15-Sep-04
doc.: IEEE 802.15-04-0447-01-004a
Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs)
Submission Title: [Indoor UWB Channel Measurements from 2 GHz to 8 GHz]
Date Submitted: [16 September, 2004]
Source: [Ulrich G. Schuster] Company [Communication Technology Laboratory, ETH Zurich]
Address [Sternwartstr. 7, ETH Zentrum, 8092 Zürich, Switzerland]
Voice:[+41 (44) 632 5287], FAX: [+41 (44) 632 1209], E-Mail:[schuster@nari.ee.ethz.ch]
Re: [IEEE 802.15.4a Channel Modeling Subcommittee Call for Contributions]
Abstract: [This presentation describes UWB channel measurements from 2 to 8 GHz, conducted in two
office buildings at ETH Zurich, Switzerland. Measurements were taken for LOS, OLOS and NLOS
settings in a corridor and a large entrance lobby, with transmitter-receiver separations ranging from 8 m to
28 m. A different method for small scale statistical modeling is proposed]
Purpose: [To provide additional data for the proposed generic 802.15.4a channel model and discuss some
of the modeling aspects used in the generic model]
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.
Submission
1
Ulrich G. Schuster, ETH Zurich
Indoor UWB Channel Measurements
from 2 GHz to 8 GHz
Ulrich Schuster and Helmut Bölcskei
ETH Zurich
September 16, 2004
IEEE 802.14-04-0447-01-004a
1
Objectives
Main goal: verify existing UWB channel models and establish (if
applicable) new models suitable for theoretical analysis.
Main issues:
• Individual and Joint tap statistics
• Scaling of stochastic degrees of freedom with bandwidth
• Validity of the uncorrelated scattering assumption
Genuine focus was not IEEE 802.15.4a channel modeling work, hence not
all parameters of the IEEE 802.15.4a standard model were extracted.
IEEE 802.14-04-0447-01-004a
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Measurement Setup — Schematic
Measurement
Control
HP 8722D VNA
2m
Skycross UWB antenna
Minicircuits ZVE 8G
2m
Diadrive positioner
H&S Sucoflex 104 cables
Skycross UWB antenna
25 m
custom RF amp
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2m
3
Measurement Setup — Details
Measurements were taken in the frequency domain
• HP 8722D vector network analyzer (VNA), 50 MHz – 40 GHz
• Minicircuits ZVE 8G power amplifier, 2GHz – 8 GHz, 30 dB gain
• Skycross SMT-3TO10M UWB antannas (prototype), Omni
• Custom RF amplifier, 20 dB gain up to 10 GHz, NF < 6
• H&S Sucoflex 104 cables
• Custom modified Diadrive 2000 positioning table
• Control via Matlab (Instrument Control & Data Acquisition Toolboxes)
IEEE 802.14-04-0447-01-004a
4
VNA Settings
• Option 12, “direct sampler access”, for improved dynamic range
• Frequency range 2–8 GHz, divided into two bands
• 1601 points per band, for a total of 3201 points
• 1.875 MHz point spacing
• Max. resolvable delay of 533 ns, equivalent to 160 m path length
• IF bandwidth 300 Hz
• Total sweep time 19s
• Calibration included the entire equipment except for the antennas,
considered as part of the channel
IEEE 802.14-04-0447-01-004a
5
Environments
We measured two different environments at the premises of ETH Zurich,
Switzerland, in typical European style office buildings.
• Corridor, e.g. for sensing applications; brick walls, windows, concrete
floor and ceiling
• Entrance lobby, typical public space; tiled floor, large glass windows,
concrete walls
All measurements were taken during night time on weekends to ensure
a static channel.
