16582/16418 Wireless Communication
Lecture Notes 7: Mobile RadioLecture Notes 7: Mobile Radio Channel Modeling II
St ti ti l M d l f F diStatistical Models for Fading Processes
Dr. Jay Weitzen
ContentsContents• Quick Review of Fading Models• Statistical Models for Channel Fading Process
– Rayleigh– Rician– Nakagami
C l l ti F d D ti R t d D th• Calculating Fade Durations, Rates, and Depths• Case Study: Characterizing the MMDS Wireless
ChannelC b i F di• Combating Fading– Diversity– Interleaving
E li ti– Equalization– Rake Receiver– OFDM
Appendix: Introduction to MIMO for 4th generationc 2007-2012 Dr. Jay Weitzen
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• Appendix: Introduction to MIMO for 4th generation systems
Quick Review of Fading ModelsQuick Review of Fading Models
• Dispersion in Time and Frequency EffectDispersion in Time and Frequency Effect Channel model
• In Time look at relation between multipathIn Time, look at relation between multipath spread and bit duration– Selective or Flat FadingSe ect e o at ad g– BW of channel vs. BW of signal
• In frequency look at Doppler SpreadIn frequency look at Doppler Spread relative to inverse of Bit Duration– Fast or Slow Fading
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g– Signaling rate vs. channel change rate
Types of Small-scale FadingSmall-scale FadingTypes of Small scale Fadingg(Based on Multipath Tİme Delay Spread)
Flat Fading F S l ti F diFlat Fading
1. BW Signal < BW of Channel 2. Delay Spread < Symbol Period
Frequency Selective Fading
1. BW Signal > Bw of Channel2. Delay Spread > Symbol Periody p y 2. Delay Spread Symbol Period
Small-scale Fading(Based on Doppler Spread)
Slow FadingFast Fading
1 High Doppler Spread
Slow Fading
1. Low Doppler Spread1. High Doppler Spread2. Coherence Time < Symbol Period3. Channel variations faster than baseband
signal variations
2. Coherence Time > Symbol Pe3. Channel variations smaller tha
signal variationsc 2007-2012 Dr. Jay Weitzen
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signal variations g
Impulse Response of the Fading M lti th M d lMultipath Model
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Flat FadingFlat Fading
• Occurs when symbol period of the• Occurs when symbol period of the transmitted signal is much larger than the Delay Spread of the channelDelay Spread of the channel
– Bandwidth of the applied signal is narrow.
• Occurs when the amplitude of the receivedOccurs when the amplitude of the receivedsignal changes with time
• For example according to Rayleigh DistributionFor example according to Rayleigh Distribution
• May cause deep fades. – Increase the transmit power to combat this situation
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Increase the transmit power to combat this situation.
Flat FadingFlat Fading
h(t,s(t) r(t)
TS
0 TS 0 0 TS+
Occurs when:BS << BC
and
BC: Coherence bandwidthBS: Signal bandwidthTS: Symbol period
TS >> S y p
: Delay Spread
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Frequency Selective FadingFrequency Selective Fading
• Occurs when channel multipath delay• Occurs when channel multipath delay spread is greater than the symbol period.
Symbols face time dispersion– Symbols face time dispersion– Channel induces Intersymbol Interference
(ISI)(ISI)• Bandwidth of the signal s(t) is wider than
the channel impulse responsethe channel impulse response.
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Frequency Selective FadingFrequency Selective Fading
h(t,s(t) r(t)
TS
0 TS 0 0 TS+TS
Causes distortion of the received baseband signalCauses distortion of the received baseband signal
Causes Inter-Symbol Interference (ISI)
Occurs when:Occurs when:BS > BC
andTS <
As a rule of thumb: TS <
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ISI is result of Selective FadingS s esu t o Se ect e ad g
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Fast FadingFast Fading• Due to Doppler Spread
• Rate of change of the channel characteristicsis larger than the
Rate of change of the transmitted signal• The channel changes during a symbol period. • The channel changes because of receiver motion. • Coherence time of the channel is smaller than the
symbol period of the transmitter signal y p g
Occurs when: BS: Bandwidth of the signalBS < BD
andTS > TC
S gBD: Doppler SpreadTS: Symbol PeriodTC: Coherence Bandwidth
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Slow FadingSlow Fading• Due to Doppler Spread
• Rate of change of the channel characteristics• Rate of change of the channel characteristicsis much smaller than the
Rate of change of the transmitted signal
Occurs when: B B d idth f th i lOccurs when:BS >> BD
andTS << TC
BS: Bandwidth of the signalBD: Doppler SpreadTS: Symbol PeriodTC: Coherence BandwidthC
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Different Types of FadingDifferent Types of FadingTS
Flat Fast
Symbol Period of
Flat SlowFading
Flat Fast Fading
Symbol Period ofTransmitting Signal
Frequency Selective Frequency Selective
TTC
Slow Fading Fast Fading
Transmitted Symbol PeriodTS
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With Respect To SYMBOL PERIOD
Different Types of FadingDifferent Types of FadingBS
Frequency SelectiveSlow Fading
Frequency Selective Fast Fading
Transmitted B b d B
Flat Fast
BasebandSignal Bandwidth
Flat Slow
BC
BBD
Fading Fading
Transmitted Baseband Signal BandwidthBS
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With Respect To BASEBAND SIGNAL BANDWIDTH
Statistical Models For Small Scale Fading
Three Major Effects: Attenuation, Long-term Fading (Shadowing), and Short-term Fading.
