Theoretical Data on Support of a Unified Indoor Geolocation Channel Model

1
Theoretical Data on Support of a Unified Indoor
Geolocation Channel Model

Giftet
Inc.

• Ilir F. Progri, Giftet Inc., Pomona, CA
• William R. Michalson, WPI, Worcester, MA
• Jinling Wang, University of New South Wales,
  Sydney, Australia
• Matthew C. Bromberg, Elected Engineering, MA
• Presented at
• ION-NTM 2007, January 22-24, 2007
• San Diego, CA

2
Overview

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• What is a unified indoor geolocation channel
  model?
• Path lossfunction of the transmitter and
  receiver distance and frequency
• Multipath distributionRayleigh, Rician,
  Lognormal, and Nakagami with m degrees of
  freedom, Weibull (not discussed in this paper)
• The purpose of this paper is two fold
• to provide a better interpretation of the sets of
  theoretical data for the indoor channel model
• to explain the lack of fit of the well-known
  multipath distribution models from the previous
  measurement data sets reported in the literature

3
Overview Cont.

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Inc.

• Unified indoor geolocation path loss model
• LOS signal degradations (power or gain) due to
  physical propagation properties
• Unified multipath distribution model. Multipath
  distributions can be classified as being more
  suitable for
• Gain calculations (Rayleigh, Rician, and
  Lognormal)
• Power calculations (Nakagami with m-degrees of
  freedom).
• Gain calculations based on Rayleigh, Rician, and
  Lognormal
• Reflection (or NLOS) gains of the observable
  paths.
• Power calculations based on Nakagami with
  m-degrees of freedom
• Reflection (or NLOS) powers of the observable
  paths (future work)

4
Unified Path Loss Model

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• The unified path loss model consists of an
  approach for linking together the path loss
  models of
• Type such as (macro-outdoor, micro-outdoor, and
  indoor)
• Geometry such as the distance between the
  transmitter and receiver, R
• Geometry index n 2, 3, 4, 5, 6
• Signal characteristics such the frequency of
  operation, f
• Frequency index m 2.1, 2.2, 2.3, 2.4, 2.5
• All the remaining effects are grouped into Zero
  Mean Gaussian Noise N(0,s) s 0.5, 1, 2, etc
• LOS power or gain calculations which we are
  concerned about!

5
Indoor Geolocation Path Loss

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Inc.
3.2 dB
40 dB
80 dB
5 dB

• The observed LOS path gain degradation ranges
  from
• ?20 dB to ?60 dB _at_ 10 m
• ?40 dB to ?120 dB _at_ 100 m

• The observed LOS path gain degradation ranges
  from
• ?4.8 dB to ?7 dB _at_ 2 GHz
• ?20 dB to ?2.5 dB _at_ 10 GHz

6
Multipath Distribution Model

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• Why is multipath distribution very important?
• To provide the framework for all the available
  multipath distribution channel models
• To enable the computation of observable path
  gains or powers.
• Multipath distributions are classified into two
• More suitable for reflection gain computations
  (Rayleigh, Rician, and Lognormal)
• More suitable for reflection power calculations
  (Nakagami with m-degrees of freedom).
• Why?
• Lets start with the 1st (or multipath
  distributions for gain calculations)

7
Unified Indoor Geolocation Multipath Distribution
Model

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• Why Rayleigh, Rician, and Lognormal are more
  suitable for gain calculations?
• Assuming than channel gain is a random variable.
• Statistical parameters such as mean and variance
  of the gain are directly linked in a simplified
  form with the distribution parameters.
• If we know the statistical parameters and the
  individual distribution we can obtain the
  distribution parameters and vice versa!!
• A unified multipath distribution model is simply
  a linear combination (or an expansion of the
  distribution models)

Four theorems!! My WTS 2006 paper!!
8
Unified Indoor Geolocation Multipath Distribution
Model Cont

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• The composite cdf and pdf which contains a
  Lognormal, Rician, and Rayleigh fading channel
  for ma ? 0.6 and sa ? 0.0626 and n ? 0.25, 0.35,
  0.4
• There is an infinite number of possible
  combinations between these distributions!!
• There is a much greater possibility that the
  observed multipath distribution is a combination
  of the above!!

