‫دانشکده مهندس ی کامپیوتر‬
‫ّ‬
‫مخابرات سیار (‪)40-626‬‬
‫چند مسیری‬
‫ّ‬
‫ل‬
‫نیمسال او ‪91-92‬‬
‫افشین ّ‬
‫همتیار‬
Handling Changes in Channel (1)
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 Traditional transmission:
 Send at higher powers to those who have
worse channels (Channel Inversion, similar to
power control in CDMA).
 This has been always used in the past mainly
because the goal has been to transmit voice
signals.
 For voice, you can not tolerate to lose signal
when channel is not in good condition.
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Handling Changes in Channel (2)
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Channel Inversion
 Similar to CDMA power control approach.
 Fading inverted to maintain constant SNR and fixed rate.
 Also has smaller delay, so better for voice/video
applications.
 However, greatly reduces capacity for a given TX power
or leads to infinite power for nonzero capacity in case of
a Rayleigh channel.
 Therefore, combine with diversity to increase capacity.
 Truncated inversion
 Invert channel above cutoff fade depth.
 Truncation greatly increases capacity (Close to optimal).
 Constant SNR (fixed rate) above cutoff.
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 Receiver only needs to know when we are below cutoff.
Handling Changes in Channel (3)
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 Adaptive Transmission:
 If we can tolerate some delay (true for data
transmission), we can wait until our desired
channel
becomes good and then transmit at higher rate.
 Send more to those who have better channels
(Also known as Water-filling in information
theory).
 New techniques are moving more to this more
intelligent choice as we move more to data
transmission.
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Handling Changes in Channel (4)
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Variable Rate Coding
Optimum rate, so more suitable for data applications
(rather than fixed rate voice communication)
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Tb
Introduction to Diversity
 What can be done to improve performance in the
presence of Fading?
 Basic Idea:
1) Obtain diversity “branches”:
 Send same bits over independent fading paths.
 Independent fading paths obtained by time, space,
frequency, polarization, etc.
2) Combine “branches” properly to mitigate fading
effect.
Multiple paths unlikely to fade simultaneously
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Diversity Techniques (1)
 Spatial Diversity
 Basic option: d > λ/2
(for uniform AOA over [0, 2π]. ),
fC= 1GHz  d > 15cm
 Not valid for Base, where AOAs are not uniform.
 Larger distance required at Base locations.
 Polarization Diversity
 At the Base, narrow angles of arrival, therefore
larger distance required for independent paths.
 One solution to reduce distance is using polarized
antennas (Horizontal and Vertical) at base station.
 Polarized paths see different reflection coefficients
and therefore result in independent signals.
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Diversity Techniques (2)
 Time Diversity
 Sending multiple replicas of signal in time
distance larger than TC.
 One nice way of doing that: RAKE receiver in
CDMA systems.
 Interleaving/Coding is also a kind of time
diversity.
 Frequency Diversity
 Send same signals over more than one carrier,
separated at least by BC.
 Multicarrier techniques such as OFDM also
provide some sort of frequency diversity.
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Fading Effects
 In fading environments,
SNR is random and therefore Pb is random too.
 Performance metrics:
 Average Pb
 Outage Probability
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Average Probability (1)
 Average Pb usually used when we do not stay in
deep fade for long time (TC ~ TS).
 In Rayleigh fading, the amplitude α have Rayleigh
distribution and so γb = α2Eb/N0 will
have an exponential distribution of the form:
p(γb) = 1/Γ exp(-γb /Γ )
where Γ = (α2)av Eb/N0
(for non-fading scenario, we assume (α2)av = 1)
 Averaging over γb:
Average Pb = 1/2 [1- (Γ /(1+ Γ ))½ ] ≈ 1/(4Γ ) for large γb
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Average Probability (2)
 So, probability of error is much higher in fading
environments especially in high SNRs.
 For example, for 10-3 bit error rate, we need 8dB
SNR in AWGN, but 24dB SNR in fading!!
 So, we need to use
diversity techniques
to reduce fading
effects as much as
possible.
 Also, AGC at receiver
input can reduce
flat-fading effects to
some extent.
Although has some
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amount of noise enhancement as well.
Outage Probability (1)
 Outage Probability is the probability that Pb is
above target level.
 Equivalently, the probability that SNR is below a
target level.
 Used when TC >> TS
(channel variations are small and so receiver may
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enter deep fades for many symbols.)
Outage Probability (2)
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 Pout = p(γb < γ0) where γ0 is the minimum SNR
level acceptable for the receiver.
 For example, for voice where Pb= 10-3 is
acceptable, γ0 =7dB is selected.
 In Rayleigh fading,
p(γb) = 1/Γ exp(-γb /Γ )  Pout = 1- exp(-γ0 /Γ )
where Γ = (α2)av Eb/N0
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Outage Probability (3)
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Pout = 1- exp(-γ0 /Γ )
 Based on the above equation:Γ = (-γ0 / ln (1- Pout))
 So, Γ should exceed γ0 by Fd = -10log(- ln (1- Pout))
and performance is acceptable more than
100*(1- Pout)) percent of the time.
 Fd is usually called “fade margin” (the margin we
should keep to maintain acceptable levels most of
the time).
 For example, for BPSK modulation, assume we
want to achieve Pb< 10-4 (γ0 = 8.5dB) for 95% of
the time:
Γ = -100.85/ln(1-0.05) = 21.4dB
 So, a fade margin of about 13dB is required.
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Combined Outage and Average Probability
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 Used in combined shadowing and flat-fading.
 Pb varies slowly, locally determined by flat-fading.