IEEE 802.14-04-0447-01-004a
6
Corridor Environment
12.6 m
8.4 m
10.3 m
12.4 m
2.7 m
0
Tx Array
NLOS
LOS
0.95 m
5.1 m
5
10
15
20 m
RF Lab
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7
Lobby Environment
Rx NLOS
A
9.9m
Tx Array
LOS
27.2m
8
IEEE 802.14-04-0447-01-004a
16.3m
Tx Array
N/QLOS
27.3m
Rx OLOS
Rx LOS
9m
B
30 m
20
10
0
Virtual Array Measurements
• Virtual array should cover small scale fading area
• Grid spacing 7cm, approx. half wavelength at 2 GHz for independent
samples
7 cm
7 cm
Grid Point
• 5 × 9 grid
• Operated by stepping motors, computer controlled
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Measurement Methodology
Goal:
• Obtain enough independent samples of small scale fading for
statistical analysis
• Separate small scale from large scale effects
Achieved via:
• Measurement of two arrays per small scale location for 90 points total
• One frequency response per array point
• Several scenarios (LOS, OLOS, NLOS)
• Several distances between transmitter and receiver in each scenario
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Sample Impulse Response Power — Lobby LOS
-80
27.2 m
47 m
-90
59.9 m
-100
119.8 m
attenuation (dB)
-110
139.6 m
156.8 m
-120
-130
-140
-150
-160
-170
0
20
40
60
80
100
delay-equivalent distance (m)
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140
160
11
Average Impulse Response Power — Lobby LOS
-80
27.2 m
-90
47.0 m
attenuation (dB)
-100
59.9 m
-110
119.8 m
-120
-130
-140
0
20
40
60
80
100
delay equivalent distance (m)
IEEE 802.14-04-0447-01-004a
120
140
160
12
Average Impulse Response Power — Lobby OLOS
-95
26.9 m
-100
31.7 m
27.4 m
-105
attenuation (dB)
-110
-115
-120
-125
-130
-135
-140
0
20
40
60
80
100
delay equivalent distance (m)
IEEE 802.14-04-0447-01-004a
120
140
160
13
Average Impulse Response Power — Lobby NLOS
-105
34.9 m
-110
-115
attenuation (dB)
-120
22.2 m
-125
-130
-135
-140
-145
-150
0
20
40
60
80
100
delay equivalent distance (m)
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120
140
160
14
Average Impulse Response Power — Corridor LOS
-70
12.6 m
-80
attenuation (dB)
-90
38.7 m
23.3 m
33.1 m
-100
-110
64.4 m
58.7 m
-120
-130
-140
0
20
40
60
80
100
delay equivalent distance (m)
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120
140
160
15
Average Impulse Response Power — Corridor NLOS
-90
21.0 m
-100
17.1 m
16.0 m
attenuation (dB)
-110
-120
72.5 m
-130
-140
-150
0
20
40
60
80
100
delay equivalent distance (m)
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140
160
16
Traditional Wideband Channel Modeling
Standard continuous-time wideband fading model
N (τ )−1
h(t, τ ) =
X
ak (t)δ(τ − τk (t))ejθk (t)
k=0
assumes specular reflections: distinct, frequency independent
propagation paths.
Assumption might not hold for UWB Channels
• Frequency dependence of materials
• Diffuse reflections due to rough surfaces
• Diffraction
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Common Modeling Assumptions
Two very common and well supported assumptions:
• Communication system is band limited
• Channel is effectively time-limited
A further limitation arises due to the VNA measurement methodology:
the measured channel is quasi-static and can be modeled as an LTI
system.
With an external B Hz band limitation b(τ ), the effective channel is
hB (τ ) = (b ? h)(τ )
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Discretized Channel Representation
⇒ Complete representation through channel samples possible:
∞
X
n sin πB τ − n B
hB (τ ) =
hb
n
B
πB
τ
−
B
n=−∞
(Shannon’s Sampling Theorem)
Effective time limitation: only L non-zero samples. Hence the channel is
completely described by its non-zero taps
l
h[l] = hb
,
B
l = 0...L − 1
Modeling goal: block fading stochastic discrete-time LTI system
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Fading Tap Statistics
Antenna displacement over the array renders phase information
meaningless =⇒ assume uniform phase, use the small scale spatial
variations of the received amplitude for statistical analysis.
Goal: marginal and joint tap distribution that best approximates reality.
• Consider a set M of candidate models i.e., parametrized probability
densities gi(· | Θ):
–
–
–
–
–
Rayleigh
Rice
Nakagami
Lognormal
Weibull
This is a model selection problem. Hypothesis testing is not a
meaningful approach.
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Hypothesis Testing Review
Goal: establish if data x supports a challenging hypothesis H0 against
an incumbent hypothesis H1.
Sample space is partitioned into the region of acceptance Da and the
critical region Dc = Dac
• Type I error: H0 is true but x ∈ Dc
• Confidence level: α = P(x ∈ Dc | H0)
• Type II error: H0 false and x ∈ Da
• Test power: 1 − P(type II error)
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Goodness-of-Fit Tests
Hypothesis H0: data x is drawn according to some distribution F (x).
