering for this data set:
P1(d) = [Ptx/d3][t0/4pt0]e-2ad
Time Domain Corporation

14. Relation to Outdoor Propagation
July 2002
Relation to Outdoor Propagation
Outdoors, the delay spread increases approximately with the square root of distance [4]
Applying the same analysis, power density (in the absence of dissipative losses) gives a plausible inverse 2.5 power propagation law for this mechanism alone:
Poutside(d) = CPtx/d 2.5
Time Domain Corporation

15. July 2002
Model Constants
The theory can be generalized to non-uniform arrival rates for rays and other data sets
Values of trms(d), and hence t0 = 3 ns and t0=3 ns here, can be derived directly from UWB pulse propagation measurements
Dissipation factor 20alog(e) dB/m is found from the propagation of total power density, here a<0.006 nepers/m (<0.05 dB/m)
Time Domain Corporation

16. Implications to RAKE Gain
July 2002
Implications to RAKE Gain
The maximum possible RAKE gain based on this measurement set is the ratio of ‘total power density’ to ‘single pulse power density’
Gmax,RAKE = 10 log(d) indoors
Gmax,RAKE = 5 log(d) outside
Propagation measurements are dependent on how the power is collected with respect to multipath in the receiver
Time Domain Corporation

17. Summary Generalized propagation law in multipath is
July 2002
Summary
Generalized propagation law in multipath is
P1(d) = [Ptx/4pd2][1- exp(-t0/trms(d))]e-2ad
Which with this indoor data set for d >>t0/t0 reduces to
P1(d) = [Ptx/d3][t0/4pt0]e-2ad
Maximum possible indoor RAKE gain here is
Gmax,RAKE = 10 log(d)
The propagation law is general: also applies to narrow band signal propagation
Time Domain Corporation

18. July 2002
Conclusions
A theoretical basis for propagation law in scattering was derived, general model proposed
Propagation model can be applied to other data sets
Propagation law, attenuation losses, multipath delay spread, and RAKE gain are closely connected
Has implications on UWB channel models: channel model must couple propagation law, dissipative losses and multipath correctly
Time Domain Corporation

19. July 2002
References
[1] S. M. Yano: “Investigating the Ultra-wideband Indoor Wireless Channel,” Proc. IEEE VTC2002 Spring Conf., May 7-9, 2002, Birmingham, AL, Vol. 3, pp
[2] J.A. Högbom, “Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines,” Astron. and Astrophys. Suppl. Ser, Vol. 15, 1974
[3] William C. Jakes, Microwave Mobile Communications, 1974, IEEE Press Reprint
[4] Private communication with Henry L. Bertoni, 6 June 2002
[5] K. Siwiak, A. Petroff , “A Path Link Model for UWB Pulse Transmissions,” Conference Proceedings of the IEEE VTC-2001, Rhodes, Greece, May 6-9, May 2001
Time Domain Corporation