Fading occurs with distance on
order of ¼ B ildi wavelengthBuildings,
Trees, cars obstruct signals on a medium toon a medium to
small scale: Shadowing
Attenuation: Signal g
Attenuates with Distance
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Fading Is the Result of Constructive and D t ti W C bi iDestructive Wave Combining
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Small Scale Fading in Space and TimeS a Sca e ad g Space a d e
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Space/Time Interference patternsSpace/ e te e e ce patte s
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Impulse Response of a Multipath Ch lChannel
Aican be deterministic or random complex Gaussian Variables
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i p
Many Scatterers from same distance results in random fading at each
distance bindistance bin
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Many Waves Combine Due to Scatteringa y a es Co b e ue to Scatte g
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Real and Imaginary Parts are Gaussian D t C t l Li it ThDue to Central Limit Theorem
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Fading DistributionsFading Distributions
• Describes how the received signal amplitudeDescribes how the received signal amplitude changes with time. – Remember that the received signal is combination of multiple
signals arriving from different directions phases and amplitudessignals arriving from different directions, phases and amplitudes. – With the received signal we mean the baseband signal, namely
the envelope of the received signal (i.e. r(t)).
• Its is a statistical characterization of the• Its is a statistical characterization of the multipath fading.
• Often used distributionsOften used distributions– Rayleigh Fading– Ricean Fading– Nakagami Fading
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– Nakagami Fading
Rayleigh and Rician Di t ib tiDistributions
• Rayleigh Describes the received signal envelopeRayleigh Describes the received signal envelopedistribution for channels, where all the components are non-LOS: p
• i.e. there is no line-of–sight (LOS) component.
• Rician Describes the received signal envelopedistribution for channels where one of the multipath components is LOS component.
• i.e. there is one LOS component.
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Rayleigh FadingRayleigh Fading
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Rayleigh FadingRayleigh Fading
Rayleigh distribution has the probability density function (PDF) given by:
)( 0)(2
2
22 rer
rp
r
Rayleigh distribution has the probability density function (PDF) given by:
)( 00
)( 2
r
rp
2 is the time average power of the received signal before envelope detection. is the rms value of the received voltage signal before envelope detectiong g p
Remember: 2 power) (average rmsVP (see end of slides 5)
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Rayleigh Fading (cont’d)Rayleigh Fading (cont d)The probability that the envelope of the received signal does not exceed a specified value of R is given by the CDF:
R R
r edrrpRrPRP 2 2
2
1)()()(
specified value of R is given by the CDF:
0
2533.12
)(][
mean drrrprEr
)(21 solvingby found 177.1
20
r
median drrprmedian
2
2 0
rmsr
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Rayleigh PDF0.7
Rayleigh PDF
0.5
0.6 mean = 1.2533median = 1.177variance = 0.4292
0.3
0.4
0 1
0.2
0
0.1
0 1 2 3 4 5
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Pdf and Cdf of Rayleigh Fadingd a d Cd o ay e g ad g
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The Envelope is Rayleigh Distributede e ope s ay e g st buted
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Rayleigh Fading Marginay e g ad g a g
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Rayleigh Outage Probabilityay e g Outage obab ty
100
Rayleigh Fading
10-1
bilit
y
10-3
10-2
Out
age
Prob
ab
10-4
10-5
-10 0 10 20 30 40 50
Margin (dB)
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Digital Communication in Rayleigh F di i Diffi ltFading is Difficult
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Ricean Distribution
• When there is a stationary (non-fading)
Ricean Distribution
• When there is a stationary (non-fading) LOS signal present, then the envelope distribution is Riceandistribution is Ricean.
• The Ricean distribution degenerates to Rayleigh when the dominant componentRayleigh when the dominant component fades away.
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Rician PDFc a
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Rician Fadingc a ad g
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Nakagami Probability Distributiona aga obab ty st but o
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Nakagami Shape FactorNakagami Shape Factor
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Nakagami Fading for stationary user
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Level Crossing and Fade RatesLevel Crossing and Fade Rates
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Level Crossing Rate (LCR)Level Crossing Rate (LCR)
Threshold (R)( )
LCR is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified threshold level R in a positive going direction. It is given by:
where
22
mR efN
secondper crossings
rms) tonormalized valueenvelope (specfied
where
: /
R
rms
NrR
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Average Fade DurationAverage Fade DurationDefined as the average period of time for which the received signal isbelow a specified level Rbelow a specified level R.
