Radio Propagation

1
Radio Propagation

• CSCI 694
• 24 September 1999
• Lewis Girod

2
Outline

• Introduction and terminology
• Propagation mechanisms
• Propagation models

3
What is Radio?

• Radio Xmitter induces EM fields
• Electrostatic field components µ 1/d3
• Induction field components µ 1/d2
• Radiation field components µ 1/d
• Radiation field has E and B component
• Field strength at distance d E?B µ 1/d2
• Surface area of sphere centered at transmitter

4
General Intuition

• Two main factors affecting signal at receiver
• Distance (or delay) ? Path attenuation
• Multipath ? Phase differences

Green signal travels 1/2? farther than Yellow to
reach receiver, who sees Red. For 2.4 GHz, ?
(wavelength) 12.5cm.
5
Objective

• Invent models to predict what the field looks
  like at the receiver.
• Attenuation, absorption, reflection,
  diffraction...
• Motion of receiver and environment
• Natural and man-made radio interference...
• What does the field look like at the receiver?

6
Models are Specialized

• Different scales
• Large scale (averaged over meters)
• Small scale (order of wavelength)
• Different environmental characteristics
• Outdoor, indoor, land, sea, space, etc.
• Different application areas
• macrocell (2km), microcell(500m), picocell

7
Outline

• Introduction and some terminology
• Propagation Mechanisms
• Propagation models

8
Radio Propagation Mechanisms

• Free Space propagation
• Refraction
• Conductors Dielectric materials (refraction)
• Diffraction
• Fresnel zones
• Scattering
• Clutter is small relative to wavelength

9
Free Space

• Assumes far-field (Fraunhofer region)
• d D and d ? , where
• D is the largest linear dimension of antenna
• ? is the carrier wavelength
• No interference, no obstructions

10
Free Space Propagation Model

• Received power at distance d is
• where Pt is the transmitter power in Watts
• a constant factor K depends on antenna gain, a
  system loss factor, and the carrier wavelength

11
Refraction

• Perfect conductors reflect with no attenuation
• Dielectrics reflect a fraction of
  incident energy
• Grazing angles reflect max
• Steep angles transmit max

q
qr
qt

• Reflection induces 180? phase shift

The exact fraction depends on the materials and
frequencies involved
12
Diffraction

• Diffraction occurs when waves hit the edge of an
  obstacle
• Secondary waves propagated into the shadowed
  region
• Excess path length results in a phase
  shift
• Fresnel zones relate phase shifts to the
  positions of obstacles

13
Fresnel Zones

• Bounded by elliptical loci of constant delay
• Alternate zones differ in phase by 180?
• Line of sight (LOS) corresponds to 1st zone
• If LOS is partially blocked, 2nd zone can
  destructively interfere (diffraction loss)

Path 1
Path 2
Fresnel zones are ellipses with the TR at the
foci L1 L2l
14
Power Propagated into Shadow

• How much power is propagated this way?
• 1st FZ 5 to 25 dB below free space prop.

LOS
0 -10 -20 -30 -40 -50 -60
0o
90
180o
dB
Obstruction
Rappaport, pp. 97
Tip of Shadow
1st 2nd
Obstruction of Fresnel Zones ?
15
Scattering

• Rough surfaces
• critical height for bumps is f(?,incident angle)
• scattering loss factor modeled with Gaussian
  distribution.
• Nearby metal objects (street signs, etc.)
• Usually modelled statistically
• Large distant objects
• Analytical model Radar Cross Section (RCS)

16
Outline

• Introduction and some terminology
• Propagation Mechanisms
• Propagation models
• Large scale propagation models
• Small scale propagation (fading) models

17
Propagation Models Large

• Large scale models predict behavior averaged over
  distances ?
• Function of distance significant environmental
  features, roughly frequency independent
• Breaks down as distance decreases
• Useful for modeling the range of a radio system
  and rough capacity planning

18
Propagation Models Small

• Small scale (fading) models describe signal
  variability on a scale of ?
• Multipath effects (phase cancellation) dominate,
  path attenuation considered constant
• Frequency and bandwidth dependent
• Focus is on modeling Fading rapid change in
  signal over a short distance or length of time.