Typical tests operate as follows:
• Compute a test statistic Dn(x), some function of the n-dimensional
data vector x
• Dn has a limiting distribution Q(x) for n → ∞, which does not
depend on F (x) if H0 holds.
• Reject H0 if Dn > x0, where Q(x0) = 1 − α
• Confidence level needs to be selected in advance
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Why Hypothesis Testing is the Wrong Approach
• Hypothesis testing does not deal with approximations
– probability that the standard models are true is zero
– significance does not measure goodness of fit
• Hypothesis testing relies on ad hoc choices
– significance level arbitrary
– some tests rely on binning — how to choose the bins?
• Hypothesis testing does not compare several hypothesis
– only tests a challenging against an incumbent hypothesis
– adjusting the significance level to compare test results invalidates
the test
• Hypothesis testing deals poorly with parameter estimates
IEEE 802.14-04-0447-01-004a
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Traits of a Good Model
• Contains sufficient information about the real world
• Leads to consistent predictions
• Mathematically and computationally tractable
• Based on physical insight and measured data
• Advances intuition
IEEE 802.14-04-0447-01-004a
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Model Selection
• Goal is to approximate the unknown reality, described by PDF f (x)
• Select several parametric families of candidate models gi(x | Θ)
• Relative entropy measures discrepancy between model gi and reality
Z
D(f || g) =
f(x)
f(x) log
dx
gi(x | Θ)
= Ef [log f(X)] − Ef [log gi(X | Θ)]
• Select model to minimize the discrepancy
• Need to estimate Ef [log gi(X | Θ)] from data y
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Akaike’s Information Criterion — AIC [Akaike 1973]
An unbiased estimate of Ef [log gi(X | Θ)] is
AIC = −2 log gi(y | Θ̂(y)) + 2K
with the i.i.d. data vector y, and the ML parameter estimate Θ̂(y).
• Bias correction depends on number of estimated parameters K
• Penalizes overfitting
• Minimizes the bias–variance tradeoff
• Mathematical formulation of the principle of parsimony
• Extensively used in regression order selection
Note: Other criteria have different bias correcting terms (MDL, BIC, TIC)
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Akaike Weights
AIC values are a relative measure — only ∆i = AICi − minM AIC is
important.
AIC is an unbiased estimate of the expected log-likelihood log L(gi | y),
hence
− 12 ∆i
L(gi | y) ∝ e
Normalization to unity yields Akaike Weights:
1
e− 2 ∆i
wi = P|M|
− 12 ∆k
k=1 e
⇒ an estimate of the expected probability of model i providing the best
fit among all candidate models.
IEEE 802.14-04-0447-01-004a
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Akaike Weights, Averaged Impulse Response — Lobby LOS
1
Rayleigh
Rice
Nakagami
Lognormal
Weibull
0.9
0.8
Akaike Weight
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
attenuation (dB)
-80
-90
-100
-110
-120
-130
0
200
400
600
800
1000
1200
1400
time domain sample index
IEEE 802.14-04-0447-01-004a
1600
1800
2000
2200
28
Fading Model Selection
We computed Akaike Weights for all scenarios
• Rayleigh provides on average the best fit
– AIC penalizes presence of the extra parameter in Nakagami, Ricean
and Weibull models
– Rayleigh is not good at the start of a cluster
• LOS component is often Weibull distributed
• Lognormal is almost always the worst model
– lognormal apparently good for first cluster taps
– but no conclusions about the model are possible due to
time-of-flight differences across array: a specular component is
recorded in different taps at different grid positions
IEEE 802.14-04-0447-01-004a
29
Model Selection Conclusion
• Akaike weights shows significant variations across taps
– might explain different selected models in different measurement
campaigns
– shows that candidate models are quite close
– different findings might be due to methodology and measurement
errors rather than different realities
• Rayleigh amplitude plus uniform phase assumption leads to circularly
symmetric complex Gaussian taps — good news for theoretical work
• Need more independent measurements using information criteria
(AIC, BIC, MDL) to support or challenge these findings
IEEE 802.14-04-0447-01-004a
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Complete Statistical Description
So far: marginal distribution is complex Gaussian
Conjecture: joint distribution is jointly complex Gaussian
⇒ complete description obtained through mean and covariance matrix
• Significant eigenvalues correspond to stochastic degrees of freedom
– independent diversity branches
– delay spread only provides a first order estimate, assuming
independent taps
– important open question: scaling with bandwidth
• Following work by Knopp (2004), we are currently working on the
analysis of the stochastic degrees of freedom
IEEE 802.14-04-0447-01-004a
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Parameters for the IEEE 802.15.4a Standard Model
IEEE 802.14-04-0447-01-004a
32
Parameters for the Nakagami distribution — Lobby LOS
Although AICc shows a higher probability for Rayleigh, the standard
model uses the Nakagami distribution.
