introduction to propagation modeling -...
TRANSCRIPT
Introduction to Propagation
Modeling Dr. Jussi Salmi
GETA Winter School 2012
13.2.2012
Outline
• Motivation
• Physical Propagation Mechanisms – Free space, reflection, diffraction, scattering
• Statistical Descriptions – Path loss, shadowing and small-scale fading
• Deterministic Abstractions – Bandwidth and Signal duration, Tapped Delay Line model, and
Double Directional Propagation Path model
• Application example: UWB MIMO Radar
13.2.2012 Jussi Salmi
Motivation
• Radiowave propagation is a key factor in any wireless
localization system
– Line-of-sight (LOS) vs. Non-line-of-sight (NLOS)
– Path loss modeling and fading due to multipath
• The scope of this talk is to
– Introduce typical physical propagation mechanisms
– Familiarize with statistical modeling concepts
– Introduce the concept of double-directional propagation paths
– Application example: UWB MIMO Radar
13.2.2012 Jussi Salmi
Physical Description vs. Statistical (or
Deterministic) Abstractions • Physical description of propagation mechanisms include
– Free space ”attenuation”
– Reflection
– Diffraction
– Scattering
– Waveguiding
• Statistical descriptions include – Path loss
– Shadow (slow) fading
– Small-scale (fast) fading
• Deterministic Abstraction – Tapped delay line model
– Double directional propagation path modeling
13.2.2012 Jussi Salmi
Physical Propagation Mechanisms
• Introductory description of
– Free space ”attenuation”
– Reflection
– Diffraction
– Scattering
– Waveguiding
• This part is mostly based on:
A. F. Molisch, ”Wireless Communications”,
2nd edition, Wiley 2011
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Free Space Attenuation • Tx antenna in free space
– Transmitted power 𝑃𝑇𝑥 is distributed into free space
– For an isotropic radiator, the power density per m2 at distance 𝑑
is given by 𝑃𝑇𝑥 4𝜋𝑑2
– An integral of the power density over any closed surface
surrounding the Tx antenna must be equal to 𝑃𝑇𝑥
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Free Space Attenuation
• Tx and Rx in free space
– For an isotropic radiator, the power density per m2 at distance 𝑑
is given by 𝑃𝑇𝑥 4𝜋𝑑2
– And the received power, for an antenna with an ”effective area”
of 𝐴𝑅𝑥 as a function of distance is
𝑃𝑅𝑥(𝑑) = 𝑃𝑇𝑥
1
4𝜋𝑑2𝐴𝑅𝑥
13.2.2012 Jussi Salmi
• Non-isotropic Tx
– If the Tx antenna is not isotropic, but has gain 𝐺𝑇𝑥 towards the
direction of the Rx, then we have
𝑃𝑅𝑥(𝑑) = 𝑃𝑇𝑥𝐺𝑇𝑥
1
4𝜋𝑑2𝐴𝑅𝑥
Physical propagation mechanisms:
Free Space Attenuation
13.2.2012 Jussi Salmi
• Rx Gain vs. effective area
– Rx gain can be expressed as
– i.e. for fixed antenna area, antenna gain increases with
frequency
𝐺𝑅𝑥 =4𝜋
𝜆2𝐴𝑅𝑥
Physical propagation mechanisms:
Free Space Attenuation
13.2.2012 Jussi Salmi
• Friis’ law
– Solving for effective area of the Rx antenna yields
– Inserting to equation of received power
– which is known as the Friis’ law
𝐴𝑅𝑥 = 𝐺𝑅𝑥
𝜆2
4𝜋
𝑃𝑅𝑥 𝑑 = 𝑃𝑇𝑥𝐺𝑇𝑥
1
4𝜋𝑑2𝐴𝑅𝑥 = 𝑃𝑇𝑥𝐺𝑇𝑥𝐺𝑅𝑥
𝜆
4𝜋𝑑
2
Physical propagation mechanisms:
Free Space Attenuation
13.2.2012 Jussi Salmi
• Note that the ”attenuation” in free space does not increase with frequency – However Friis’ equation seems to indicate that
– The spreading of the signal energy over a sphere can not
depend on the frequency
• The seeming contradiction is caused by the fact that the antenna gain 𝐺𝑅𝑥 is assumed to be independent of the frequency – The size of a similar type of antenna (having the same gain)
decreases; thus the effective area decreases
𝑃𝑅𝑥 𝑑 = 𝑃𝑇𝑥𝐺𝑇𝑥𝐺𝑅𝑥
𝑐
4𝜋𝑑𝑓
2
Physical propagation mechanisms:
Free Space Attenuation
𝑓 = 𝑐/𝜆
13.2.2012 Jussi Salmi
• If on the other hand the effective area of the Rx antenna
is independent of the frequency, then the received
power would be independent of the frequency too
• Note also that the validity of the Friis’ law is restricted to
the far field of the antenna, requiring
– Moreover, (at least) the 1st Fresnel zone needs to be free of
obstacles
𝑑 >2𝐿𝑎
2
𝜆 𝑑 ≫ 𝜆
Physical propagation mechanisms:
Free Space Attenuation
13.2.2012 Jussi Salmi
• Free space attenuation model as such is applicable only in very few terrestrial radio services – Fixed radio links or relays ar an example of such, but these
would not be of interest from localization point of view
• Free space attenuation provides a baseline for other path loss models
• Note that also the antenna gains 𝐺𝑇𝑥 and 𝐺𝑅𝑥 may have significant influence on received signal strength (RSS) based positioning techniques
Physical propagation mechanisms:
Free Space Attenuation
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Reflection
• Examples of reflection from conductive material
– Round conductive object -> another source of a (semi)spherical
wavefront (within a limited angle)
– Flat conductive object
-> reflection at a specific direction
Incoming planewave
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Reflection
• Dielectric surface
– Characterized by complex dielectric constant
Where 𝜖 is the dielectric constant, and 𝜎𝑒 is conductivity (relative
magnetic permeability is assumed to be 𝜇𝑟 = 1)
• Radiowave is partially reflected, partially transmitted
– Reflection angle is equal to the incidence angle Θ𝑟 = Θ𝑒
– Transmission angle is given by Snell’s law:
𝛿 = 𝜖 − 𝑗𝜎𝑒
2𝜋𝑓𝑐
sin(Θ𝑟)
sin (Θ𝑒)=
𝛿1
𝛿2
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Reflection
• The amplitude and phase of the reflected
and transmitted wave depend on
– Dielectric constants of the media
– Angle of incidence
– Polarization
• Example, concrete at 1 GHz
– 𝛿𝑟 = 7 − 𝑗0.85
Reflection and transmission from dielectric interface
(from A. F. Molisch, Wireless Communications, 2nd ed.)