19
Large Scale Models

• Path loss models
• Outdoor models
• Indoor models

20
Free Space Path Loss

• Path Loss is a measure of attenuation based only
  on the distance to the transmitter
• Free space model only valid in far-field
• Path loss models typically define a close-in
  point d0 and reference other points from there

What is dB?
21
Log-Distance Path Loss Model

• Log-distance generalizes path loss to account for
  other environmental factors
• Choose a d0 in the far field.
• Measure PL(d0) or calculate Free Space Path Loss.
• Take measurements and derive ? empirically.

22
Log-Distance 2

• Value of ? characterizes different environments

Rappaport, Table 3.2, pp. 104
23
Log-Normal Shadowing Model

• Shadowing occurs when objects block LOS between
  transmitter and receiver
• A simple statistical model can account for
  unpredictable shadowing
• Add a 0-mean Gaussian RV to Log-Distance PL
• Markov model can be used for spatial correlation

24
Outdoor Models

• 2-Ray Ground Reflection model
• Diffraction model for hilly terrain

25
2-Ray Ground Reflection

• For d hrht,
• low angle of incidence allows the earth to act as
  a reflector
• the reflected signal is 180? out of phase
• Pr ? 1/d4 (?4)

26
Ground Reflection 2

• Intuition ground blocks 1st Fresnel zone
• Reflection causes an instantaneous 180? phase
  shift
• Additional phase offset due to excess path length
• If the resulting phase is still close to 180?,
  the gound ray will destructively interfere with
  the LOS ray.

180?
27
Hilly Terrain

• Propagation can be LOS or result of diffraction
  over one or more ridges
• LOS propagation modelled with ground
  reflection diffraction loss
• But if there is no LOS, diffraction can
  actually help!

28
Indoor Path Loss Models

• Indoor models are less generalized
• Environment comparatively more dynamic
• Significant features are physically smaller
• Shorter distances are closer to near-field
• More clutter, scattering, less LOS

29
Indoor Modeling Techniques

• Modeling techniques and approaches
• Log-Normal, ?
• Log-Normal shadowing model if no LOS
• Partition and floor attenuation factors
• Computationally intensive ray-tracing based on
  3-D model of building and attenuation factors for
  materials

30
Outline

• Introduction and some terminology
• Propagation Mechanisms
• Propagation models
• Large scale propagation models
• Small scale propagation (fading) models

31
Recall Fading Models

• Small scale (fading) models describe signal
  variability on a scale of ?
• Multipath effects (phase cancellation) dominate,
  path attenuation considered constant
• Frequency and bandwidth dependent
• Focus is on modeling Fading rapid change in
  signal over a short distance or length of time.

32
Factors Influencing Fading

• Motion of the receiver Doppler shift
• Transmission bandwidth of signal
• Compare to BW of channel
• Multipath propagation
• Receiver sees multiple instances of signal when
  waves follow different paths
• Very sensitive to configuration of environment

33
Effects of Multipath Signals

• Rapid change in signal strength due to phase
  cancellation
• Frequency modulation due to Doppler shifts from
  movement of receiver/environment
• Echoes caused by multipath propagation delay

34
The Multipath Channel

• One approach to small-scale models is to model
  the Multipath Channel
• Linear time-varying function h(t,?)
• Basic idea define a filter that encapsulates the
  effects of multipath interference
• Measure or calculate the channel impulse response
  (response to a short pulse at fc)

t
35
Channel Sounding
SKIP

• Channel sounding is a way to measure the
  channel response
• transmit impulse, and measure the response to
  find h(?).
• h(?) can then be used to model the channel
  response to an arbitrary signal y(t)
  x(t)?h(?).
• Problem models the channel at single point in
  time cant account for mobility or environmental
  changes

h(t,?)
?
?
36
Characterizing Fading
Adapted from EE535 Slides, Chugg 99

• From the impulse response we can characterize the
  channel
• Characterizing distortion
• Delay spread (?d) how long does the channel ring
  from an impulse?
• Coherence bandwidth (Bc) over what frequency
  range is the channel gain flat?
• ?d?1/Bc