For Rayleigh distributed fading signal, it is given by:
eN
RrN
11]Pr[1 2
RR
rR
fe
NN
,21
2
rmsm rf 2
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ADF for Different DistributionsADF for Different Distributions
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Fading Model –Gilbert Elliot ModelGilbert-Elliot Model
Fade PeriodSignalg
Amplitude
Threshold
Time t
Good(Non-fade)
Bad(Fade)
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Gilbert-Elliot Model
G d B d
1/AFD
Good(Non-fade)
Bad(Fade)
1/ANFD
The channel is modeled as a Two-State Markov Chain. Each state duration is memory-less and exponentially distributed.
The rate going from Good to Bad state is: 1/AFD (AFD: Avg Fade Duration)The rate going from Bad to Good state is: 1/ANFD (ANFD: Avg Non-Fade
Duration))
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16 582 C St d16.582 Case Study:Channel Measurements for
2G MMDS and applicability to 4G LTE and WiMax
CreditsCredits
• Based on slides from Dhananjay Gore• Based on slides from, Dhananjay Gore, Stanford UniversityConducted for Sprint Broadband 1999• Conducted for Sprint Broadband, 1999-2000
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Goal of ProgramGoal of ProgramTo characterize wireless channels for 2G MMDS but 4G has beenfor 2G MMDS but 4G has been deployed in this band
BTS CPEChannel
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What Is MMDS?What Is MMDS?
• MMDS (Microwave Multipoint distributionMMDS (Microwave Multipoint distribution System), is a band of frequencies at 2.5 GHz, allocated for fixed and mobile digital
i ticommunication– Originally viewed as a “wireless cable” system for
broadcast digital servicesg– Viewed as mostly TDD
• Business case required self installable CPE t d d t k li bilit dantennas and need to know reliability and
channel characteristics
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Typical ScenarioTypical Scenario
BTS
Co-Channel BTS
50’-100’
Ht 8’-15’
0.1 - 4 miles
Distance to mobile
scatterers
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Scenario Dimensions• Terrain
– Rural, Suburban, Urban, Hilly • Antenna Configuration
– BTS, CPE antenna heights & spacing– Polarization, Beam-width,
• Reuse Factor– 1 and 31 and 3
• Sectorization3
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– 3
Antenna ConfigurationsAntenna Configurations• BTS antenna heights
– 35’, 50’, 80’,120’ (35-120 ft)• CPE antenna heights
– Under the eaves: 85” to 95”, (~7 ft)– Patio of a Condominium: 130” (~10 ft)
Rooftop: 175” to 220” (15 20 ft)– Rooftop: 175 to 220 (15-20 ft)• CPE antenna spacing
0 5 5 wavelengths– 0.5 - 5 wavelengths • Beam-width 900 at BTS and 500 at CPE
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Measurement Set-upMeasurement Set up
Ant 1Ant 1 DAQ Card
NI PCI-MIO-16E-1
Dual Rx 2 x IQ
Ant 1
custom
Ant 1DualPA
custom
Matlab
Pre-processing
Hi LO
SignalGenerator
Lo LO
HP 4433B
SignalGenerator
SignalGenerator
2 x HP 4433B
SignalGenerator
ADClock
C++
DataAnalysis
PC
Matlab
RubidiumClock
DividerCircuit
HP 4433BHP 8648C
DividerCircuit
RubidiumClock
10MHz / 1PPS10MHz / 1PPS
PCBTS
CCI CPE2480 MHz4 MHz BW
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Measured Channel ParametersMeasured Channel Parameters
• Path Loss• K-factor• Delay Spread• Delay Spread• Doppler Power Spectrum• Level Crossing Rates (LCR)• Average Duration of Fade (ADF)g ( )• Antenna Correlation • C/I ratios
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• C/I ratios
Path-Loss MeasurementsPath Loss Measurements
• Published literature (AT&T measurements)Published literature (AT&T measurements)• SU measurements only for 0.1-4 miles
SU measurements made in multiple Bay• SU measurements made in multiple Bay area locationsS &• SU measurements agree with AT&T measurements
SU: Stanford University
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SU: Stanford University
G2 MMDS Path Loss ModelG2 MMDS Path Loss Model
Median Path Loss:
hf PLPLsddAdBPL )/(log10)( 010
where for d > d0
)/4(l20 dA
, 10 meters < hb < 80 meters
b h
cbha
)/4(log20 010 dA (free space path loss)
, b
b
b hbha
is the wavelength
(mean path loss exponent)
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is the wavelength
Path Loss Model (contd.)Path Loss Model (contd.)