0 10 20 30 40 50 60 70 80 90
-180
-90
0
e
arg
( )
(deg
)
TM
TE
0 10 20 30 40 50 60 70 80 900
0.2
0.4
0.6
0.8
1
e
| |
TM
TE
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Diffraction
• Radiowaves do propagate ”around the corner”
• Models exist for several typical cases
– Knife-edge – single or multiple (conductive) edges
– Lossy wedge
– Polarization also plays a role
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Diffraction
• The magnitude behind a single edge is given by
where 𝐹 𝑣𝐹 is the Fresnel integral, and the Fresnel
parameter is obtained by
𝜃𝑑
𝑑𝑅𝑥 𝑑𝑇𝑥 Tx Rx
Knife-edge 𝑣𝐹 = 𝜃𝑑
2𝑑𝑇𝑥𝑑𝑅𝑥
𝜆(𝑑𝑇𝑥+𝑑𝑅𝑥)
1
2−
exp𝑗𝜋4
2𝐹 𝑣𝐹
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Diffraction
• Example: Single Knife-edge
– Field strength at 1 GHz in a given point behind knife-edge
-10 0 10 20 30 40 500
5
10
15
20
25
30
x (m)
y (
m)
-25
-20
-15
-10
-5
0
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Scattering
• Wave interaction with ”rough” surfaces
– Sometimes ”roughness” in wireless channel modeling is also
used to describe irregularities in building structures e.g. bookshelves, windowsills etc.
𝜌𝑠𝑚𝑜𝑜𝑡ℎ 𝜌𝑟𝑜𝑢𝑔ℎ
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Scattering
• Example: Kirchoff theory of scattering from rough
surfaces
– Reflection coefficient is modified
as
– Where 𝜎ℎ is the standard deviation
of the height distribution
• Generalization for including spatial correlation and
”effective dielectric constant” exist (perturbation theory)
𝜌𝑟𝑜𝑢𝑔ℎ = 𝜌𝑠𝑚𝑜𝑜𝑡ℎ ∙ exp (−2 ∙2𝜋
𝜆𝜎ℎ sin Θ𝑒
2
)
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Waveguiding
• Typical description of propagation in e.g. street canyons,
corridors and tunnels
• Refers to both
– Theoretical waveguiding modes, specific to the shape and
dimension of the environment (while being in the order of
wavelength or so)
– Geometric optics approximation of waves being ”guided” along a
pathway
• Waveguiding may yield a path loss exponent smaller
than 2, i.e. that of free space propagation
– Typically irregularities and lossy materials increase attenuation
13.2.2012 Jussi Salmi
Physical propagation mechanisms:
Conclusion
• Free-space attenuation forms a baseline for path loss
modeling
– Frequency dependency is only due to assumption about the
antenna type!
• Material interactions may have frequency dependency
– Excluding reflection from a conductive surface…
– Material parameters as well as polarization have significant
influence on reflection, diffraction, scattering, waveguiding
13.2.2012 Jussi Salmi
Statistical Propagation Descriptions
• Path loss
• Shadow (slow) fading
• Small-scale (fast)fading
• Doppler
– This part is mostly based on:
L. J. Greenstein, A. F. Molisch, and M. Shafi, ”Propagation
issues for Cognitive Radio”, to appear in a book.
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Po
wer
(d
B)
Received power
Shadow fading
Median Path Gain
13.2.2012 Jussi Salmi
Statistical Propagation Descriptions:
Path Loss vs. Shadow Fading vs. Fast Fading
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Pow
er (
dB
)
Received signal strength (RSS)
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Pow
er (
dB
)
Received power
"Slow" fading
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Pow
er (
dB
)
Received power
Shadow fading
Median Path Gain
13.2.2012 Jussi Salmi
Statistical Propagation Descriptions:
Path Loss
• Power gain, 𝐺, of a radio link is defined as the average
power over
– The frequency interval of interest
𝐹 ∈ 𝑓𝑐 −𝑊
2, 𝑓𝑐 +
𝑊
2
of bandwidth 𝑊 around center frequency 𝑓𝑐
– The local spatial domain around the potential coordinates of the
Tx and Rx positions, denoted by 𝒙
• If either link end is fixed, no averaging over that local
neighbourhood is necessary
𝐺 = 𝐴𝑣𝑒𝒙1
𝑊 𝐻(𝑓, 𝒙) 2 𝑑𝑓𝐹
=𝐴𝑣𝑒𝒙1
𝑊 ℎ(𝜏, 𝒙, 𝐹) 2 𝑑𝜏𝜏
13.2.2012 Jussi Salmi
Statistical Propagation Descriptions:
Path Loss
• The impulse response can then be written as
– Where 𝐴𝑣𝑒𝒙1
𝑊 ℎ (𝜏, 𝒙, 𝐹)
2𝑑𝜏
𝜏= 1
• 𝐺 varies in large-scale manner, both in terms of – location (tens of wavelengths)
– frequency (hundreds of MHz)
• ℎ (𝜏, 𝒙, 𝐹) varies in small-scale, i.e., potentially within – fraction of the wavelength or
– within communication signal bandwidth (tens of MHz or smaller)
ℎ 𝜏, 𝒙, 𝐹 = 𝐺 ∙ ℎ (𝜏, 𝒙, 𝐹)
13.2.2012 Jussi Salmi
• Path loss (in dB) is defined as
𝐿 = −10 ∙ log 10(𝐺)
Statistical Propagation Descriptions:
Path Loss
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Po
wer
(d
B)
Received power
Shadow fading
Median Path Gain
101
102
103
55
60
65
70
75
80
85
90
95
100
Pat
h L
oss
(d
B)
Distance (m)
13.2.2012 Jussi Salmi
• A generic formula for the power gain of a wireless link:
– 𝑃𝑅 denotes average over signal BW and local area
– 𝑑0 is a reference distance, e.g. 1 m
– 𝑎 and 𝛾 are dimensionless model parameters
– For example, for free space path attenuation with 𝐺𝑅 = 𝐺𝑇 = 1:
𝐺(𝑑) =𝑃𝑅
𝑃𝑇~𝑎
𝑑
𝑑0
−𝛾
Statistical Propagation Descriptions:
Path Loss
𝑎 =𝜆
4𝜋𝑑0
2 and 𝛾 = 2
13.2.2012 Jussi Salmi
• Note that typically 𝛾 is greater than 2
– However, also 𝛾 < 2 is possible as mentioned, due to
waveguiding effects in some environments
• The above relation is not accurate for all distances
– Hence it should be rather treated as the median power gain:
𝐺(𝑑) ~𝑎𝑑
𝑑0
−𝛾
Statistical Propagation Descriptions:
Path Loss
𝐺𝑚𝑒𝑑 𝑑 = 𝑎𝑑
𝑑0
−𝛾
13.2.2012 Jussi Salmi
• A more accurate model can be achieved by
• Turning this into path loss in dB
– With 𝐴 = −10 ∙ log 10 𝑎 and 𝑆 = −10 ∙ log10 𝜉
– Hence we have: 𝑃𝐿𝑚𝑒𝑑 = 𝐴 + 𝛾 ∙ 10 ∙ log 10𝑑
𝑑0
Statistical Propagation Descriptions:
Path Loss
𝐺 𝑑 = 𝑎𝑑
𝑑0
−𝛾
∙ 𝜉 = 𝐺𝑚𝑒𝑑 𝑑 ∙ 𝜉
𝐿 𝑑 = 𝐴 + 𝛾 ∙ 10 ∙ log 10𝑑
𝑑0+ 𝑆
(𝐿 = −10 ∙ log 10(𝐺))
13.2.2012 Jussi Salmi
• An example of a model for the median path loss is the
Hata-Okumura
– Urban environment, user terminal at 1.5 m, and 𝑑0=1.5 km, and
base station height ℎ𝑏 (in m), carrier frequency 𝑓𝑐 (in MHz)
• The frequency dependency stems partly from aperture effect and
partly due to diffraction loss increasing with frequency
Statistical Propagation Descriptions:
Path Loss
𝑃𝐿_𝑚𝑒𝑑 = 𝐴 + 𝛾 ∙ 10 ∙ log 10𝑑
𝑑0
𝐴 = 69.55 + 26.16 ∙ log10 𝑓𝑐 − 13.82 ∙ log10 ℎ𝑏
𝛾 = 4.49 − 0.655 ∙ log10 ℎ𝑏
13.2.2012 Jussi Salmi
• The variable 𝑆 represents random variation about the
median path loss
• Empirical studies have indicated that 𝑆 (in dB) is best
modeled as a zero mean normal distributed RV
– with the standard deviation 𝜎𝑠 depending on the environment
Statistical Propagation Descriptions:
Shadow Fading
𝐿 𝑑 = 𝐴 + 𝛾 ∙ 10 ∙ log 10𝑑
𝑑0+ 𝑆
𝑆~𝑁(0, 𝜎𝑆2)
13.2.2012 Jussi Salmi
• The term shadow fading stems from history of cellular
network modeling, as buldings were ”shadowing” the
signal between BS and MS
Statistical Propagation Descriptions:
Shadow Fading
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Pow
er (
dB
)
Received power
Shadow fading
Median Path Gain
101
102
103
-5
-4
-3
-2
-1
0
1
2
3
4
5
Sh
ado
w f
adin
g (
dB
)
Distance (m)
13.2.2012 Jussi Salmi
• Typical values for 𝜎𝑆 range between 3-12 dB
• Spatial correlation and dynamics of shadowing are less
studied
– These would be useful for localization modeling purposes too!
• One potential model is given by
– Where 𝑋𝑐 is so-called correlation distance of shadow fading
• Values can range from 10 m in urban microcells to 500 m in rural
macrocells
– Often too simple, but easy to implement via an AR(1) process
Statistical Propagation Descriptions:
Shadow Fading
𝜌 Δ𝑥 = 𝑆 𝑥 𝑆(𝑥 + Δ𝑥) = 𝜎𝑆2 ∙ exp (−
Δ𝑥
𝑋𝑐)
13.2.2012 Jussi Salmi
• Recall
– With 𝐺 𝑑 = 10−𝑃𝐿𝑚𝑒𝑑+𝑆
10 and 𝐴𝑣𝑒𝒙1
𝑊 ℎ (𝜏, 𝒙, 𝐹)
2𝑑𝜏
𝜏= 1
Statistical Propagation Descriptions:
Small-scale Fading
101
102
103
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
Distance (m)
Pow
er (
dB
)
Received power
Shadow fading
Median Path Gain
0 100 200 300 400 500 600 700 800 900 1000-25
-20
-15
-10
-5
0
5
10
15
Distance (m)
Pow
er (
dB
)
Fast fading
ℎ 𝜏, 𝒙, 𝐹 = 𝐺 ∙ ℎ (𝜏, 𝒙, 𝐹)
|ℎ (𝜏, 𝒙, 𝐹)|
13.2.2012 Jussi Salmi
• Demo for WLAN 802.11g
– 20 MHz, 52 OFDM subcarriers
– 10 random reflectors + LOS, Rx moves at 1 m/s
Statistical Propagation Descriptions:
Small-scale Fading
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 10 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20lo
g 10(|
H(f
)|)
(dB
)
13.2.2012 Jussi Salmi
• ”Ideal” model was used, where the channel is given by
where 𝑑𝑝denotes the path length of the pth multipath component
Statistical Propagation Descriptions:
Small-scale Fading
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 10 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20lo
g 10(|
H(f
)|)
(dB
)
ℎ 𝑓, 𝑡 = 𝑑𝑝−1exp (−𝑗2𝜋
𝑓
𝑐𝑑𝑝)
𝑝
13.2.2012 Jussi Salmi
• Demo for WLAN 802.11g
– 20 MHz, 52 OFDM subcarriers
– 10 random reflectors + LOS, Rx moves at 1 m/s
Statistical Propagation Descriptions:
Small-scale Fading
0 2 4 6 8 10
5
10
15
20
25
30
35
40
45
50
Time (s)
Subca
rrie
r in
dex
-50
-45
-40
-35
-30
-25
-20
0 2 4 6 8 10-55
-50
-45
-40
-35
-30
-25
-20
-15
Time (s)
20lo
g 10(|
H(f
)|)
(dB
)
13.2.2012 Jussi Salmi
• Small-scale fading results from the constructive and
destructive interplay of signal arrivals via different paths,
i.e., multipath propagation
Statistical Propagation Descriptions:
Small-scale Fading
The phase of the signal at
reception point depends on
the path length and
interactions, e.g. phase
change during reflection etc.
