1. EE424 Communication Systems
Mobile Radio Propagation:
Small Scale Fading
HW: 5.6, 5.7,5.8, 5.13, 5.28,5 .30
Due Monday Dec 5

2. Introduction to Radio Wave Propagation
The mobile radio channel places fundamental limitations on the performance of wireless communication systems
Mobile radio path is severely obstructed by buildings, mountains, and foliage,……………….
Radio channels are extremely random and do not offer easy analysis
The speed of motion impacts how rapidly the signal level fades as a mobile terminals moves in the space
Modeling radio channel is one of the most difficult part and typically done in a statistical manner based on measurements

6. Large Scale Propagation Models
Introduction to Radio Wave Propagation
Large Scale Propagation Models
Propagation models are usually required to predict the average received signal strength at a given distance from the transmitter and estimating the coverage area (averaged over meters).
Small-Scale models (fading models)
Propagation models that characterize rapid fluctuations of the received signal strength over very short travel distances (few wavelengths) or short time duration (on the order of seconds).

7. Small Scale and Large-Scale fading for an indoor radio

8. Propagation models
Most radio propagation models are derived using a combination of analytical (from a set of measured data) and empirical methods. (based on fitting curves)
All propagation factors through actual field measurements are included. 
Some classical propagation models are now used to predict large scale coverage for mobile communication systems design.

9. Large Scale Path Loss Radio Propagation Mechanisms Reflection
Conductors & Dielectric materials
Propagation wave impinges on an object which is large as compared to wavelength
- e.g., the surface of the Earth, buildings, walls, etc.
Diffraction
Radio path between transmitter and receiver obstructed by surface with sharp irregular edges
Waves bend around the obstacle, even when LOS (line of sight) does not exist. (Huygen’s principal)
Scattering
The through which the wave travels consists of objects with dimensions smaller than the wavelength and where the number of obstacles per unit volume is large – rough surfaces, small objects, foliage, street signs, lamp posts.
In mobile communication, the actual received signal is often stronger than that is predicted by reflection and diffraction models.

10. Practical Link Budget Design Using Path Models
Large Scale Path Loss
Practical Link Budget Design Using Path Models
Most of the models are derived from combined
(i) analytical studies
(ii) experimental methods
The empirical approach is based on fitting curves and analytical expressions that recreate a set of measured data
All propagation factors then considered
It should not be directly used in other conditions such as frequency, environment,… unless additional measured data is achieved.

11. Large Scale Path Loss
Log Distance Path Loss Model
In dB format:
(PL)dB = PL(do) + 10nlog(d/do)
The ‘PL’ includes all possible average path losses.
Bars denote the ensemble average of all possible path loss values for a given d
On a log-log scale plot, the modeled path loss is a straight line with a slope equal to 10n dB per decade.
do ~ 1 km for Large cell
do ~ 1 to 100 m for microcell

12. Large Scale Path Loss Log-normal shadowing
averaged received power in log distance model is inconsistent with measured data
The environmental conditions in Log-Distance model not necessarily to be the same at two different locations having the same T-R separation.
Measurement have shown that at any value of d, the path loss PL(d) at a particular location is random and distributed log-normally about the mean distance-dependent value.

13. Thus, [PL(d)]dB = PL(d) + Xσ = PL(do) + 10nlog(d/do) + Xσ
Large Scale Path Loss
Log-normal shadowing
Thus, [PL(d)]dB = PL(d) + Xσ = PL(do) + 10nlog(d/do) + Xσ
where Xσ is Gaussian distributed random variable with zero mean (in dB) and standard deviation σ (dB).
The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations.
n and σ are computed from measured data
Log Normal Distribution - describes random shadowing effects
for specific Tx-Rx, measured signal levels have normal distribution
about distance dependent mean (in dB)
occurs over many measurements with same Tx-Rx & different
clutter standard deviation,  (also measured in dB)

14. Indoor Propagation Models
Large Scale Path Loss
Indoor Propagation Models
The indoor radio channel differs from the traditional radio channel in two aspects:
The distances covered are much smaller.
The variability of the environment is much greater for a much smaller range of T-R separation distances.
Propagation within building is strongly affected by:
The layout of the building .
The construction materials.
The building type.
The mechanisms are the same as outdoor models but the conditions are much more variable
… Signal levels strongly affected whether the interior doors are open or closed, antenna mounting, far field conditions…………

15. Introduction Small Scale Fading
Large-scale fading represents the average signal power attenuation or the path loss due to motion over large areas. This phenomenon is affected by prominent terrain contours (hills, forests, billboards, clumps of buildings, and so on) between the transmitter and the receiver.
The receiver is often said to be “shadowed” by such prominences. The statistics of large-scale fading provide a way of computing an estimate of path loss as a function of distance. This is described in terms of a mean-path loss (nth-power law) and a log-normally distributed variation about the mean.