• is a lognormal shadow fadings is a lognormal shadow fading – zero mean
terrain dependent standard deviation
s
– terrain dependent standard deviation• is the BTS height in metersbh
b• are constants dependent on the terrain category
cba , ,
• is chosen as 100m (reference distance)• is the distance from BTS
odd
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is the distance from BTSd
Correction TermsCorrection Terms
• Frequency correction terms• Frequency correction terms
2000log7.5 fPLf f in MHz
• CPE height correction term (> 2 meters)
2000
)2log(8.10 CPEh
hPL 1 meter < hCPE < 8 meters)2g(h
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Path Loss Scatter PlotPath Loss Scatter Plot-60
SU Measurements-100
-80
SU easu e e s
*-140
-120
From Erceg Model
h Lo
ss [d
B]
-180
-160-Pat
h
10-1 100 101-200
180
Base-Terminal Distance (km)
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( )
Mean Path Loss vs Distance Mean Path Loss vs Distance -80
-120
-100
]
Super Cell
-140
-120
Pat
h-Lo
ss [d
B]
Erceg
-180
-160Mea
n
g
10-1 100 101-200
Base-Terminal Distance (km)
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Base-Terminal Distance (km)
K-factor MeasurementsK-factor Measurements
t)( tt di icomponent (mean) fixedin power K
K = -10 dB K = 6 dB
component)(scatteredin varyingpower Typical Signal Envelope:
K 10 dB K 6 dB
-80
-75
-80
-75
-90
-85
RS
L(dB
)
RS
L(dB
)-90
-85
0 20 40 60 80 100 120 140 160 180 200-100
-95
Time (sec) Time (sec)0 20 40 60 80 100 120 140 160 180 200
-100
-95
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( ) ( )
K-factor ModelK factor Model
• Erceg model for K-factor• Erceg model for K-factorudKFFFK obhs
• Fs is a seasonal factor– 1.0; summer (leaves)– 2.5; winter (no leaves)
• Fh is the height factorh g– (h/3)0.46 (h is the CPE height in meters)
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K-factor Model (contd.)K factor Model (contd.)
• F is the beamwidth factor• Fb is the beamwidth factor– Fb = (b/10)-0.62; (b in degrees)
K d i ffi i t• Ko and are regression coefficients– Ko = 10; = -0.5
• u is a lognormal variable – zero mean– std. deviation of 8.0 dB
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K-factor Scatter PlotK factor Scatter Plot
40ht = 15m, 90 deg. Rx antenna
30
40
SU Measurements
10
20
-Fac
tor i
n dB
From Erceg Model
-10
0
K-
hr = 3m
10-1
100
101
-20
Distance in km
99.9% reliability
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K-factor and ReliabilityK factor and Reliability
• K-factors are highly variable
• To ensure 99.9% reliability, systems must be designed for zero K-factormust be designed for zero K-factor (Rayleigh fading)
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Delay Spread ModelDelay Spread Model
• Spike-Plus-Exponential Model (Erceg)Spike Plus Exponential Model (Erceg)
)()( /
iBAP i
A, B, o and are experimentally
)()(0
/
ieBAPi
i o
determinedT
2/2/
• Good Model for directive antennas
oo eeTrms 2/2/
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• Good Model for directive antennas
Delay Spread Scatter PlotDelay Spread Scatter Plot(Suburban)
0
5
10
osec
onds
(dB
)
SU Measurements
10
-5
0
Spre
ad in
Mic
ro
From Erceg Model
-20
-15
-10
RM
S D
elay
S
10-1
100
101
-25
Distance in km
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Doppler Power SpectrumDoppler Power Spectrum
122 126
-126
-124
-122
-130
-128
-126
-132
-130
-128db
fD ~0.4Hz-136
-134
-132db
fD ~2Hz
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5-134
fD(Hz)
High Wind
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-138
fD(Hz)
Low Wind
Rounded Spectrum with fD~ 0.1Hz- 2Hz
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Level Crossing Rate (LCR)Level Crossing Rate (LCR)
LCR is the rate (in sec) at which the signal crosses ( ) ga certain level
Level
Level Crossingsgnal
Lev
el
g
Sig
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Time
LCR (measured)LCR (measured)
101
LCR vs BTS antenna height for "UNDER THE EAVES" CPE
100
r sec
)
10-2
10-1
LCR
(pe
bts 35ft
bts 50ft
bts 80ft
-14 -12 -10 -8 -6 -4 -2 0 2 4 610
-3
bts 80ft
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level (dB) w.r.t. mean power
Average Duration of Fade (ADF)(ADF)
ADF i th d ti (i ) f hi h th i l l lADF is the average duration (in secs) for which the signal levelstays below a certain threshold
t t t t t
Level
t1 t2 t3 t4 t5
gnal
Lev
el