13.2.2012 Jussi Salmi
• Special case: Rayleigh fading
– Signal is a superposition from many multipath components (MPCs)
with similar magnitude -> Central limit theory applies, and the
signal can be modeled as a complex Gaussian
– Phase has uniform pdf over (−𝜋, 𝜋], and magnitude 𝑟 has a
Rayleigh pdf:
where σ is the standard deviation of the underlying Gaussian process
Statistical Propagation Descriptions:
Small-scale Fading
𝑝𝑑𝑓 𝑟 =𝑟
𝜎2 ⋅ exp −𝑟2
2𝜎2 0 ≤ 𝑟 < ∞
13.2.2012 Jussi Salmi
• Rayleigh fading cont.
– The squared magnitude 𝑝 of a Rayleigh fading has a decaying
exponential pdf:
where 𝑝 𝑟 = 2𝜎2 is the mean power (local spatial average)
– Dynamic range between the 1st and 99th percentile is 26.6 dB!
• Fading at a given frequency can be very significant!
Statistical Propagation Descriptions:
Small-scale Fading
𝑝𝑑𝑓 𝑝 =1
𝑝 𝑟⋅ exp −
𝑝
𝑝 𝑟 0 ≤ 𝑝 < ∞
13.2.2012 Jussi Salmi
• The spread of the multipaths influences the ”fastness” of
the fading
– If MPCs arrive at similar directions, fading is not that ”fast”
– ”Fastest” fading occurs when MPC arrive from all directions
Statistical Propagation Descriptions:
Small-scale Fading
13.2.2012 Jussi Salmi
• Examples: 100 reflectors, evenly spread
Statistical Propagation Descriptions:
Small-scale Fading
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 10 s
0 1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
r
Empirical
Rayleigh
13.2.2012 Jussi Salmi
• Examples: 10 reflectors, randomly spread
Statistical Propagation Descriptions:
Small-scale Fading
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 10 s
0 1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
r
Empirical
Rayleigh
13.2.2012 Jussi Salmi
• Examples: 10 reflectors, in similar direction, no LOS
Statistical Propagation Descriptions:
Small-scale Fading
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 10 s
0 1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
r
Empirical
Rayleigh
13.2.2012 Jussi Salmi
• Notes about Rayleigh distribution
– Excellent approximation in a large number of scenarios
• However, many scenarios exists (LOS etc.) where Rayleigh fails
– Depends on a single parameter – the mean received power – only
– Mathematically convenient: Often enables analytical analysis in
closed form
– Spatial (temporal) correlation needs to be modelled separately
Statistical Propagation Descriptions:
Small-scale Fading
13.2.2012 Jussi Salmi
• More general case: Ricean fading
– The magnitude distribution is modelled Ricean, if there is a
dominant component with power 𝑝 𝑑
– Given total average received power 𝑝 𝑟, the average power of the
weaker components is 𝑝 𝑠 = 𝑝 𝑟 − 𝑝 𝑑
– The Ricean K factor is defined as the ratio
and the pdf of the received amplitude is defined as:
Statistical Propagation Descriptions:
Small-scale Fading
𝐾 =𝑝 𝑑𝑝 𝑠
𝑝𝑑𝑓 𝑟 = 2𝑟exp (−𝐾)
𝑝 𝑠⋅ exp −
𝑟2
𝑝 𝑠⋅ 𝐼0
4𝑟2𝐾
𝑝 𝑠
13.2.2012 Jussi Salmi
• Ricean fading cont.
– 𝐾 = 0 equals Rayleigh
– For large K, approximates
to Gaussian distribution
• Mean depends on the
dominant component
• Spread depends on the
variance of the weaker
components
– 𝐾 = ∞, single component,
i.e. no fading (amplitude is
deterministic)
Statistical Propagation Descriptions:
Small-scale Fading
0 1 2 3 4 5 6 7 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
pd
f
r
K=0
K=1
K=10
13.2.2012 Jussi Salmi
• Notes about Ricean distribution
– Also the phase of the Ricean signal has a non-uniform distribution
– Ricean fading model is a good example of a mathematical tool
whose invention had no relation to wireless systems
• Solution to the problem of having deterministic phasor added to a
zero-mean complex Gaussian distribution
Statistical Propagation Descriptions:
Small-scale Fading
13.2.2012 Jussi Salmi
• Another popular fading model is the Nakagami distribution
– Does not have as clear physical interpretation
– Has been succesfully fitted to numerous empirical data
– Parameterized by the Nakagami m-factor, defined as
Statistical Propagation Descriptions:
Small-scale Fading
𝑚 =𝑝 𝑟2
< 𝑟2 − 𝑝 𝑟2 >
13.2.2012 Jussi Salmi
• The aforementioned description of small scale fading is
related to spatial domain
– Channel variations only occur if there is movement
• Temporal variation is a result of physical motion in the
environment
– If nothing in the propagation environment is varying – the channel
is constant
Statistical Propagation Descriptions:
Doppler
13.2.2012 Jussi Salmi
• Considering the simulation model introduced earlier
– Complex bandpass signal (phase only) of a single path
– After downconversion (e.g. multiplied by exp −𝑗2𝜋𝑓𝑐𝑡 )
Statistical Propagation Descriptions:
Doppler
𝑓𝑐
ℎ𝑝,𝑏𝑝 𝑓, 𝑡 = exp 𝑗2𝜋𝑓(𝑡 − 𝜏𝑝) = exp(𝑗2𝜋(𝑓𝑐 + Δ𝑓)(𝑡 − 𝜏𝑝))
With 𝜏𝑝 =𝑑𝑝
𝑐 and 𝑓 = 𝑓𝑐 + Δ𝑓
ℎ𝑝,𝑙𝑝 𝑓, 𝑡 = exp 𝑗2𝜋 𝑓𝑐 + Δ𝑓 𝑡 − 𝜏𝑝 exp −𝑗2𝜋𝑓𝑐𝑡
= exp (−𝑗2𝜋 𝑓𝑐𝜏𝑝 − Δ𝑓𝑡 + Δ𝑓𝜏𝑝 )
13.2.2012 Jussi Salmi
– After ”equalization”, e.g. multiplying by exp −𝑗2𝜋Δ𝑓𝑡 , the single
path phase term reduces to
– On the other hand, if something is moving, then
𝜏𝑝 = 𝜏𝑝 𝑡 =𝑑𝑝(𝑡)
𝑐=
𝑑𝑝(0)
+ 𝑣𝑝,𝑟 ⋅ 𝑡
𝑐
• Where 𝑣𝑝,𝑟 denotes the relative velocity, i.e., the rate of change of the
path length (depends on the direction of signal vs. that of motion etc.)