9
Unified Indoor Geolocation Multipath Distribution
Model Cont

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• The composite cdf and pdf does not contain a
  Lognormal, Rician, and Rayleigh fading channel
  for ma ? 0.6 and sa ? 0.0626 and n ? 0.4137,
  0.5023, 4.3884 or -0.2136, 1.7936, -0.0015
• Because a uniform distribution is an independent
  distribution and cannot be decomposed into
  Lognormal, Rician, and Rayleigh!!

10
Unified Indoor Geolocation Multipath Distribution
Model Cont

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Inc.

• Why Nakagami with m-degrees of freedom is more
  suitable for power calculations?
• Assuming than channel power is a random variable.
• Statistical parameters such as mean and variance
  of the power are directly linked in a simplified
  form with the distribution parameters.
• If we know the statistical parameters and the
  individual distribution we can obtain the
  distribution parameters and vice versa!!
• A unified multipath distribution model is simply
  a linear combination (or an expansion of the
  distribution models)
• Future work!!

11
Observable Path Gain Computations

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Inc.

• Let assume that a is the path gain which fits a
  Rayleigh distribution given by its probability
  density function
• where l is the parameter.
• The line-of-sight path gain is the expected value
  of the distribution which is given by

12
Observable Path Gain Computations Cont.

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Inc.

• The probability that the path gains i.e., the
  non line of sight (NLOS) gains will be smaller or
  equal the LOS gain is equal to
• In other words, the probability that the NLOS
  path gains is greater than the LOS path gain is
• Once every 10 seconds i.e., very probable!!

13
Observable Path Gain Computations Cont.

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Inc.

• Lets assume that there exits a 1st reflection
  that has a gain of 3dB greater than the LOS gain.
  The probability that the path gains will be
  smaller than the this gain is
• On the other hand the probability that the NLOS
  path gain will be greater than the 3dB path LOS
  gain is
• If we were to convert this number in days we get
  1 out of 6.3 days. Not very probable!!

14
Observable Path Gain Computations Cont.

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Inc.

• If we assume that the NLOS path gain will be
  greater than the 5dB LOS path gain than the
  probability of that event is
• In other words if this event was to occur one
  second out of seconds or 1 seconds out of 6072
  years.
• The occurrence of this event seems to go even
  beyond Biblical times.
• It seems that none of us will be around to
  observe this event.

15
Observable Path Gain Computations Cont.

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Inc.

• Lets assume that the multipath distribution is
  either Lognormal or Rician.
• For these gains both Lognormal and Rician
  distributions are under the Rayleigh
  distribution.
• The tale probability that the NLOS path gain is
  greater than 3 dB than the LOS path gain is the
  smallest for the Lognormal distribution and the
  largest for the Rayleigh distribution

16
Illustration of Gain Calculations

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Inc.
LOS Gain at 0.6
NLOS Gain at 1.972 gt 3dB gain
Rician under Rayleigh
Lognormal is under Rayleigh
17
Conclusions

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Inc.

• We have revisit the unified geolocation channel
  model and have arrived at the following
  conclusions
• The unified path loss model
• To an extent represents the complete path loss
  model for all available geolocation systems.
• Propose a system design that will account for 40
  to 80 dB of indoor LOS signal gain degradations.
• The unified multipath distribution
• Presents the complete multipath distribution
  model
• Provides the framework for all required
  computations for observable path gains or powers

18
Conclusions Cont.

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Inc.

• From the theoretical data it appears that
  reflections with gain 3dB or higher are on the
  order of 1 out of 6.2 days
• On the other hand, reflections with gain 5dB or
  greater than the LOS gain are of the order of 1
  out of 6072 years.
• And this is the most important conclusion of this
  work that for simulation or implementation
  purposes we should never consider reflections
  with gains up to 5 dB greater than the LOS gain.

19
Future Work

Giftet
Inc.

• We are in lookout for experimental data to
  validate our models.
• Investigate other distributions such as Weibull
  and others which we do not know yet.
• Complete our unified geolocaiton multipath
  distribution model for power calculations!!
• Pending journal paper!

20
Giftet Inc.

Giftet
Inc.

• Giftet is a privately held company for
  developing, marketing, and distributing global
  navigation, software, and web solutions for
  Indoor Geolocation Systems, GPS, GLONASS,
  Galileo, QZSS, and other Global Satellite and/or
  Pseudolite Navigation (or Positioning and/or
  Timing) Systems based on customers needs.
• Giftet philosophy is based on partnership!
• Giftet welcomes partnership!
• Giftet was founded on December 26, 2006, Pomona,
  CA.
• http//www.giftet.com/