ADF = ti )/N
Sig i )
N: No. of fades
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Time0 T
ADF (measured)ADF (measured)
102
10 3
ADF vs BTS antenna height for "UNDER THE EAVES" CPE
100
101
F (s
ec)
10-2
10-1
AD
bts 35ft
-14 -12 -10 -8 -6 -4 -2 0 2 4 610
-3
level (dB) w.r.t. mean power
bts 50ftbts 80ft
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level (dB) w.r.t. mean power
Antenna Correlation (Spatial)Antenna Correlation (Spatial)
s1(t)
s2(t)s2(t)
|]s|]E[|sE[|-|]ssE[| 2121]|])s[||sE[(|]|])s[||sE[(|
2
222
11s,s 21 EE
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CPE Antenna CorrelationCPE Antenna Correlation Coefficient vs Antenna Spacing
0.7
0.8
cien
t
BTS ht 35’
0 5
0.6
orre
latio
n co
effi BTS ht 35
CPE (V. Pol)
0.4
0.5
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
CPE ht 97"
Antenna separation (wavelengths)
Co
Antenna separation (wavelengths)
• 0.75 - 1 wavelength spacing adequate for under the eaves CPE
• 10 wavelengths sufficient for BTS antenna spacing
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g p g
Frequency ReuseFrequency Reuse
77
1
23
1
23
1
23
77
BTS (1)7
9
1
23
1
23
4
65
79
79
4
65
4
65
7
89
7
89
22 2
1
23
1
23
7
89
7
89
First Tier
Second Tier
1
23
4
65
7
89
4
7
89
89
4
65
1
23
1
23
89
89
44
7
89
7
89
4
65
4
65
1
23
1
23
1
Second Tier84
65
8
1
23
7
89
1
23
7
89
4
65
4
65
7
89
44
8 8
1
23
1
23
74
Reuse Factor 3 x 9
65
65
1
23
1
23
1
23
89
65
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Reuse Factor 3 x 9
Measured C/I (Cell Edge)Measured C/I (Cell Edge)Excellent Conditions
-140
-120Electioneer Rd Reuse = 3 Rx Ant 1
Loss
[-dB
] C/I: 29.6447 dBPrimary
C/I = 29.6dB
20 40 60 80 100 120 140 160-180
-160
Time (s)
Pat
h L
CCIPrimaryCCI
120Electioneer Rd Reuse = 3 Rx Ant 2
-160
-140
-120
th L
oss
[-dB
] C/I: 33.8216 dBPrimary
C/I = 33.8dB
20 40 60 80 100 120 140 160-180
Pa
CCIPrimaryCCI
Reuse 3c 2007-2012 Dr. Jay Weitzen
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Reuse 3
Measured C/I (Cell Edge)Measured C/I (Cell Edge)Poor Conditions
-140
-120Welch Rd Reuse = 3 Rx Ant 1
Loss
[-dB
] C/I: 8.3504 dBPrimary
C/I = 8.3 dB
20 40 60 80 100 120 140-180
-160
Time (s)
Pat
h L
CCIPrimaryCCI
120Welch Rd Reuse = 3 Rx Ant 2
-160
-140
-120
th L
oss
[-dB
] C/I: 0.21909 dBPrimary
C/I = 0.21 dB
20 40 60 80 100 120 140-180
Pa
CCIPrimaryCCI
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Reuse 3
CDF of C/ I at the Cell Edge (Reuse= 3 x 9)
1
0.8
1
•C/I statistics
0.6
he C
ell E
dge - Randomly populate subs
- Compute path loss and
shadow loss
0.2
0.4
CD
F at
th shadow loss
- Compute C/I
- Average over many trials
-10 0 10 20 30 400
C/I (dB)
80 % coverage for cell edge
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Summaryy• Over 200 hrs of measurement effort
M d t (P th L K f t• Measured parameters (Path Loss, K-factor and Delay Spread) appear to conform to AT&T resultsAT&T results
• Consistency in new measurements of Doppler antenna correlation LCR and ADFDoppler, antenna correlation, LCR and ADF
• We feel reasonably comfortable that measurements capture the true nature ofmeasurements capture the true nature of MMDS propagation
• More measurements plannedc 2007-2012 Dr. Jay Weitzen
80
More measurements planned
ReferencesReferences• V. Erceg et. al, “An empirically based path loss model for wireless
channels in suburban environments,” IEEE JSAC, vol. 17, no. 7, July 1999, pp. 1205-1211.V Erceg et al “A model for the multipath delay profile of fixed wireless• V. Erceg et.al, A model for the multipath delay profile of fixed wireless channels,” IEEE JSAC, vol. 17, no.3, March 1999, pp. 399-410.
• Larry J. Greenstein et.al, “A new path-gain/Delay-spread propagation Model for digital Cellular Channels,” IEEE Trans. On Vehicular Technology vol 46 no 2 May 1997Technology, vol. 46, no. 2, May 1997.
• L.J. Greenstein, S. Ghassemzadeh, V.Erceg, and D.G. Michelson, “Ricean K-factors in narrowband fixed wireless channels: Theory, experiments, and statistical models,” Proceedings of WPMC’99, Amsterdam, September 1999.Amsterdam, September 1999.
• David Parsons, “The Mobile Radio Propagation Channel,” John Wiley and Sons, 1992.
• L. J. Greenstein and Vinko Erceg, “Gain Reductions Due to Scatter on Wireless Paths with Directional Antennas ” IEEE CommunicationsWireless Paths with Directional Antennas, IEEE Communications Letters, vol. 3, No. 6, June 1999.