– A couple ways to proceed from here…
Statistical Propagation Descriptions:
Doppler
ℎ𝑝 𝑓, 𝑡 = exp (−𝑗2𝜋 𝑓𝑐𝜏𝑝 + Δ𝑓𝜏𝑝 )
13.2.2012 Jussi Salmi
• Approach #1:
• Approach #2:
Statistical Propagation Descriptions:
Doppler
ℎ𝑝 𝑓, 𝑡 = exp −𝑗2𝜋 𝑓𝜏𝑝 = exp −𝑗2𝜋 𝑓𝑑𝑝
(0)+ 𝑣𝑝,𝑟 ⋅ 𝑡
𝑐
= exp(−𝑗2𝜋 𝑓 ⋅ 𝜏𝑝0 +
𝑣𝑝,𝑟
𝑐𝑓 ⋅ 𝑡
A initial phase Doppler frequency
ℎ𝑝 𝑓, 𝑡 = exp −𝑗2𝜋 𝑓𝑐𝜏𝑝 + Δ𝑓𝜏𝑝
= exp −𝑗2𝜋 𝑓𝑐 ⋅ 𝜏𝑝0 +
𝑣𝑝,𝑟
𝑐𝑓𝑐 ⋅ 𝑡 exp −𝑗2𝜋 Δ𝑓𝜏𝑝
Only model Doppler here
Doppler w.r.t. carrier only (or Δ𝑓 = 0) A initial phase (at the carrier)
13.2.2012 Jussi Salmi
• The former loses the notion of absolute delay, i.e., path
length over time
– However, Doppler may be infered from frequency samples
• The latter maintains parameterization of the absolute
delay as well
– Doppler estimation requires sampling over time
Statistical Propagation Descriptions:
Doppler
13.2.2012 Jussi Salmi
• Real wireless channel comprises of many paths
– Each path has unique Doppler (depends on the relative velocity,
i.e. the direction of signal vs. movement)
– The paths have different amplitudes
– Other aspects influence the phase (evolution) as well, such as
material interactions)
• All this supports Doppler to be described as a spectrum
Statistical Propagation Descriptions:
Doppler Spectrum
13.2.2012 Jussi Salmi
• Example from the simulator (𝑓𝑐 = 2.4 GHz)
– 𝑣𝑚𝑎𝑥 = 1 m/s ⇒ 𝑓𝐷,𝑚𝑎𝑥 =𝑣𝑚𝑎𝑥
𝑐𝑓𝑐 = 8 Hz
– 100 reflectors randomly placed
Statistical Propagation Descriptions:
Doppler Spectrum
-80 -60 -40 -20 0 20 40 60 80
-80
-60
-40
-20
0
20
40
60
80
x (m)
y (
m)
Time: 10 s
-10 -5 0 5 10-20
-15
-10
-5
0
5
10
15
20
fD
(Hz)
PS
D
13.2.2012 Jussi Salmi
• Example from the simulator (𝑓𝑐 = 2.4 GHz)
– 𝑣𝑚𝑎𝑥 = 1 m/s ⇒ 𝑓𝐷,𝑚𝑎𝑥 =𝑣𝑚𝑎𝑥
𝑐𝑓𝑐 = 8 Hz
– 10 reflectors randomly placed
Statistical Propagation Descriptions:
Doppler Spectrum
-80 -60 -40 -20 0 20 40 60
-60
-40
-20
0
20
40
60
x (m)
y (
m)
Time: 10 s
-10 -5 0 5 10-35
-30
-25
-20
-15
-10
-5
0
5
fD
(Hz)
PS
D
13.2.2012 Jussi Salmi
• Example from the simulator (𝑓𝑐 = 2.4 GHz)
– 𝑣𝑚𝑎𝑥 = 1 m/s ⇒ 𝑓𝐷,𝑚𝑎𝑥 =𝑣𝑚𝑎𝑥
𝑐𝑓𝑐 = 8 Hz
– 100 reflectors on a circle with equal amplitudes
Statistical Propagation Descriptions:
Doppler Spectrum
-80 -60 -40 -20 0
-50
-40
-30
-20
-10
0
10
20
30
40
x (m)
y (
m)
Time: 10 s
-10 -5 0 5 1020
25
30
35
40
45
50
55
fD
(Hz)
PS
D
13.2.2012 Jussi Salmi
• The Doppler power spectrum depends on the movement,
and direction distribution of the signal components
• A classical example is the Clarke-Jakes spectrum, which
is the case when signals arrive uniformly from all
directions (on the plane) at equal amplitudes
– As seen from the
previous examples,
this rarely holds
Statistical Propagation Descriptions:
Doppler Spectrum
-10 -5 0 5 10-30
-20
-10
0
10
20
fD
(Hz)
PS
D (
dB
)
-10 -5 0 5 100
2
4
6
8
10
12
fD
(Hz)
PS
D (
lin
ear)
𝑆𝑑 𝑓𝐷 =𝑝 𝑟
𝜋 𝑓𝐷,𝑚𝑎𝑥2 − 𝑓𝐷
2
13.2.2012 Jussi Salmi
• The Fourier transform of the Doppler Spectrum is the auto-correlation
function (ACF)
– Assuming stationary movement and uniform angular distribution on
horizontal plane, the ACF for the Jakes spectrum is
– Different ACF can be derived for
different angular distributions
such as von Mises distribution,
see e.g.
Statistical Propagation Descriptions:
Doppler Spectrum
𝐴𝐶𝐹 Δ𝑡 = 𝐽0(2𝜋𝑓𝐷,𝑚𝑎𝑥Δ𝑡)
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
d/
AC
F
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.5
1
t (s) (vmax
= 1 m/s)
AC
F
Small scale fading
decorrelated at 0.4𝜆
J. Salmi, et al., "Incorporating diffuse scattering
in geometry-based stochastic MIMO channel
models," EUCAP 2010.