16. Introduction Small Scale Fading
Small-scale fading refers to the dramatic changes in signal amplitude and phase that can be experienced as a result of small changes (as small as a half wavelength) in the spatial positioning between a receiver and a transmitter. Small-scale fading manifests itself in two mechanisms: time-spreading of the signal (or signal dispersion) and time-variant behavior of the channel.
Fading is used to describe the rapid fluctuation of the amplitude of the radio over a short period of time or travel distance so that the large scale path loss effect may be ignored.
Fading is caused by interference between two or more
versions of the transmitted signal which arrive at the receiver at slightly different times.

17. Small Scale Multipath Propagation
Multipath in the radio channel creates small-scale fading effects. The three most important effects are:
Rapid changes in signal strength over a small travel distance or time interval.
Random frequency modulation due to varying Doppler shifts on different multipath signals.
Time dispersion caused by multipath propagation delays.

18. Factors Influencing Small Scale Fading
Multi-path propagation
The presence of reflecting objects and scatterers in the propagation path (buildings, signs, trees, fixed and moving vehicles)
Speed of the Mobile
Random Frequency Modulation due to different Doppler shifts of each of the multipath components
Speed of the surrounding objects
Time varying Doppler shift on multipath components
If the surrounding objects move at a greater rate than the mobile , then this effect dominates the small scale fading
The transmission bandwidth of the signal
If the transmitted radio signal bandwidth is greater than the bandwidth of the multipath channel, the received signal will be distorted

19. The apparent change in frequency fd = /2t = v cos/
Doppler shift
 The shift in received signal frequency due to motion  is directly proportional to the velocity and direction of motion of the mobile with respect to the direction of arrival of the received multipath wave.
Remote source
L is the difference in path length traveled by the wave from source s to the mobile at points X and Y
 L = d cos = v t cos
t is the time required for the mobile
to travel from point X to Y
The phase change in the received
signal due to the difference in path
length is  = 2L/
Illustration of Doppler effect
v is constant
The apparent change in frequency fd = /2t = v cos/

20. Doppler shift
The Doppler shift is positive (i.e., the apparent received frequency is increased), if the mobile is moving toward the direction of arrival of the wave.
 The Doppler shift is negative (i.e. the apparent received frequency is decreased), if the mobile is moving away from the direction of arrival of the wave.
 Multipath components from a CW signal which arrive from different directions contribute to Doppler spreading of the received signal, thus increasing the signal bandwidth.

21. Example 5.1

22. Impulse Response Model of a Multipath Channel
The small scale fading can be directly related to the impulse response of the mobile radio channel.
The impulse response is a wideband channel characteristics
It contains all information necessary to analyze any type of radio transmission through the channel
Mobile radio channel may be modeled as a linear filter with a time varying impulse response, where time variation is due to receiver motion in space.

23. Impulse Response….
For a fixed position d, the channel between the transmitter and the receiver can be modeled as a linear time invariant system.
The different multipath waves have propagation delays which vary over different spatial locations of the receiver. The impulse response should be a function of the receiver position.
Therefore the channel impulse response can be expressed as h(d,t)

24. x(t) transmitted signal
y(d,t) Received signal at d
For a causal system h(d,t) = 0 for t < 0
d = vt

25. Since v is constant y(vt,t) is just a function of t and then,
It is clear that the mobile radio channel can be modeled as a linear time varying channel where the channel changing with time and distance.