• L.J. Greenstein et.al, “Moment-method estimation of the Ricean K-factor,” IEEE Communications Letters, vol.3, no.6, June 1999, pp. 175-176.
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Diversity in Mobile Radio Systems
Space Time Fading: Wide Beam
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Space time Fading, narrow bbeam
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Independent PathsIndependent Paths
.4• Space Diversity
– Multiple antenna elements separated by decorrelation distancedecorrelation distance.
• Polarization Diversity– Two transmit or receive antennas with differentTwo transmit or receive antennas with different
polarizations• Frequency Diversity f
Bc
– Multiple narrowband channels separated by channel coherence bandwidth
• Time DiversityTc
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Time Diversity– Multiple timeslots separated by channel coherence
time.
t
Introduction to DiversityIntroduction to Diversity
• Basic Idea– Send same bits over independent fading
paths– Combine paths to mitigate fading effectsTbb
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tMultiple paths unlikely to fade simultaneously
How To Maximize DiversityHow To Maximize Diversity
• Want 2 or more signals with approximately same average power
• Want signals to be uncorrelatedg
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Combining TechniquesCombining Techniques
• Selection Combining• Selection Combining– Fading path with highest gain used
• Equal Gain Combining– All paths cophased and summed with equal p p q
weighting
M i l R ti C bi i• Maximal Ratio Combining– All paths cophased and summed with optimal
i hti t i i bi t t SNRc 2007-2012 Dr. Jay Weitzen
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weighting to maximize combiner output SNR
Maximum ratio combining (MRC)(MRC)
h1*
h1
h2
yx
h2*
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Maximum ratio combining (cont’d)a u at o co b g (co t d)
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Selection combining (SC)Selection combining (SC)
Monitor Select
h1
MonitorSNR
Selectbranch
h2
yx
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Switched diversitySwitched diversity
• Switched diversity• Switched diversity– Switch-and-stay combining (SSC)– Switch-and-examine combining (SEC) ComparatorChannel
estimatorswitchingthreshold
h1
x
h2
x
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Calculating Probability of ErrorIntroduction• Improvements related to a reduced fading level are
Ca cu at g obab ty o o
• Improvements related to a reduced fading level are commonly quantified by average error rate curves.
• Th t i b • The average error rate may in some cases be difficult to evaluate analytically.
MotivationMotivation• Quantify the severity of fading by using a measure
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directly related to the fading distribution.
Diversity PerformanceDiversity Performance
M i l R ti C bi i (MRC)• Maximal Ratio Combining (MRC)– Optimal technique (maximizes output SNR)– Combiner SNR is the sum of the branch SNRsCombiner SNR is the sum of the branch SNRs.– Distribution of SNR hard to obtain.– Exhibits 10-40 dB gains in Rayleigh fading.
• Selection Combining (SC)– Combiner SNR is the maximum of the branch SNRs.Combiner SNR is the maximum of the branch SNRs.– Diminishing returns with # of antennas.– CDF easy to obtain, pdf found by differentiating.
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– Can get up to about 20 dB of gain.
Multiuser diversity GainMultiuser diversity GainSystem throughput for N users > than for 1 user
1
2Spatial diversity SCSEC
KSEC
User 1
User 2Multiuser diversity•Combiner = Base station•Antennas = Individual users
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Antennas Individual users
Multi-User Diversity (cont’d)
Introduction
u t Use e s ty (co t d)
Introduction• Always searching for the best user results in
a high and determinstic feedback load.a high and determinstic feedback load.Motivation• Utilize switched diversity algorithms reportedUtilize switched diversity algorithms reported
in the literature as multiuser access schemes to reduce the average feedback load.
• The base station probes the users in a sequential manner, looking not for the best
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user but for an acceptable user.
Combating Rayleigh Fading: S Di itSpace Diversity
• Fortunately, Rayleigh fades are very short and last a small
D
very short and last a small percentage of the time
• Two antennas separated by several wavelengths will not generally experience fades at thegenerally experience fades at the same time
• “Space Diversity” can be obtained by using two receiving antennas
d it hi i t t b i t t tand switching instant-by-instant to whichever is best
• Required separation D for good decorrelation is 10-20
Signal received by Antenna 1
Si l i d – 12-24 ft. @ 800 MHz.
– 5-10 ft. @ 1900 MHz.
Signal received by Antenna 2
Combined
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Combined Signal
Space Diversity Application LimitationsLimitations
• Space Diversity can be applied only th i i d f li k
D
on the receiving end of a link. • Transmitting on two antennas
would:fail to produce diversity since– fail to produce diversity, since the two signals combine to produce only one value of signal level at a given point --g g pno diversity results.