13.2.2012 Jussi Salmi
• Modeling the K-factor (for Ricean fading) or m-factor
(Nagakami fading) is sufficient for statistical
characterization of the small scale fading
– Doppler spectrum and related ACF provide means for modeling
spatial correlation
• Combined with path loss modeling (including shadowing)
one can have a complete statistical description for
independent channel realizations
– Also spatial correlation of shadowing is of interest
Statistical Propagation Descriptions:
Conclusion
13.2.2012 Jussi Salmi
Deterministic Propagation Abstractions
• Signal Bandwidth and Duration
• Tapped Delay Line Model
• Double Directional Propagation Modeling
– Description of the channel through the (deterministic) geometry
13.2.2012 Jussi Salmi
Deterministic Propagation Abstractions:
Signal Bandwidth and Duration • Signal bandwidth and duration play important role in wireless
channel estimation
– Hence, they are also crucial for e.g. time-of-arrival based positioning
systems
From A. F. Molisch, Wireless Communications, 2nd ed., Wiley 2011
Wideband system Narrowband system
13.2.2012 Jussi Salmi
• WLAN example cont. – Nc = 52, W=(52-1)/64*20 MHz, fc= 2.4 GHz
– Δ𝑓 =𝑊
𝑁𝑐= 312.5 kHz
– 𝜏𝑚𝑎𝑥 =1
Δ𝑓= 3.2 μs 3.2 ⋅ 10−6 s
– Δ𝜏 =𝜏𝑚𝑎𝑥
𝑁𝑐=
1
𝑊≈ 63 ns (63 ⋅ 10−9 s)
• Translated to propagation distance
– Δ𝑥 = Δ𝜏 ⋅ 𝑐 ≈ 19 m
– 𝑥𝑚𝑎𝑥 = 𝜏𝑚𝑎𝑥 ⋅ 𝑐 ≈ 960 m
Deterministic Propagation Abstractions:
Signal Bandwidth and Duration
2400 2402 2404 2406 2408 2410 2412 2414 2416 2418 24200
0.5
1
|H(f
)|
2400 2402 2404 2406 2408 2410 2412 2414 2416 2418 2420-1
0
1
arg
(H(f
))
Frequency (MHz)
0 2 4 6 8 10 120
0.5
1
Delay (s)
Re/
Im
Re
Im
13.2.2012 Jussi Salmi
• WLAN example cont., number of carriers fixed, smaller bandwidth – Nc = 52, W=(52-1)/64* 5 MHz, fc= 2.4 GHz
– Δ𝑓 =𝑊
𝑁𝑐= 78.125 kHz
– 𝜏𝑚𝑎𝑥 =1
Δ𝑓= 12.8 μs
– Δ𝜏 =𝜏𝑚𝑎𝑥
𝑁𝑐=
1
𝑊≈ 246 ns
• Translated to propagation distance
– Δ𝑥 = Δ𝜏 ⋅ 𝑐 ≈ 74 m
– 𝑥𝑚𝑎𝑥 = 𝜏𝑚𝑎𝑥 ⋅ 𝑐 ≈ 3.84 km
2400 2402 2404 2406 2408 2410 2412 2414 2416 2418 24200
0.5
1
|H(f
)|
2400 2402 2404 2406 2408 2410 2412 2414 2416 2418 2420-1
0
1
arg
(H(f
))
Frequency (MHz)
0 2 4 6 8 10 120
0.5
1
Delay (s)
Re/
Im
Re
Im
Deterministic Propagation Abstractions:
Signal Bandwidth and Duration
13.2.2012 Jussi Salmi
• WLAN example cont. – Nc = 52, W=(52-1)/64* 20 MHz, fc= 2.4 GHz
– 3 paths: LOS (51 m), S1 (175 m), S2 (280 m)
-100 -50 0 50 100-100
-50
0
50
100
x (m)
y (
m)
Time: 20 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20lo
g 10(|
H(f
)|)
(dB
)
0 200 400 600 800-100
-80
-60
-40
-20
0
Path length, x (m)2
0lo
g 10(|
h(x
)|)
(dB
)
Δ𝑥 = Δ𝜏 ⋅ 𝑐 ≈ 19 m
Deterministic Propagation Abstractions:
Signal Bandwidth and Duration
13.2.2012 Jussi Salmi
• WLAN example cont. – Nc = 52, W=(52-1)/64* 5 MHz, fc= 2.4 GHz
– The same 3 paths: LOS (51 m), S1 (175 m), S2 (280 m)
-100 -50 0 50 100-100
-50
0
50
100
x (m)
y (
m)
Time: 20 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20lo
g 10(|
H(f
)|)
(dB
)
0 1000 2000 3000-100
-80
-60
-40
-20
0
Path length, x (m)
20lo
g 10(|
h(x
)|)
(dB
)
Δ𝑥 = Δ𝜏 ⋅ 𝑐 ≈ 74 m
Deterministic Propagation Abstractions:
Signal Bandwidth and Duration
13.2.2012 Jussi Salmi
• WLAN example cont. – Nc = 52, W=(52-1)/64* 20 MHz, fc= 2.4 GHz
– 2 paths with path lengths: d1=140 m, d2= 1230 m
• The longer path gets aliased and is falsely observed at 1230 m -960 m = 270 m with
the 20 MHz channel!