 Declare outage when average Pb is above target
value.
 In outage areas, bit error is too high to be
measured.
 Outside outage areas, average Pb is meaningful.
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Performance Improvement
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Deep fades become rarer
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Time Diversity (1)
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 Time Diversity can be obtained by interleaving
and coding symbols across different coherent
time periods.
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Time Diversity (2)
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 Example: GSM
 Amount of diversity is limited by delay constraint
and how fast channels varies.
 In GSM, delay constraint is 40mS (voice).
 Full diversity of 8, needs V > 30Km/hr.
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Frequency Diversity
2
 Example: GSM
However, if the mobile is moving slowly (for
example a person walking at 3Km/hr), there
might not be much time diversity.
 Then, GSM can use frequency hopping to get
diversity in frequency.
 With coherence BW of around a few KHz, GSM
can use its 25MHz band to switch to another
frequency at different time slots and get diversity
in frequency domain.
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Cooperative Diversity
2
 Different users can form a distributed antenna
array to help each other in increasing diversity.
 Distributed versions of space time codes may be
applicable.
 Interesting characteristics:
 Users have to exchange information and this
consumes bandwidth.
 Operation is typically in half-duplex mode.
 Broadcast nature of the wireless medium can
be exploited.
 More on this issue later!
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Diversity Options
2
 Micro-diversity:
 Use diversity to combat small-scale fading.
 Mainly in receiver side.
 Recently Tx diversity also proposed through
space-time coding
 Macro-diversity:
 Use diversity to combat large-scale shadowing
effects.
 Use of multiple base stations and select the
one which is not in shadow.
 Use of largely separated antennas at Base to
improve reverse link.
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Combining Techniques (1)
2
 Scanning Combining
Use a signal above threshold level and keep it
until it is above threshold. (less switching)
 Selection Combining
Fading path with highest gain is used.
 Maximal Ratio Combining (MRC)
All paths co-phased and summed with optimal
weighting to maximize combiner output SNR.
 Equal Gain Combining (EGC)
All paths co-phased and summed with equal
weighting. (less complexity than MRC and not
much lower performance)
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Combining Techniques (2)
2
Selection Combining
 Assume M independent Rayleigh fading branches
at receiver.
 Assume each branch has average SNR = Γ
 If each branch has instantaneous SNR = γi, then,
since the amplitude α has Rayleigh distribution,
fading power α2will have exponential distribution
of the form:
p(γi ) = 1/ Γ exp(-γi /Γ )
 Therefore, the probability that a branch has
signal power less than some threshold γ, is given
by:
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Pr[γi< γ ] = 1 – exp(-γ /Γ )
Combining Techniques (3)
2
Selection Combining
 Now, the probability that all branches are below
threshold is given by:
Pr[γ1, γ2, …, γM ≤γ ]=Pr[γmax<γ ] = (1 –exp(-γ /Γ ))M
 Prob. density function of γ is :
PM(γ ) = d/dγ ((1 –exp(-γ /Γ ))M)
= M/Γ (1 –exp(-γ /Γ ))M-1exp(-γ /Γ )

γav = ∫PM(γ ) dγ = Γ Σ(1/i) , i=1:M
 Maximum change in γav is when M changes
from 1 to 2.
 Therefore most advantage in using diversity
comes from 2 antennas and that is what we
mostly see at Base stations.
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Combining Techniques (4)
2
Selection Combining
 Example:
for M=1, probability of
output of selection
diversity be more than
γ /Γ =-20dB, is only 99%.
 But for M =2,
the probability goes
up to 99.99%.
 Up to 20dB gain
with one more antenna.
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Combining Techniques (4)
2
Maximal Ration Combining
 Signals ri from each M diversity branches are
co-phased and individually weighted by Gi
optimally to maximize SNR: rM= ΣGiri
 Since noise power is also given by: NT = N Σ(Gi)2
 Output SNR = (rM)2/NT = 1/N (ΣGiri)2/ Σ(Gi)2
 Gi s should be found such that output SNR is
maximized: Gi= ri/N
Output SNR = 1/N Σri2= Σγi
(Output SNR = Sum of SNRs of all branches)

γav = MΓ
 About 22dB improvement for same scenario
 2 dB improvement compared with selection
combining, but at much higher complexity.

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Multiuser Diversity (1)
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Diversity in wireless systems arises from
independent signal paths.
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Multiuser Diversity (2)
2
 Traditional forms of diversity includes time,
frequency and antennas.
 Multiuser diversity arises from independent
fading channels across different users.
 Fundamental difference: Traditional diversity
modes pertain to point-to-point links, while
multiuser diversity provides network-wide benefit.
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Multiuser Diversity (3)
2
 In a large system with users fading independently, there is
likely to be a user with a very good channel in any time.
 Long term total throughput can be maximized by always
serving the user with the strongest channel.
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Multiuser Diversity (4)
2
 Multiuser diversity provides a system-wide benefit.
 Challenges:
 Share the benefit among the users in a fair way.
 Measure and send back channel condition to TX side.
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Multiuser Diversity (5)
2
 Mobile measures the channel based on the pilot and
predicts the SINR to request a rate.
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Multiuser Diversity (6)
2
Proportional Fair Scheduler (PFS)
 Schedule the user with the highest ratio RK /TK
where:
RK = current requested rate of user K
TK = average throughput of user K
in the past time slots.
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Multiuser Diversity (7)
2
Higher Mobility and Channel Dynamics
Channel varies faster and has more dynamic range
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in mobile environments.
Multiuser Diversity (8)
2
Diversity gain reduces with higher mobility.
Can only predict the average of the channel
fluctuations, not the instantaneous values.
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