– produce objectionable nulls in the radiation at some angles
Signal received by Antenna 1
Si l i d • Therefore, space diversity is applied only on the “uplink”, i.e.., reverse path
there isn’t room for two
Signal received by Antenna 2
Combined
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– there isn t room for two sufficiently separated antennas on a mobile or handheld
Combined Signal
Polarization DiversityWhere Space Diversity Isn’t Convenientp y
• Sometimes zoning considerations or aesthetics preclude using separate diversity receive antennasdiversity receive antennas
• Dual-polarized antenna pairs within a single radome are becoming popular– Environmental clutter scatters RF
energy into all possible polarizations– Differently polarized antennas receive
signals which fade independentlyIn urban environments this is almost as
V+Hor\+/ – In urban environments, this is almost as
good as separate space diversity• Antenna pair within one radome can be V-
H polarized, or diagonally polarizedA B A B
\+/
– Each individual array has its own independent feedline
– Feedlines connected to BTS diversity inputs in the conventional way; TX
Antenna AAntenna BCombined
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inputs in the conventional way; TX duplexing OK
Combined
The Reciprocity PrincipleDoes it apply to Wireless?Does it apply to Wireless?
Between two antennas, on the same exact frequency, path loss is the
i b th di tisame in both directions• But things aren’t exactly the same in
cellular --– transmit and receive 45 MHz.
-148.21 db@ 870.03 MHz
apart– antenna: gain/frequency slope?– different Rayleigh fades
up/downlinkup/downlink– often, different TX & RX antennas– RX diversity
• Notice also the noise/interference-148.21 db Notice also the noise/interference environment may be substantially different at the two ends
• So, reciprocity holds only in a general sense for cellular
@ 870.03 MHz
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sense for cellular-151.86 db@ 835.03 MHz
Frequency DiversityFrequency Diversity
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Frequency Hopping for DiversityFrequency Hopping for Diversity
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Frequency Hopping and C/IFrequency Hopping and C/I
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Receive Diversity PerformancePerformance
Diversity gain
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Interleaving and De-interleaving for Fading interleaving for Fading
Channels
Motivation for InterleaverMotivation for Interleaver
• Interleaving is a form of time diversity• Interleaving is a form of time diversity– Usually combined with coding to provide
protection against burst errors caused byprotection against burst errors caused by fading
• Viterbi Algorithm used for detection of• Viterbi Algorithm used for detection of convolutional codes is not effective against burst errors We add interleaver toburst errors. We add interleaver to distribute burst error.
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Forward Error Correction for Fading Channels
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Theory of Interleaving
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Error Performance on Fading Channels
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Block Interleaver
Original Message
0 0 1 1
Writing00110101110000111011
Original Message
0 1 0 1
eadi
ng
00101011001001111011
Interleaver
1 1 0 0
0 0 1 1
Re
Burst Error
1 0 1 100110101001001111011
The order of original Message is
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g gchanged by Block Interleaver.
Block Deinterleaveroc e e ea e
0 1 1 1
Reading
00110101001001111011
Received Message
0 0 0 1
Wri
tin
g Burst ErrorDeInterleaver
1 1 0 0
1 0 1 1
W 01110001110010110011
0 0 1 1Distributed Error
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Example: CD InterleavingExample: CD Interleaving
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Example: Satellite C i tiCommunications
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Performance with InterleavingPerformance with Interleaving
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Combating Effects of Multipath and Fading in Wireless Systems
What to do against ISI?What to do against ISI?
• Wideband signals:Wideband signals:– channel delay = many symbol periods
heavy distortion of the received signal– heavy distortion of the received signal. • Several techniques can be applied to reduce or
get rid of ISI in wideband signal transmissionget rid of ISI in wideband signal transmission – Equalization (2nd gen)
spread signal modulation (3rd gen)– spread-signal modulation (3rd gen)– OFDM (4th gen)
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EqualizationEqualization
• The received signal is filtered in such a way thatThe received signal is filtered in such a way that ISI is eliminated or reduced. – Ideal ISI elimination is achieved when the filter is the
inverse of the channel response. – Clearly, the channel must be known, or accurately
estimated to perform effective equalizationestimated, to perform effective equalization. – Therefore, the equalizer needs to be trained to adapt
itself to the time-varying channel in wireless systems. y g yUsually this is achieved by transmitting a training sequence.
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• Equalization of the signal results in a decrease of ISI at the cost of a lower signal-to-noise ratio (SNR)
Direct sequence spread tspectrum
• In DS-SS modulation, the signal is multiplied with a code that results in a signal with a much wider bandwidth than the originalresults in a signal with a much wider bandwidth than the original information-bearing signal. In a time-dispersive multipath channel, the spread signal replicas, which travel via different paths, are un-correlated if the path delays are more than onepaths, are un correlated if the path delays are more than one symbol period apart from each other. After decorrelation in the receiver, the signal replicas from different paths are combined in a Rake receiver, thus all received energy is effectively used. gy y
• A disadvantage of using DS-SS with high bit-rate signals is that to achieve a sufficiently high processing gain, a very large bandwidth is required. This is especially the case in an indoor q p yenvironment, where the delay times between the paths are very short, in the order of 1 ns.