-100 -50 0 50 100
-600
-500
-400
-300
-200
-100
0
100
x (m)
y (
m)
Time: 20 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20
log 1
0(|
H(f
)|)
(dB
)
0 200 400 600 800-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
Path length, x (m)
20
log 1
0(|
h(x
)|)
(dB
)
No window
Hann window
𝑥𝑚𝑎𝑥 = 𝜏𝑚𝑎𝑥 ⋅ 𝑐 ≈ 960 m
-100 -50 0 50 100
-600
-500
-400
-300
-200
-100
0
100
x (m)
y (
m)
Time: 20 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20
log 1
0(|
H(f
)|)
(dB
)
0 1000 2000 3000-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
Path length, x (m)
20
log 1
0(|
h(x
)|)
(dB
)
No window
Hann window
20 MHz channel 5 MHz channel
Deterministic Propagation Abstractions:
Signal Bandwidth and Duration
13.2.2012 Jussi Salmi
• If a bandlimited 𝑓𝑐 −𝑊
2, 𝑓𝑐 +
𝑊
2 signal passes through a
number of paths with complex gains 𝑎𝑝 at delays 𝜏𝑝, the
channel impulse response is mathematically given by
– 𝜉 𝑥 = 𝑊 ⋅ sinc(𝑥) is
called interpolation
function with null-to-null
width 2/W
– Note that 𝜏𝑝 may be
irregularly spaced -100 -50 0 50 100-100
-50
0
50
100
x (m)
y (
m)
Time: 20 s
0 200 400 600 800 1000-15
-10
-5
0
5x 10
-3
Path length, x (m)
h(
)
Re
Im
ℎ 𝜏 = 𝑎𝑝 ⋅ 𝜉 𝜏 − 𝜏𝑝
𝑃
𝑝=1
Deterministic Propagation Abstractions:
Tapped Delay Line Model
13.2.2012 Jussi Salmi
• If 𝑊𝜏𝑃,𝑚𝑎𝑥 ≪ 1 ⇔ 𝜏𝑃,𝑚𝑎𝑥 ≪1
𝑊= Δ𝜏, the channel is flat
fading
• If 𝑊𝜏𝑃,𝑚𝑎𝑥 > 1, channel consists of several ”delay
resolution bins”, channel is considered wideband
• Sampling at 1
𝑊= Δ𝜏 interval yields tapped delay line as
– Where
ℎ 𝜏 = 𝑐𝑚 ⋅ 𝜉 𝜏 − 𝑚 ⋅ Δ𝜏
𝑀
𝑚=1
𝑐𝑚 = 𝑎𝑝 ⋅ 𝜉 𝑚 ⋅ Δ𝜏 − 𝜏𝑝𝑝
Deterministic Propagation Abstractions:
Tapped Delay Line Model
13.2.2012 Jussi Salmi
• Time varying tapped delay line
– The coefficients 𝑐𝑚(𝑡) are typically fading
• They are comprised of a superposition of multipaths
– However, the path coefficients 𝑎𝑝 𝑡 = 𝑎𝑝 𝑡 ⋅ exp 𝑗𝜙𝑝 𝑡 do
not suffer from multipath fading
ℎ 𝜏, 𝑡 = 𝑐𝑚 𝑡 ⋅ 𝜉 𝜏 − 𝑚 ⋅ Δ𝜏
𝑀
𝑚=1
𝑐𝑚 𝑡 = 𝑎𝑝 𝑡 ⋅ 𝜉 𝑚 ⋅ Δ𝜏 − 𝜏𝑝𝑝
Deterministic Propagation Abstractions:
Tapped Delay Line Model
13.2.2012 Jussi Salmi
• Demo: Comparison of a few well distinct paths vs. dense
multipath environment
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 20 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20lo
g 10(|
H(f
)|)
(dB
)
0 200 400 600 800-100
-90
-80
-70
-60
-50
-40
-30
Path length, x (m)
20lo
g 10(|
h(x
)|)
(dB
)
No window
Hann window
𝜏𝑖 − 𝜏𝑗 > Δ𝜏
𝜏𝑖 − 𝜏𝑗 < Δ𝜏
-100 -50 0 50 100-100
-80
-60
-40
-20
0
20
40
60
80
100
x (m)
y (
m)
Time: 20 s
2395 2400 2405 2410 2415 2420-70
-60
-50
-40
-30
-20
-10
0
Frequency (MHz)
20
log 1
0(|
H(f
)|)
(dB
)
0 200 400 600 800-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
Path length, x (m)
20
log 1
0(|
h(x
)|)
(dB
)
No window
Hann window
Deterministic Propagation Abstractions:
Tapped Delay Line Model
13.2.2012 Jussi Salmi
Power Delay Profile, RMS Delay Spread
and Frequency Correlation • Power Delay profile (PDP) and the RMS delay spread (DS)
– Evaluation using sinc interpolator for ℎ 𝑡, 𝜏 (rectangular window in
frequency domain) may not be wise
• sinc2 has discontinuous derivative, and the second central moment does
not converge
– Frequency correlation function (FCF) is given by the Fourier transform
of the PDP
• Coherence bandwidth is inversely proportional to 𝜏𝑟𝑚𝑠 (exact value depends
on the PDP shape)
𝑃 𝜏 =1
𝑊𝐸𝑡 ℎ 𝑡, 𝜏 2 𝜏𝑟𝑚𝑠 = 𝑃 𝜏 𝜏2𝑑𝜏
∞
0
− 𝑃 𝜏 𝜏𝑑𝜏∞
0
2
13.2.2012 Jussi Salmi
Summary of System vs. Correlation
Functions and Their Special Cases
From R. Katterbach, Characterisierung zeitvarianter Indoor Mobilfunkkanäle mittels ihrer System- und Korrelationsfunktionen, Dissertation an der Universität GhK Kassel, Aachen 1997. Here copied from A. F. Molisch, Wireless Communications, 2nd ed., Wiley 2011.
These relations hold for WSSUS (ercodig) channel, i.e., defining correlation functions w.r.t. time and frequency differences only.
Deterministic Propagation Abstractions:
Double Directional Propagation Path Model
• Description of the radiowave
propagation between two
points in space as a
superposition of discrete
”paths”
– Going ”behind” the tapped
delay line
– Independent of the application
(may depend on frequency)
• Mapping those paths into a
MIMO Channel transfer
function between the input and
output ports
– System specific
13.2.2012 Jussi Salmi
Influence of the Tx and Rx
- Obtained by calibration
Influence of the antennas
- Calibration and parametric model required
Propagation channel parameters
- Depend only on the channel itself
)(),(),()()()(1
,,
T
,,
,,
,, fGafGf T
P
p
pTpTT
pVVpHV
pVHpHH
pRpRRpfR
AAH
Deterministic Propagation Abstractions:
Double Directional Propagation Path Model
Jussi Salmi
P
p
pTpTTpRpRRpf fffaf1
,,
T
,, ),,()(),,()()( AΓAH
• Narrowband model
– Antenna responses and RF interactions (electric properties of interacting
materials) are constant within the signal band
• (Semi-)wideband model
– Antenna responses are frequency dependent
• Obtained by calibration (or analytically)
– Frequency dependency of RF interactions?