In time domain, roughly corresponds to the
fidelity of the response sharper pulse
requires wider band
37
Effect of Delay Spread

• Does the channel distort the signal?
• if W
• Amplitude and phase distortion only
• if W Bc Frequency Selective Fading
• If T
• For narrowband systems (W ? 1/T), FSF ? ISI.
• Not so for wideband systems (W 1/T)

For a system with bw W and symbol time T...
38
Qualitative Delay Spread
Typical values for ? Indoor 10-100 ns Outdoor
0.1-10 ?s
Noise threshold
Power(dB)?
Delay?
39
Characterizing Fading 2

• Characterizing Time-variation How does the
  impulse response change with time?
• Coherence time (tc) for what value of ? are
  responses at t and t? uncorrelated? (How quickly
  is the channel changing)
• Doppler Spread (fd) How much will the spectrum
  of the input be spread in frequency?
• fd?1/tc

40
Effect of Coherence Time

• Is the channel constant over many uses?
• if T
• Slow adaptation required
• if T tc Fast fading
• Frequent adaptation required
• For typical systems, symbol rate is high compared
  to channel evolution

For a system with bw W and symbol time T...
41
Statistical Fading Models

• Fading models model the probability of a fade
  occurring at a particular location
• Used to generate an impulse response
• In fixed receivers, channel is slowly
  time-varying the fading model is reevaluated at
  a rate related to motion
• Simplest models are based on the WSSUS principle

42
WSSUS

• Wide Sense Stationary (WSS)
• Statistics are independent of small perturbations
  in time and position
• I.e. fixed statistical parameters for stationary
  nodes
• Uncorrelated Scatter (US)
• Separate paths are not correlated in phase or
  attenuation
• I.e. multipath components can be independent RVs
• Statistics modeled as Gaussian RVs

43
Common Distributions

• Rayleigh fading distribution
• Models a flat fading signal
• Used for individual multipath components
• Ricean fading distribution
• Used when there is a dominant signal component,
  e.g. LOS weaker multipaths
• parameter K (dB) defines strength of dominant
  component for K-?, equivalent to Rayleigh

44
Application of WSSUS

• Multi-ray Rayleigh fading
• The Rayleigh distribution does not model
  multipath time delay (frequency selective)
• Multi-ray model is the sum of two or more
  independent time-delayed Rayleigh variables

Rappaport, Fig. 4.24, pp. 185.
45
Saleh Valenzuela (1987)
Rappaport, pp. 188

• Measured same-floor indoor characteristics
• Found that, with a fixed receiver, indoor channel
  is very slowly time-varying
• RMS delay spread mean 25ns, max 50ns
• With no LOS, path loss varied over 60dB range and
  obeyed log distance power law, 3 n 4
• Model assumes a structure and models correlated
  multipath components.

46
Saleh Valenzuela 2

• Multipath model
• Multipath components arrive in clusters, follow
  Poisson distribution. Clusters relate to building
  structures.
• Within cluster, individual components also follow
  Poisson distribution. Cluster components relate
  to reflecting objects near the TX or RX.
• Amplitudes of components are independent Rayleigh
  variables, decay exponentially with cluster delay
  and with intra-cluster delay

47
References

• Wireless Communications Principles and Practice,
  Chapters 3 and 4, T. Rappaport, Prentice Hall,
  1996.
• Principles of Mobile Communication, Chapter 2, G.
  Stüber, Kluwer Academic Publishers, 1996.
• Slides for EE535, K. Chugg, 1999.
• Spread Spectrum Systems, Chapter 7, R. Dixon,
  Wiley, 1985 (there is a newer edition).
• Wideband CDMA for Third Generation Mobile
  Communications, Chapter 4, T. Ojanpera, R.
  Prasad, Artech, House 1998.
• Propagation Measurements and Models for Wireless
  Communications Channels, Andersen, Rappaport,
  Yoshida, IEEE Communications, January 1995.