26. v can be assumed constant over a short time or distance interval
x(t) represent the transmitted bandpass waveform
y(t) the received signal waveform
h(t,) the impulse response of the time varying multipath radio channel
t represents the time variations due to motion
 represents the channel multipath delay for a fixed value of t

27. If the multipath channel is assumed to be a band limited bandpass channel, then h(t,) may be equivalently described by a complex baseband impulse response hb(t, ) with the input and output being the complex envelope representations of the transmitted and received signals respectively
Bandpass channel impulse response model
x(t)
y(t)
Baseband equivalent channel impulse response
c(t)
r(t)

28. The factor ½ is due to the properties of the complex envelope in order to represent the passband radio system at baseband.
The lowpass characterization removes the high frequency variations caused by the carrier.
The average power of a bandpass signal x2(t) is equal to 0.5c2(t) [Couch3]

29. Discretizing the multipath delay axis
Discretize the multipath axis delay of the impulse response into equal time delay segments called excess delay bins
Each bin has a time delay width  = i+1 – i
o = 0 (the first arriving signal at the receiver)
1 = , then i = i i = 0 to N-1
N is the total number of possible equally-spaced multipath components.
Quantizing the delay bins determines the time delay resolution of the channel model
The useful frequency span of the model = 2/
The model can be used to analyze transmitted RF signals having bandwidths which are less than 2/
The maximum excess delay = N

30. The received signal consists of a series of
attenuated,
time delayed,
phase shifted replicas of the transmitted signal
The baseband impulse response of a multipath channel can be expressed as
ai(t,) the amplitude of the ith multipath component
i the excess delay of the ith multipath component
2fci (t) the phase shift due to free space propagation of the ith multipath component
i(t, ) any additional phase shifts which are encountered in the channel.

31. In general, the phase term can be simply represented by a single variable (t, i)
and δ( - i(t))  is the unit impulse function which determines the specific multipath bins that have components at time t
and excess delays i

32. Discretize the multipath delay axis
Here an example is a good idea.
Discretize the multipath delay axis

33. If the channel impulse response is assumed to be time invariant, then the channel impulse response may be simplified as
When measuring or predicting hb() a probing pulse p(t) which approximates a delta function is used at the transmitter.
That is,
p(t)  (t-)

34. Relationship Between Bandwidth and Received Power
We will consider two extreme channel sounding cases as a means of demonstrating how the small-scale fading behaves quite differently for two signals with different bandwidths in the identical multipath channel.
(1) Consider a pulsed, transmitted RF signal of the form
p(t) is a repetitive baseband pulse train with very narrow pulse width Tbb and repetition period TREP which is much greater than the maximum measured excess delay max
Such a wideband pulse will produce an output that approximates hb(t,)

35. Let
= 0 elsewhere
The low pass channel output r(t) closely approximates the impulse response , It is given by
r(t) = p(t)  (1/2)hb(t,)

36. Note that if all the multipath components are resolved by the probe p(t), j-i > Tbb for all j  i then 

37. For a wideband probing signal p(t):
Tbb is smaller than the delays between multipath components in the channel
Equation (5.18):
The total received power is simply related to the sum of the powers in the individual multipath components, and is scaled by the ratio of the probing pulse’s width and amplitude, and the maximum observed excess delay of the channel.
Assuming that the received power from the multipath components forms a random process where each component has a random amplitude and phase at any time , the average small-scale received power for the wideband probe is found from Equation (5.17) as

38. In Equation (5.19), Ea,θ[•] denotes the ensemble average over all possible values of ai and θi in a local area, and the overbar denotes sample average over a local measurement area
small-scale received power is simply the sum of the average powers received in each multipath component.
In practice, the amplitudes of individual multipath components do not fluctuate widely in a local area. Thus, the received power of a wideband signal such as p(t) does not fluctuate
significantly when a receiver is moved about a local area[Rap89].