Nakagami m factor for the LOS tap
Distance
m
27 m
8.7
24 m
9.1
21 m
5.4
18 m
10.2
15 m
7.6
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Parameters for the Nakagami distribution — Lobby LOS
Nakagami m parameters for later clusters, i.e. not due to the LOS
component but maybe other specular reflections
Distance
m
27 m
4.0, 7.5
24 m
3.7, 10.7
21 m
3.1, 12.7
18 m
6.3, 11.5
15 m
2.9, 3.5, 8.1
Most other (non-specular) taps have m ≈ 1, consistent with the Rayleigh
model.
IEEE 802.14-04-0447-01-004a
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Small Scale Parameters — Time Dispersion
Mean delay and delay spread often used to characterize time
dispersiveness of the channel. They are not the most general description.
Estimates can be computed as
PL−1
τ̄ =
l=0 |h| [l]
PL−1
l=0 |h| [l]
mean delay
v
u PL
2
u
l=1 (l − τ̄ ) |h| [l]
t
s=
PL−1
l=0 |h| [l]
delay spread
Mean and standard deviation can now be computed over all small scale
positions of the virtual array.
IEEE 802.14-04-0447-01-004a
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Mean Delay and Delay Spread Statistics — Lobby LOS
Mean Delay
Delay Spread
Distance
µτ̄
στ̄
µs
σs
27 m
27.13 ns
1.74 ns
49.5 ns
2.08 ns
24 m
27.15 ns
2.86 ns
49.23 ns
3.37 ns
21 m
30.99 ns
2.30 ns
53.62 ns
2.25 ns
18 m
29.86 ns
2.11 ns
52.23 ns
1.64 ns
15 m
27.26 ns
1.75 ns
49.20 ns
1.63 ns
IEEE 802.14-04-0447-01-004a
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Mean Delay and Delay Spread Statistics — Lobby OLOS
Mean Delay
Delay Spread
Distance
µτ̄
στ̄
µs
σs
27 m
49.82 ns
7.78 ns
74.08 ns
7.04 ns
24 m
46.86 ns
6.33 ns
71.07 ns
5.91 ns
21 m
45.61 ns
5.70 ns
71.23 ns
4.43 ns
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Mean Delay and Delay Spread Statistics — Corridor
LOS Setting
Mean Delay
Delay Spread
Distance
µτ̄
στ̄
µs
σs
12.5 m
7.55 ns
0.88 ns
21.08 ns
1.65 ns
10.5 m
10.68 ns
1.69 ns
24.70 ns
2.19 ns
8.5 m
9.93 ns
2.15 ns
23.74 ns
2.86 ns
NLOS Setting
Mean Delay
Delay Spread
µτ̄
στ̄
µs
σs
24.44 ns
1.16 ns
31.11 ns
1.87 ns
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Small Scale Parameters — The Saleh-Valenzuela Model
The proposed 802.15.4a channel model is continuous-time and specular:
h(t) =
L−1
X K−1
X
ak,lδ(t − Tl − τk,l,)
l=0 k=0
with L clusters and K rays per cluster. Ray and cluster arrivals are
described by Poisson processes with interarrival probabilities
P(Tl | Tl−1) = Λ exp{−Λ(Tl − Tl−1)}
Ray and cluster power decay are exponential
h
2
E |ak,l|
i
h
2
= E |a0,0|
i
τk,l
Tl
exp −
exp −
Γ
γ
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Saleh-Valenzuela Model Parameter Extraction
Our discrete time model does not fit into this framework ⇒ cannot
extract all parameters since there are no rays. Using the methodology
presented by Balakrishnan in doc. 802.15-04-0342-00-004a, we
computed
• Cluster decay coefficient Γ
• Inter-cluster decay coefficient γ
• Cluster interarrival time Λ
The S-V model fit is not always satisfactory, as can be seen in the
following plots. We only extracted S-V parameters for the LOS scenarios,
where clusters were observable.
