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Final Seminar in Satellite and Mobile
Communication Analysis of M-ary Phase-Shift
Keying with Diversity Reception for Land-Mobile
Satellite Channels Lecturer Prof. Shlomi
Arnon Student Eran Shecter
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Agenda
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• Fading Multipath Channels Characterization
• System Performance Measures
• Modeling of Flat Fading Channels
• Satellite Channel Model
• Diversity Reception
• Land Mobile Satellite Performance Measures
• Numerical Results
• Diversity Simulation
• Summary and conclusions

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Fading Multipath Channels Characterization
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• Multipath occurs when there is more then one beam
  reaching the receiver with different amplitude or
  phase

Direct beam
Delayed beam
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Fading Multipath Channels Characterization -
Summary

• Multipath Classifying
• Discrete Multipath -
• Equivalent lowpass received signal, and for
  unmodulated carrier sum of a number of time
  variant vectors (phasors), at time adding
  destructively and at times constructively
• Continuous Multipath
• Where , are the Attenuation factor
  and Propagation delay for the signal received on
  the nth path respectively

Fading Channel
Channel Correlation
- coherence time of the channel
- coherence bandwidth of the channel
- frequency-nonselective, Flat Fading
- Slow fading
- frequency-selective Fading
- Fast fading
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Fading Multipath Channels Characterization
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System Performance Measures
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• Average SNR

• Moment Generation Function

Channel Model
X Transmitted signal corresponding to an
information symbol k Complex channel gain Y
Received signal

• Outage Probability

• Average Bit Error Probability

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Modeling of Flat Fading Channels
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• Rayleigh Model- Mobile systems , no LOS-
  Ship-to-Ship Radio links- Reflected Refracted
  paths through the troposphere and ionosphere

• Rice Model- Direct LOS as well as a multipath
  component comprising multiple scattered
  reflected paths- LOS paths of microcellular
  urban and suburban land-mobile- Factory
  environments- Dominant LOS path of satellite

n Ricean factor, ratio of the power in the LOS
path to the power in the diffuse paths
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Modeling of Flat Fading Channels
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• Log-Normal Shadowing- Terrestrial and satellite
  land-mobile systems- Link Quality is affected by
  slow variation of the mean signal level due to
  shadowing from terrain, buildings, trees

• Suzuki Model- Rayleigh multipath fading
  superimposed on log-normal shadowing- Congested
  downtown areas with slow moving pedestrians and
  vehicles- Land mobile satellite systems subject
  to vegetative and/or urban shadowing- Over local
  area ,the fading envelope obeys a Rayleigh
  distribution with mean power, but due to
  changing topographical features, varies over
  larger areas following a log-normal distribution

- Hermite Polynomial
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Modeling of Flat Fading Channels
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• Rayleigh vs. AWGN Non Faded Channel- BPSK

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Satellite Channel Model

• For a fraction of the time (1-A), the channel is
  in the good state modeled as a Rician random
  process
• For the remaining fraction of the time A, the
  channel is in the bad state modeled as a
  lognormally shadowed Rayleigh random process, or
  equivalently, a Suzuki random process

PDF
MGF
CDF
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Diversity Reception
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Purpose combat the effects of multipath fading

• Diversity combining consists of receiving
  redundantly the same information-bearing signal
  over two or more fading channels
• The intuition behind this concept is to exploit
  the low probability of concurrence of deep fades
  in all the diversity channels to lower the
  probability of error and of outage
• if p is the probability that any one signal will
  fade below some critical value, then is the
  probability that all L independently fading
  replicas of the same signal will fade below the
  critical value

• Combining Techniques
• Maximal Ratio Combining (MRC)
• Selection Combining

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Diversity Reception
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There are several ways in which we can provide
the receiver with L independently fading replicas
of the same information-bearing signal

• Frequency Diversity the same information is
  transmitted over multiple frequency channels
  which are separated by at least the coherence
  bandwidth of the channel (frequency
  hopping or multicarrier systems)
• Time Diversity the signal is transmitted in L
  different time slots, where the separation
  between successive time slots equals or exceeds
  the coherence time of the channel (coded
  systems)
• Space Diversity - Using multiple receiver
  antennas (antenna or site diversity). The
  antennas must be spaced sufficiently far apart
  that the multipath components in the signal have
  significantly different propagation delays at the
  antennas. Usually a separation of at least 10
  wavelengths is required between two antennas in
  order to obtain signals that fade independently

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MRC Diversity
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The combined received signal is equal to
The receiver will be implemented according to the
Min Per?MAP Algorithm
The received system

y
Decision Device


Channel Measurement
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MRC Diversity
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In terms of SNR
Statistics
MGF
CDF