39. 2) Now, instead of a pulse, consider a CW signal which is transmitted into the exact same channel, and let the complex envelope be given by c(t) = 2.
Then, the instantaneous complex envelope of the received signal is given by the phasor sum
and the instantaneous power is given by

40. The average received power over a local area is then given by
As the receiver is moved over a local area, the channel induces changes on r(t), and the received signal strength will vary at a rate governed by the fluctuations of ai and θi. As mentioned earlier, ai varies little over local areas, but θi will vary greatly due to changes in propagation distance over space, resulting in large fluctuations of r(t) as the receiver is moved over small distances (on the order of a wavelength).
The average received power over a local area is then given by

41. Note that when cos (i - j) = 0 and/or rij = 0,
then the average power for a CW signal is equivalent to the average received power for a wideband signal in a small-scale region. This is seen by comparing Equation (5.19) and Equation (5.24).
Carrier 4GHz
Measured wideband and narrowband received signals over a 5λ (0.375 m) measurement
Wideband (Tbb = 10 ns)
Narrowband (CW 4GHz)
Local average is the same

42. Example 5.2
Assume a discrete channel impulse response is used to model urban RF
radio channels with excess delays as large as 100 μs and microcellular
channels with excess delays no larger than 4 μs. If the number of multipath bins is fixed at 64, find (a)  and (b) the maximum RF bandwidth which the two models can accurately represent. Repeat the exercise for an indoor channel model with excess delays as large as 500 ns. As described in section 5.7.6, SIRCIM and SMRCIM are statistical channel models based on Equation (5.12) that use parameters in this example.

43. Example 5.3
Assume a mobile traveling at a velocity of 10 m/s receives two multipath
components at a carrier frequency of 1000 MHz. The first component is
assumed to arrive at τ = 0 with an initial phase of 0° and a power of
–70 dBm, and the second component which is 3 dB weaker than the first
component is assumed to arrive at τ = 1μs, also with an initial phase of
0°. If the mobile moves directly toward the direction of arrival of the first
component and directly away from the direction of arrival of the second
component, compute the narrowband instantaneous power at time intervals of 0.1 s from 0 s to 0.5 s. Compute the average narrowband power received over this observation interval. Compare average narrowband and wideband received powers over the interval, assuming the amplitudes ofthe two multipath components do not fade over the local area.
Solution
Given v = 10 m/s, time intervals of 0.1 s correspond to spatial intervals of
1 m. The carrier frequency is given to be 1000 MHz, hence the wavelength
of the signal is

44. The narrowband instantaneous power can be computed using Equation (5
Note –70 dBm = 100 pW. At time t = 0, the phases of both multipath components are 0°, hence the narrowband instantaneous power is equal to
Now, as the mobile moves, the phase of the two multipath components changes in opposite directions.

45. Since the mobile moves toward the direction of arrival of the first component, and away from the direction of arrival of the second component, θ1 is positive, and θ2 is negative.
Therefore, at t = 0.1 s, θ1 = 120°, and θ 2 = –120°, and the instantaneous power is equal to
Similarly, at t = 0.2 s, θ1 = 240°, and θ 2 = –240°, and the instantaneous power is equal to

46. Similarly, at t = 0.3 s, θ1 = 360° = 0°, and θ 2 = –360° = 0°, and the instantaneous power is equal to
It follows that at t = 0.4 s, |r (t )|2 = 79.3pW, and at t = 0.5 s, |r (t )|2 = 79.3 pW.
The average narrowband received power is equal to

47. Using Equation (5.19), the wideband power is given by
As can be seen, the narrowband and wideband received power are virtually identical when averaged over 0.5 s (or 5 m). While the CW signal fades over the observation interval, the wideband signal power remains constant over the same spatial interval.

48. Small-Scale Measurements
Direct pulse measurements
Spread spectrum sliding correlator measurements
Swept frequency measurement

49. A wideband pulsed bistatic radar
Direct RF Pulse System
A simple approach to determine rapidly the power delay profile of any channel
A wideband pulsed bistatic radar
Transmits a repetitive pulse of width Tbb
Receiver with a wide bandpass filter = 2/Tbb
The signal is amplified, detected and displayed
Immediate measurement of the square of the channel impulse response convolved with the probing pulse. If the oscilloscope is set on averaging mode, the system can provide a local average power delay profile.