48
The End
49
Scattering 2

• hc is the critical height of a protrusion to
  result in scattering.
• RCS ratio of power density scattered to receiver
  to power density incident on the scattering
  object
• Wave radiated through free space to scatterer and
  reradiated

50
Free Space 2a

• Free space power flux density (W/m2)
• power radiated over surface area of sphere
• where Gt is transmitter antenna gain
• By covering some of this area, receivers antenna
  catches some of this flux

51
Free Space 2b

• Fraunhofer distance d 2D2/?
• Antenna gain and antenna aperture
• Ae is the antenna aperture, intuitively the area
  of the antenna perpendicular to the flux
• Gr is the antenna gain for a receiver. It is
  related to Ae.
• Received power (Pr) Power flux density (Pd) Ae

52
Free Space 2c

• where L is a system loss factor
• Pt is the transmitter power
• Gt and Gr are antenna gains
• ? is the carrier wavelength

53
LNSM 2

• PL(d)dB PL(d0) 10nlog(d/d0) X?
• where X? is a zero-mean Gaussian RV (dB)
• ? and n computed from measured data, based on
  linear regression

54
Ground Reflection 1.5

• The power at the receiver in this model is
• derivation calculates E field
• Pr E2Ae Ae is ant. aperture
• The breakpoint at which the model changes from
  1/d2 to 1/d4 is ? 2?hthr/?
• where hr and ht are the receiver and transmitter
  antenna heights

55
Convolution Integral

• Convolution is defined by this integral

Indexes relevant portion of impulse response
Scales past input signal
56
Partition Losses

• Partition losses same floor
• Walls, furniture, equipment
• Highly dependent on type of material, frequency
• Hard partitions vs soft partitions
• hard partitions are structural
• soft partitions do not reach ceiling
• open plan buildings

57
Partition Losses 2

• Partition losses between floors
• Depends on building construction, frequency
• Floor attenuation factor diminishes with
  successive floors
• typical values
• 15 dB for 1st floor
• 6-10 dB per floor for floors 2-5
• 1-2 dB per floor beyond 5 floors

58
Materials

• Attenuation values for different materials

59
What does dB mean?

• dB stands for deciBel or 1/10 of a Bel
• The Bel is a dimensionless unit for expressing
  ratios and gains on a log scale
• Gains add rather than multiply
• Easier to handle large dynamic ranges

60
dB 2

• Ex Attenuation from transmitter to receiver.
• PT100, PR10
• attenuation is ratio of PT to PR
• PT/PRdB 10 log(PT/PR) 10 log(10) 10 dB
• Useful numbers
• 1/2dB ? -3 dB
• 1/1000dB -30 dB

61
dB 3

• dB can express ratios, but what about absolute
  quantities?
• Similar units reference an absolute quantity
  against a defined reference.
• n mWdBm n/mWdB
• n WdBW n/WdB
• Ex 1 mWdBW -30 dBW

62
Channel Sounding 2

• Several Channel Sounding techniques can measure
  the channel response directly
• Direct RF pulse (we hinted at this approach)
• Sliding correlator
• Frequency domain sounding

63
Channel Sounding 3

• Direct RF Pulse
• Xmit pulse, scope displays response at receiver
• Can be done with off-the-shelf hardware
• Problems hard to reject noise in the channel
• If no LOS
• must trigger scope on weaker multipath component
• may fail to trigger
• lose delay and phase information

64
Channel Sounding 4

• Sliding correlator
• Xmit PseudoNoise sequence
• Rcvr correlates signal with its PN generator
• Rcvr clock slightly slower PN sequences slide
• Delayed components cause delayed correlations
• Good resolution, good noise rejection

65
Channel Sounding 5

• Frequency domain sounding
• Sweep frequency range
• Compute inverse Fourier transform of response
• Problems
• not instantaneous measurement
• Tradeoff between resolution (number of frequency
  steps) and real-time measurement (i.e. duration
  as short as possible)

66
Digression Convolutions

• The impulse response box notation implies the
  convolution operator, ?
• Convolution operates on a signal and an impulse
  response to produce a new signal.
• The new signal is the superposition of the
  response to past values of the signal.
• Commutative, associative

67
Convolutions 2

• y(t) is the sum of scaled, time-delayed responses

x(t)

?
h(t)
Each component of the sum is scaled by the
x(t)dt at that point in this example, the
response is scaled to 0 where x(t) 0.