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OFDMOFDM• Symbols of high bit rate signal are distributed over a
large number of subcarriers. g– Low symbol rate per carrier. – Individual carrier signals see flat fading (no ISI).
Promising techniq e for f t re high bit rate• Promising technique for future high bit-rate applications.
• However, it suffers from a number of problems: , p– a very linear amplifier in the transmitter is required to prevent
signal distortion, – accurate synchronization in the receiver is neededaccurate synchronization in the receiver is needed, – in the transmitter and receiver real-time discrete Fourier
transform (DFT) operations have to be computed.
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Improving Performance of Improving Performance of Wireless Channels using MIMO
(the next generation of diversity)diversity)
MIMO is the Next generation of Di i SDiversity Systems
• Single-input, single-output (SISO) channelNo spatial diversity
• Single-input, multiple-output (SIMO) channelg p p pReceive diversity
• Multiple-input, single-output (MISO) channel Multiple input, single output (MISO) channel Transmit diversity
• Multiple input multiple output (MIMO) • Multiple-input, multiple-output (MIMO) channelC bi d t it d i di it
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Combined transmit and receive diversity
Introduction to the MIMO Channel
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Capacity of MIMO Channels
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Single Input- Single Output systems (SISO)systems (SISO)
x(t): transmitted signalx(t): transmitted signaly(t): received signalg(t): channel transfer functionn(t): noise (AWGN, 2)
g
y(t) = g • x(t) +x(t)
y(t)
y(t) = g • x(t) + n(t)
ESignal to noise ratio : Capacity : C = log2(1+)
2x2
σEρ g
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p y g2( )
Single Input- Multiple Output (SIMOM lti l I t Si l O t t (MISOMultiple Input- Single Output (MISO
• Principle of diversity systems (transmitter/Principle of diversity systems (transmitter/ receiver)
• +: Higher average signal to noise ratioRobustness
• - : Process of diminishing returnBenefit reduces in the presence of
correlationMaximal ratio combining• Maximal ratio combining
• Equal gain combining• Selection combining
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• Selection combining
Transmit Diversity
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Transmit Diversity with Feedback
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TX diversity with frequency weighting
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TX Diversity with antenna hopping
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TX Diversity with channel coding
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Transmit diversity via delay diversity
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Transmit Diversity Options
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MIMO Wireless Communications: Combining TX and RX Di itRX Diversity
• Transmission over Multiple Input Multiple Output (MIMO) radio channelsradio channels
Ad t I d S Di it d Ch l• Advantages: Improved Space Diversity and Channel Capacity
• Disadvantages: More complex, more radio stations and
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Disadvantages: More complex, more radio stations and required channel estimation
MIMO Model MIMO Model
TNTMMNTN WXHY T: Time index
W: Noise
• Matrix RepresentationW: Noise
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– For a fixed T
Multiple Input- Multiple Output systems (MIMO)systems (MIMO)
1 1H11
HNx1Mx1NxMNx1
nxy HHN1
HM N
H1M
• Average gain
HNM
HH 1H22 E
2t t lP
• Average gain HH
,H ijE
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22
totalP• Average signal to noise ratio
Shannon capacity
H22
T2
H2x
2 MσPdetlog
σEdetlogC HHIHHI g
H
2 Mρdetlog
Mσσ
HHI
K= rank(H): what is its range of values?
M
Parameters that affect the system capacity• Signal to noise ratio • Distribution of eigenvalues (u) of H
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Interpretation I: The parallel channels approachThe parallel channels approach
• “Proof” of capacity formula
• Singular value decomposition of H: H = S·U·VH
• S, V: unitary matrices (VHV=I, SSH =I)U : = diag(uk), uk singular values of Hk k
• V/ S: input/output eigenvectors of H• Any input along vi will be multiplied by ui
and will appear as an output along si
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Vector analysis of the signals
1. The input vector x gets projected onto the v ’svi s
2. Each projection gets multiplied by a diff t idifferent gain ui.
3. Each appears along a different si.uu1
u2
<x,v1> · v1 <x,v1> u1 s1
2<x,v2> · v2 <x,v2> u2 s2
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uK<x,vK> · vK
<x,vK> uK sK
Capacity = sum of capacities
• The channel has been decomposed into K parallel subchannelsK parallel subchannels
• Total capacity = sum of the subchannel iticapacities
• All transmitters send the same power:Ex=Ek
KK
ρ1logCC K E
222EuvxEu
1i
k21i
k ρ1logCC
1i
222 1logC kk uE
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2
kk2
k
kkk σ
Eu
s,nE
v,xEuρ
Interpretation II: pThe directional approach
Sing lar al e decomposition of H H• Singular value decomposition of H: H = S·U·VH
• Eigenvectors correspond to spatial directions• Eigenvectors correspond to spatial directions (beamforming)
1 1 (si)1
M N(si)N
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Example of directional interpretationinterpretation
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End of Module 7End of Module 7