• MRC provides the maximum performance improvement
  relative to all other diversity combining
  techniques by maximizing the signal to noise
  ratio at the combiner output
• MRC has the highest complexity of all combining
  techniques since it requires knowledge of the
  fading amplitude and phase in each signal branch

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Selection Combining Diversity
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• Measures the SNR at each branch and selects the
  branch with the highest SNR value
• In case L-branch diversity is employed and the
  mean noise power per branch is the same for all
  branches, the decision criteria reduce to

Choose Max SNR
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Selection Combining Diversity
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• The probability that

are all simultaneously less than or equal to
Some is
- Uncorrelated and identically distributed
Probability CDF
for the power in one branch raised to the power L
Statistics
CDF
MGF
- Laguerre

• SDC does not require knowledge of the signal
  phases on each branch the least complicated
  combining technique
• In practice the diversity branches may have
  unequal average SNRs due to different noise
  figures, or feeding length
• To obtain significant diversity improvement
  independent fading in the channels should be
  achieved

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Land Mobile Satellite Performance Measures
Average BER
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Binary PSK
Using the alternate form of the complementary
error function
Closed Form Expressions
If
Where
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Land Mobile Satellite Performance Measures
Average BER
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Binary PSK
Closed Form Expressions (Continued)
SDC Suzuki
MRC Suzuki
MRC Rice
Binary DPSK
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Land Mobile Satellite Performance Measures
Average BER
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M-PSK / M-DPSK
Average BER is the Hamming distance between the
ith and jth symbols divided by the number of
bits per symbol
Where , the CDF of the phase error
M-PSK
M-DPSK
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Land Mobile Satellite Performance Measures Outage
Probability
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The percentage of time that the instantaneous BER
is above a predetermine threshold
Binary PSK
Binary DPSK
M-PSK / M-DPSK
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Numerical Results
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BER of Shadowed (A1) about 16dB
worse then unshadowed M4,8,16,32 ?
SNRunshadowed 6.3,9,13,17.4/ SNRshadowed
23.8,25.5,29,32.8
BER of MRC diversity L2,5 ? SNR
Gain of 7.1,13.1 over no diversity 16-ary PSK
L2 surpasses BPSK/QPSK without diversity
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Numerical Results
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D-QPSK BER of L2,3,4 ? SNR
improvement over the non diversity case of
SDC6.2,8.3,9.4 , MRC7.6,10.7,12.5 As L
increases the incremental savings in SNR
decreases e.g. L20
DPSK/MRC - Declining dependence on the fading
environment as the diversity order increases BER
of L2,3,4 ? difference in SNR
between the city and highway 7.8,5.5,4.8 BER
of L2,3,4 ? difference in SNR
between the city and highway 6.7,2.6,1.3
Satellite systems ? Single transmitter serves
multiple environments ?Increasing the diversity
order? reducing the excess signal power in
favorable environments
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Numerical Results
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DPSK/SNR20dB BER as a function of the
elevation angle BER decreases as the elevation
angle increases due to decrease in shadowing
effects Although improving the BER the
diversity techniques do not mitigate the
elevation angle effects-elevation angle affects
primarily the shadowing degree Shallow slope ?
Advantage? implies a certain degree of elevation
independence for the mobile user
SNR15dB - Significant improvement for the Outage
probability For BPSK/QPSK threshold of
- L5, Availability 100!
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Numerical Results
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DPSK/MRC L 1,2,3/SNR10dB the effect of
shadowing in the city environment is readily seen
Microdiversity provides a significant decrease
in outage
M-ary PSK fixed threshold of M2/4,8,16
Required BER less than at least 90 of
the time - non diversity SNR 22,25,29,L5 MRC
SNR 10,13,17
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Diversity Simulation
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MRC Analytical vs. Simulation results
MRC Analytical Rayleigh/BPSK
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Diversity Simulation
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SDC Analytical vs. Simulation results
SDC Analytical Rayleigh/BPSK
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Diversity Simulation
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MRC vs. SDC Simulation results
L2
L3
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Summary Conclusions
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• Analytical expressions well suited to numerical
  analysis for the average BER and outage
  probability of the Land-Mobile Satellite Channels
  were presented.
• Considering both coherent and non coherent M-ary
  PSK
• Both selection diversity and MRC diversity were
  presented
• The expressions presented were powerful in that
  they are functions of the MGF and CDF of the
  fading channels can be easily adapted to any
  channel model provided
• Two-state Rician/Suzuki channel model have been
  considered
• Without diversity BER performance is poor and
  bandwidth-efficient modulation schemes could not
  be utilized (Mgt4).
• Diversity reception provided significant
  improvements in both the BER and outage
  probability e.g. using two-branch MRC
  diversity,16-ary PSK out performed BPSK without
  diversity
• Increasing the number of diversity branches
  reduced the BER and outage probability on the
  fading environment
• Elevation angle was found to have little effect
  on the BER performance

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Thank you!