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Cluster Decay — Corridor LOS
2
Γ = 33.0ns
0
Cluster Power
Linear Least Squares Fit
-2
-4
Power ( log|a|2 )
-6
-8
-10
-12
-14
-16
-18
0
50
100
150
200
250
Cluster Delay (ns)
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300
350
400
41
Intra-Cluster Decay — Corridor LOS
5
Tap Power
Linear Least Squares Fit
γ = 16.2 ns
Tap Power ( log|a|2 )
0
-5
-10
-15
0
10
20
30
40
50
60
Intra-Cluster Excess Delay (ns)
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80
90
42
Cluster Interarrival Times — Corridor LOS
1
0.9
1
= 29.4ns
Λ
0.8
Cumulative Distribution
0.7
0.6
0.5
Cluster Interarrival Times
Exponential CDF Fit
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
Interarrival Time (ns)
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70
80
90
43
Cluster Decay — Lobby LOS
0
Cluster Power
Least Squares Fit
Γ = 50.8 ns
Power ( log|a|2 )
-5
-10
-15
0
50
100
150
200
250
Cluster Delay (ns)
300
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350
400
450
44
Intra-Cluster Decay — Lobby LOS
5
Tap Power
Linear Least Squares Fit
γ = 59.5 ns
0
Tap Power ( log|a|2 )
-5
-10
-15
-20
0
50
100
150
IntraCluster Excess Delay (ns)
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250
45
Cluster Interarrival Times — Lobby LOS
1
0.9
1
= 67.5 ns
Λ
Cumulative Probability
0.8
0.7
0.6
0.5
0.4
Cluster Interarrival Times
Exponential CDF Fit
0.3
0.2
0.1
0
0
50
100
150
Cluster Interarrival Time (ns)
IEEE 802.14-04-0447-01-004a
200
250
46
PDP Fit — Lobby NLOS
NLOS 1
fit 1
NLOS
fit 2
-6
-6.5
-7
Power (log-scale)
-7.5
-8
-8.5
-9
-9.5
-10
-10.5
0
500
1000
1500
Sample Index
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2500
47
PDP Fit Parameters — Lobby NLOS
Setting
χ
γrise
γ1
Ω1
NLOS 1
0.88
28 ns
117 ns
0.0020
NLOS 2
0.85
30 ns
134 ns
0.0014
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Large Scale Parameters — Path Loss
The simplest pathloss model consists of a single slope with exponential
decay
d
10 log P (d) = G0 + 10ν log , d ≥ d0
d0
with d0 = 1m, an arbitrarily chosen reference distance, and G0 the
reference loss at d0.
Our measurements are not targeted at pathloss extraction; only in three
settings enough large scale data points are available to yield crude
estimates, as can be observed from the following scatter plots.
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Path Loss Fit — Lobby LOS
-66
Impulse Response Power
Linear Fit
-67
received power (dB)
-68
-69
-70
-71
-72
-73
-74
12.6
14.1
15.8
17.8
20.0
22.4
25.1
distance (m, log10 scale)
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28.2
31.6
35.5
50
Path Loss Fit — Lobby OLOS
-72
Impulse Response Power
Linear Fit
-73
received power (dB)
-74
-75
-76
-77
-78
-79
20.9
21.9
22.9
24.0
25.1
distance (m, log10 scale)
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26.3
27.5
28.8
51
Path Loss Fit — Corridor LOS
received power (dB)
-60
Impulse Response Power
Linear Fit
-65
-70
-75
7.9
8.9
10
11.2
12.6
distance (m, log10 scale)
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14.1
15.8
52
Pathloss Coefficients
Setting
ν
G0
Lobby LOS
1.6
-49 dB
Lobby OLOS
2.2
-45 dB
Corridor LOS
1.2
-51 dB
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Conclusions
• Presented results from a UWB measurement campaign for indoor
public spaces and hallways; largest transmitter-receiver separation
reported so far (> 27 m)
• Continuous-time specular model probably not suitable for UWB —
used a discrete-time model instead
• AIC for fading tap model selection
– Rayleigh assumption still valid for UWB
– differences to Rice, Nakagami and Weibull small
• Most IEEE 802.15.4a standard model parameters as expected
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