50. The minimum resolvable delay between multipath components is equal to the probing pulse width Tbb.
Disadvantages
It is subject to interference and noise due to the wide passband filter required for multi-path time resolution
If the first arriving signal is blocked or fades, severe fading occurs. (triggering oscilloscope with the first arrival signal is important)
The phases of the individual multipath components are not received due to the use of an envelope detector
Here I will talk about measuring current & voltage & the resistance of meters. I will use demos EM377 & EM378

51. Wideband probing signal
Spread Spectrum Sliding Correlated Chanel Sounding
Wideband probing signal
Can be detected using a narrowband receiver preceded by a wideband mixer
Improving the dynamic range of the system compared to the direct RF pulse system.
A carrier signal is spread over a large bandwidth by mixing it with a binary pseudo-noise PN sequence having a chip duration Tc and a chip rate Rc equal to 1/Tc Hz. The power spectrum envelope of the transmitted spread signal is given by
The null-to-null RF bandwidth (BW) = 2Rc

52. Spread Spectrum Channel Impulse Response Measurement System

53. The spread spectrum signal is received, filtered, and despread using a PN sequence generator identical to that used at the transmitter.
PN sequence are identical
The transmitter chip clock is run at a slightly faster rate than the receiver chip clock
Mixing the chip sequence in this fashion implements a sliding correlator.
When the PN code of the faster chip clock catches up with the PN code of the slower chip clock, the two chip sequences will virtually identical aligned (maximal correlation)

54. When the two sequences are not maximally correlated, mixed signals will spread into large bandwidth. Then narrow band filter can reject almost all the incoming signal power.
Processing gain (PG) = 2 Rc/Rbb = 2Tbb/Tc
Tbb = 1/Rbb is the period of the baseband information.
The time resolution () of multipath components using a spread spectrum system with sliding correlation is
 = 2 Tc = 2/Rc
The system can resolve two multipath components as long as they are equal to or greater than 2Tc s a part.

55. The time between maximal correlations is

57. Frequency Domain Channel Sounding
Disc 18, #3

58. The number and spacing of the frequency steps impact the time resolution of the impulse response measurement.
For each frequency step, the S-parameter test set: transmits a known signal level at port 1
monitors the received signal level at port 2
Frequency domain is then converted to Time domain using inverse discrete Fourier transform given a band limited version of the impulse response
The technique is useful in very close measurements
It is also non real time nature of the measurement.

59. For time varying channels, the channel frequency response can change rapidly, giving an erroneous impulse response measurement. This effect can be overcome by fast sweep time.
The technique has been used successfully for indoor propagation studies.

60. 5.4 Parameters of Mobile Multipath Channels
 Many multipath channel parameters are derived from the
power delay profile:
Power delay profiles are generally represented as plots of relative received power as a function of excess delay with respect to a fixed time delay reference.
Power delay profiles are found by averaging instantaneous power delay profile measurements over a local area in order to determine an average small-scale power delay profile.

61. Depending on the time resolution of the probing pulse and
the type of multipath channels studied
From 450 MHz to 6 GHz
sample at spatial separations of /4
over receiver movements < 6 m in outdoor channels
< 2 m in indoor channels
Avoids averaging bias in the resulting small-scale statistics 

62. Typical power delay profile plots
Outdoor channels, determined from a large number of closely sampled instantaneous profiles
Measured multipath power delay profile at 900 MHz cellular system (San Francisco)

63. Typical power delay profile plots
indoor channels, determined from a large number of closely sampled instantaneous profiles.
Inside store at 4 GHz

64. Time Dispersion Parameters
The mean excess delay
RMS delay spread
These delays are measured relative to the first detectable arriving at the receiver at o = 0
Power is plotted in relative amplitudes

65. Typical measured values of RMS delay spread

66. Maximum excess delay
The maximum excess delay of the power delay profile is defined to be the time delay during which multipath energy falls to X dB below the maximum.

67. Coherence Bandwidth Coherence Bandwidth Bc
It is a statistical measure of the range of frequencies over which the channel can be considered flat (A channel which passes all spectral components with approximately equal gain and linear phase.
Two sinusoids with frequency separation greater than Bc are affected quite differently by the channel.
If the coherence bandwidth is defined as the bandwidth over which the frequency correlation function is above 0.9, then
If the definition is relaxed so that the frequency correlation function is above 0.5 then

68. Example 5.5
Calculate the mean excess delay, rms delay spread, and the maximum excess delay (10dB) for the multipath profile given in the figure below. Estimate the 50% coherence bandwidth of the channel. Would this signal to be suitable for AMPS and GSM service without the use of equalizer