• More difficult and complex to model
P
p
pTpTT
pVVpHV
pVHpHH
pRpRRpfaf1
,,
T
,,
,,
,, ),(),()()(
AAH
Deterministic Propagation Abstractions:
Double Directional Propagation Path Model
Jussi Salmi
• Double directional model (DDM) vs. tapped delay line (TDL)
– Typically TDL is unable to resolve individual path components, i.e.,
each tap, or delay bin is a superposition of many and thus fading
– DDM can resolve individual paths as long as they differ in at least one
of the parameter dimensions, i.e., Rx direction, Tx direction, or delay
P
p
pTpTTpRpRRpf fffaf1
,,
T
,, ),,()(),,()()( AΓAH
ℎ 𝜏 = 𝑐𝑚 ⋅ 𝜉 𝜏 − 𝑚 ⋅ Δ𝜏
𝑀
𝑚=1
Deterministic Propagation Abstractions:
Double Directional Propagation Path Model
Jussi Salmi
• Tensor formulation (narrowband) RTf MMM
CH
)2jexp()()( fa f
f
– are the antenna responses, modeled
by e.g., the EADF (or analytically)
– is the delay-dependent phase shift of
each frequency
– is the complex path weight, i.e.,
attenuation and phase
),(),,( )()(
TT
T
tRR
R
r aa
jja ee
)(),(),(}{ )()()(
,, f
fTT
T
tRR
R
rrtfS aaa H
Deterministic Propagation Abstractions:
Double Directional Propagation Path Model
Jussi Salmi
• Measurement model may also include stochastic
component for diffuse scattering and noise
Superposition of specular-like
propagation paths
Diffuse scattering
),(~ DD RNH C 0
Measurement noise
)( 2,~ INH C 0N
RTf MMM
NDS
CHHHH
'
1'
',',
)(
',',
)(
'
)(
' )( ),(),()(P
p
pRpR
R
pTpT
T
p
f
pS aaa H
Deterministic Propagation Abstractions:
Double Directional Propagation Path Model
Jussi Salmi
Property SC DMC
Fading type N/A Rayleigh
% of power indoors 10-50 50-90
% power outdoors 20-80 20-80
Suitable representation Discrete delta-functions Continuous power distribution
DMC – Dense Multipath Component*
Jussi Salmi
• Bandwidth and signal duration (as well as other
measurement system ”apertures”) influence how the
wireless medium is perceived
– Delay resolution is inversely proportional to bandwidth and
frequency interval is inversely proportional to ”delaywidth”
• Same principles could be applied to directional perceivance
• Double directional propagation path modeling can
resolve paths beyond tapped delay line
– Resolvability in any dimension suffices
Jussi Salmi
Deterministic Propagation Abstractions:
Conclusion
Application Example:
Real-Time UWB MIMO Radar Testing
• Was conducted in September 2011 at USC, Los Angeles
Jussi Salmi
Application Example:
Real-Time UWB MIMO Radar Testing
Jussi Salmi
• Multitone (OFDM-like) sounding signal was employed
Application Example:
Real-Time UWB MIMO Radar Testing
Jussi Salmi
• The signal can be thought of as a training sequence in
communications
– In fact, a measured template of the signal is used as a reference
• The channel frequency response (CFR) is obtained
through channel estimation
• The CFR can be used for estimating the double
directional propagation path parameters, providing delays
and angles
– Also PDP, Power-angular-delay profiles (PADP), or Doppler
spectrum analysis can be done for the CFRs
– These can be used for passive localization, human detection etc.
Application Example:
Real-Time UWB MIMO Radar Testing
Jussi Salmi
• Interleaved rectangular UWB array, University of
Southern California
– Planar monopole design
– 2-7 GHz
Application Example:
Real-Time UWB MIMO Radar Testing
13.2.2012 Jussi Salmi
2.5 GHz
5.5 GHz
7.5 GHz
Application Example:
Real-Time UWB MIMO Radar Testing
13.2.2012 Jussi Salmi
Application Example:
Real-Time UWB MIMO Radar Testing
• Two balls swinging in
mid-air couple meters
from the radar
• Video
13.2.2012 Jussi Salmi
• Example of two
persons breathing
side-by-side
Application Example:
Real-Time UWB MIMO Radar Testing
13.2.2012 Jussi Salmi
Notes About the Measurements
• System can observe a human moving within a room
(potentially behind obstacles, or a wall)
– Relies on the double directional wideband model
– Goal would be to detect the precense and estimate location
passively, potentially even observe vital signs such as breathing
• Spherical modeling for the wideband array is being
developed
– Potential for increased resolution in the near field
– Will UWB radar be the next ”Kinetic”?
13.2.2012 Jussi Salmi
• M. Z. Win, A. Conti, S. Mazuelas, Y. Shen, W. M. Gifford, and D. Dardari, “Network localization and navigation via cooperation,” IEEE Commun. Mag., vol. 49, no. 5, pp. 56–62, May 2011.
• D. Dardari, A. Conti, U. J. Ferner, A. Giorgetti, and M. Z. Win, “Ranging with ultrawide bandwidth signals in multipath environments,” Proc. IEEE, vol. 97, no. 2, pp. 404–426, Feb. 2009, special issue on Ultra-Wide Bandwidth (UWB) Technology & Emerging Applications, Invited Paper.
• H. Wymeersch, J. Lien, and M. Z. Win, “Cooperative localization in wireless networks,” Proc. IEEE, vol. 97, no. 2, pp. 427–450, Feb. 2009, special issue on Ultra-Wide Bandwidth (UWB) Technology & Emerging Applications, Invited Paper.
13.2.2012 Jussi Salmi
Some Other Research on UWB-based
Localization
Conclusions for Propagation Modeling
from Localization Perspective • Several propagation mechanisms have influence on the
wireless channel – Understanding propagation is crucial for interpreting the channel
properties
• Statistical models are important especially for Received Signal Strength (RSS) –based localization
• Deterministic models can be used to enhance delay (ToA) or direction (AoA) based localization – Bandwidth has significant influence
13.2.2012 Jussi Salmi
Main References
• A. F. Molisch, Wireless Communications, 2nd ed., Wiley 2011.
• L. Greenstein, A. F. Molisch, M. Shafi, ”Propagation issues for Cognitive Radio”,
to appear in a book
– See meanwhile: A.F. Molisch, L.J. Greenstein, M. Shafi, , "Propagation Issues for Cognitive Radio,"
Proceedings of the IEEE , vol.97, no.5, pp.787-804, May 2009.
• J. Salmi, A. F. Molisch,, "Propagation Parameter Estimation, Modeling and
Measurements for Ultrawideband MIMO Radar," IEEE Transactions on Antennas
and Propagation, vol.59, no.11, pp.4257-4267, Nov. 2011.
– Upcoming: S. Sangodoyin, J. Salmi, S. Niranjayan, A. F. Molisch, ”Real-Time Ultrawideband
MIMO Channel Sounding”, EuCAP 2012, Prague, Mar. 2012.
13.2.2012 Jussi Salmi