68
Convolutions 3

• Graphical method Flip Slide

x(t)

?
Pairwise multiply xh and integrate over ?
x(?)
y(t)
and Store y(t)
69
Frequency and Time Domains

• The channel impulse response is f(time)
• It describes the channel in the time domain
• Functions of frequency are often very useful
• Space of such functions is frequency domain
• Often a particular characteristic is easier to
  handle in one domain or the other.

70
Frequency Domain

• Functions of frequency
• usually capitalized and take the parameter f
• where f is the frequency in radians/sec
• and the value of the function is the amplitude of
  the component of frequency f.
• Convolution in time domain translates into
  multiplication in the frequency domain
• y(t) x(t)?h(t) ? Y(f) X(f)H(f)

71
Frequency Domain 2

• Based on Fourier theorem
• any periodic signal can be decomposed into a sum
  of (possibly infinite number of) cosines
• The Fourier Transform and inverse FT
• Convert between time and frequency domains.
• The frequency and time representations of the
  same signal are duals

72
Flat Fading

• T ?d and W

r(t)
s(t)
h(t,?)
Delay spread

Time domain (convolve)
t
t
t
0
?
0
Ts
0
Ts?
Coherence BW
Freq domain (filter)

f
f
f
fc
fc
fc
73
Frequency Selective Fading

• T BC ? ISI

r(t)
s(t)
h(t,?)
Delay spread

Time domain (convolve)
t
t
0
?
0
Ts
0
Ts
Ts?
Coherence BW
Freq domain (filter)

f
f
f
fc
fc
fc
74
Review

• Object of radio propagation models
• predict signal quality at receiver
• Radio propagation mechanisms
• Free space (1/d2)
• Diffraction
• Refraction
• Scattering

75
Review 2

• Factors influencing received signal
• Path loss distance, obstructions
• Multipath interference phase cancellation due to
  excess path length and other sources of phase
  distortion
• Doppler shift
• Other radio interference

76
Review 3

• Approaches to Modelling
• Models valid for far-field, apply to a range of
  distances
• large scale models concerned with gross behavior
  as a function of distance
• small scale (fading) models concerned with
  behavior during perturbations around a particular
  distance

77
Relevance to Micronets

• Micronets may require different models than most
  of the work featured here
• Smaller transmit range
• Likely to be near reflectors on desk or floor.
• On the other hand, at smaller scales things are
  less smooth ground reflection may turn into
  scattering
• Outdoors, throwing sensors on ground may not
  work. Deployable tripods?

78
Relevance 2

• Consequences of Fading
• You can be in a place that has no signal, but
  where a signal can be picked up a short distance
  away in any direction
• Ability to move? Switch frequencies/antennas?
  Call for help moving or for more nodes to be
  added?
• If stuck, may not be worth transmitting at all
• Reachability topology may be completely
  irrelevant to location relationships

79
Relevance 3

• Relevant modelling tools
• Statistical models (Rice/Rayleigh/Log Normal)
• Statistical fading assumes particular dynamics,
  this depends on mobility of receivers and
  environment
• CAD modelling of physical environment and ray
  tracing approaches.
• For nodes in fixed positions this is only done
  once.

80
Relevance 4

• An approach to modelling?
• Characterize wireless system interactions with
  different materials, compare to published data
• Assess the effect of mobility in environment on
  fixed topologies, relate to statistical models
• Try to determine what environmental structures
  and parameters are most important
• Scattering vs. ground reflection?
• can a simple CAD model help?