69. The mean excess delay
rms delay spread
Coherence bandwidth

70. 5.4.3 Doppler Spread and Coherence Time
Delay Spread and Coherence bandwidth are parameters which describe the time dispersive nature of the channel.
Doppler Spread and Coherence Time are parameters which describe the time varying nature of the channel in small-scale region.
Doppler spread BD is a measure of a spectral broadening caused by the rate of change of the mobile radio channel and is defined as the range of the frequencies over which the received Doppler spectrum is essentially non-zero.
If the baseband signal bandwidth is much greater than BD, the effects of Doppler spread are negligible at the receiver. This is a slow fading channel

71. Coherence time Tc is the time domain dual of Doppler spread and is used to characterize the time varying nature of the frequency dispersiveniss of the channel in the time domain.
Tc = 1/fm (fm is the maximum Doppler shift and given by v/l)
Coherence time is actually a statistical measure of the time duration over which the channel impulse response is essentially invariant and quantifies the similarity of the channel response at different times.
If the coherence time is defined as the time over which the time correlation function is above 0.5, then
In modern digital communication Tc is defined as

72. Two signals arriving with a time separation greater than Tc are affected differently by the channel.
Vehicle traveling 60 mph (~ 95 km/h) using 900 MHz carrier
Tc= 2.22 ms from
1/Tc = 545 bps
If the symbol rate is greater than 545 b/s the channel will not cause distortion due to motion. However, channel may cause distortion from multipath time delay spread (depending on the channel impulse response)

73. Example 5.6

74. Types of Small-Scale Fading
Based on Multipath Time Delay Spread
Flat Fading
BW of the signal < BW of channel
Delay spread < Symbol period
Frequency Selective Fading
BW of the signal > BW of channel
Delay spread >Symbol period
Based on Doppler Spread
Fast Fading
High Doppler Spread
Coherence Time < Symbol period
Channel Variation Faster than baseband Signal Variations
Slow Fading
Low Doppler Spread
Coherence Time > Symbol period
Channel Variation Slower than baseband Signal Variations

75. Flat Fading Due to Multipath Time Delay Spread
The mobile radio channel has constant gain and linear phase response over a bandwidth which is greater than the bandwidth of the transmitted signal
It is the most common type of fading described in the literature.
The strength of the received signal changes with time, due to fluctuations in the gain of the channel caused by multipath

76. Flat Fading Channel Characteristics
Flat fading channel, amplitude varying channels, narrow band channels
The BW of the signal is narrow compared to the channel flat fading BW
Typical flat fading channels cause deep fade and thus may require 20 to 30 dB transmitter power increase to achieve low bit error rates during times of deep fade as compared to systems operating over non-fading channels

77. The distribution (such as Rayleigh ) of the instantaneous gain of flat fading channels is important for designing radio links

78. Frequency Selective Fading
The channel possesses a constant gain and linear phase response over a bandwidth that is smaller than the bandwidth of the transmitted signal
The channel impulse response has a multipath delay spread which is greater than the reciprocal bandwidth of the transmitted message waveform.
It is due to time dispersion of the transmitted symbols within the channel.
Bs > Bc
Ts < 

79. The received signal includes multiple versions of the transmitted waveform which are attenuated (faded) and delayed in time, and hence the received signal is distorted.
The channel induces intersymbol interference (ISI).
Certain frequency components in the received signal spectrum have greater gains than others.

80. Rate of change due to motion
Fading Effects Due to Doppler Spread
How rapidly the transmitted baseband signal changes as compared to the rate of change of the channel?
The channel impulse response changes rapidly within the symbol duration Ts > Tc (Bs<BD)
Frequency Dispersion
(signal distortion)
Fast Fading
Rate of change due to motion

81. Flat fading, fast fading channel
In the case of flat fading channel we can approximate the impulse response to be simply a delta function
Flat fading, fast fading channel
is a channel in which the amplitude of the delta function varies faster than the rate of change of the transmitted baseband signal.
Frequency selective, fast fading channel
The amplitudes, phases, and time delays, of any one of the multipath components vary faster that the rate of change of the transmitted signal.
In practice fast fading is only occurs for very low data rate

82. Slow fading
In slow fading channel, the channel impulse response changes at a rate much slower than the transmitted baseband signal s(t).
The channel may be assumed to be static over one or several reciprocal bandwidth intervals.