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8/13/2019 2.MIMO- Multiple Antenna Schemes
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M ULTI ANTENNA SYSTEM
By
Pradip Paudyal
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I NTRODUCTION TO D IVERSITY T ECHNIQUES
Diversity= state of being varied, variety[Oxford Advanced Learners Dictionary]. The basic concept of diversity: transmit the signal viaseveral independent diversity branches to getindependent signal replicas via
time diversityfrequency diversityspace diversitypolarization diversity.
High probability: all signals not fade simultaneously.High probability: the deepest fades can be avoided.Protection against fading.
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ADAPTIVE ANTENNA
An adaptive antenna system consists of severalantenna elements, whose signals are processedadaptively in order to exploit the spatialdimension of the mobile radio channel
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A DAPTIVE A NTENNA O PERATION
Conventional BTS: radiation pattern covers thewhole cell areaSmart Antenna BTS:
adaptive radiation pattern, "spatial filter
transmission/reception only to/from the desired userdirectionminimize antenna gain to direction of other users
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SISO, SIMO, MISO
Single-Input, Single-Output channel suffers fromfadingSingle-Input, Multiple-Output channel: RX diversityMultiple-Input, Single-Output channel: TX diversity,
beam-forming.
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TRANSMIT D IVERSITY
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RECEIVE DIVERSITY
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D EFINITION OF MIMO Multiple-Input, Multiple-Output channelMapping of a data stream to multiple parallel data streamsand de-mapping multiple received data streams into asingle data stream
Aims at high spectral efficiency / high data rate
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MIMO- M ULTIPLE A NTENNA S CHEMES
The transmitting end as well as the receiving ends are equippedwith multiple antenna elements.Transmission of several independent data streams in parallelover uncorrelated antennas .
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MIMO-M ODE OF OPERATION
Spatial multiplexing :used to increase the data rate spatial diversity mode: to maximize range or reliability
Figure : Spatial multiplexing and spatial diversity mode
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MIMO-M ODE OF OPERATION CONT ..
Figure: Basic operation of MIMO System
Theoretical maximum rate increase factor = Min(NTx , N Rx) in a rich scattering environment andno gain in a line-of-sight environment.
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MIMO-G AINS
The use of multiple antennas can provide gaindue to
antenna gainmore receive antennas; more power is collected
interference gaininterference nulling by beam-forming (array gain)interference averaging (to zero) due to independentobservations
diversity gain against fadingreceive diversitytransmit diversity.
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C APACITY A NALYSIS OF MIMO S YSTEM
The classic Shannon-Hartley law suggests that theachievable channel capacity increaseslogarithmically with the transmit power. Bycontrast, the MIMO capacity increases linearlywith the number of transmit antennas, providedthat the number of receive antennas is equal tothe number of transmit antennas. With the
further proviso that the total transmit power is
increased proportionately to the number oftransmit antennas, a linear capacity increase isachieved upon increasing the transmit power,which justifies the spectacular success ofMIMOs ....
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C APACITY A NALYSIS OF MIMO S YSTEM
Shannons capacity Formula The maximum achievable transmission rate for agiven channel with band width B , transmittedsignal power P and in AWGN channel thecapacity of the system is given by :
In practice, this is considered as the SISO (singleinput single output). This equation gives theupper limit for achievable error free SISOtransmission rate.
20
1 P
C B log N B
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C APACITY A NALYSIS OF MIMO S YSTEM
General Capacity formula:Consider the antenna array with elements attransmitter and antenna array with element atreceiver. The impulse response of the channel betweenthe j th transmitter element and i th receiverelement is denoted as . ,ijh t
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C APACITY A NALYSIS OF MIMO S YSTEM
MIMO Channel Matrix
1 1 1 2 1
2 1 2 2 2
1 2
t
t
r r r t
, , ,n
, , ,n
n , n , n ,n
h ,t h ,t .h ,t
h ,t h ,t .h ,t H ,t
h ,t h ,t .h ,t
y t H ,t s t u t
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C APACITY A NALYSIS OF MIMO S YSTEM
The matrix elements are complex numbers thatcorresponds to attenuation and phase shift thatwireless channel introduced to the signal.Transformation of MIMO Channel into n SISOSub-channels by SVD technique .
min ,r t n n n
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C APACITY A NALYSIS OF MIMO S YSTEM
The output of MIMO system can be expressed as:
If we assume that transmitted signal bandwidthis narrow enough that the channel response canbe treated as flat across frequency, and thendiscrete time equation is:
y t H ,t s t u t
y Hs u
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C APACITY A NALYSIS OF MIMO S YSTEM
MIMO capacity can be estimated by the followingequation:
Where H is the channel matrix, R SS is the convexmatrix of transmitted vector S , H H is the
transpose conjucate of the H matrix and P ismaximum normalized transmit power. Byconverting MIMO channel to SISO sub-channel we can fiend simplified results.
2( )max log [det( )]
ss
H
sstr R P C I HR H
min ,r t n n n
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C APACITY A NALYSIS OF MIMO S YSTEM
Then total capacity of n SISO sub-channels is thesum of individual capacities and as a result totalcapacity of MIMO channel is:
Where, P k is the power allocated to the k th sub-
channel and is its power gain. According to thesingular value decomposition algorithm , k=1,2n are the eigenvalues of matrix, which arealways non negative.
22
1
log (1 )n
k k
k C p
2
k 2k
H HH
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C APACITY A NALYSIS OF MIMO S YSTEM
The power allocation algorithm must satisfy
We noticed that achieved capacity depends on thealgorithm used for allocating power to each sub-channel. The theoretical analysis assumes thechannel state known at the receiver.When channel sate is not known at transmitter,
then,
1
n
k k
p P
/k t p p n 2log det( ) H t
pC I HH n
22
1
log (1 )n
k t k
pC n
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C APACITY A NALYSIS OF MIMO S YSTEM
When channel state is known, it can performoptimum combining methods during the powerallocation process.One method to calculate the optimum powerallocation to n sub-channel is to employ thewater-filling algorithm .
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C APACITY A NALYSIS OF MIMO S YSTEM
Consider the assumption of CSI at thetransmitter; we can proceed to the followingcapacity formula.
Where is the amount of power that is assignedto k th sub-channel.
1
22
.log 1
nk
k k
t
pC n
k
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I NTRODUCTION TO S PATIAL M ULTIPLEXING
The basic concept of multiplexing: divide(multiplex) transmit a data stream severalbranches and transmit via several (independent)channels in
Time :time division multiplexing (TDM)frequency : frequency division multiplexing (FDM)
typical example: orthogonal FDM (OFDM)
space : space division multiplexing (SDM) or spatial
multiplexingdifferent bits from different antennarequires independent channels
code : code division multiplexing (CDM)applied in 3G systems.
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L INEAR D ISPERSION C ODING
Linear dispersion coding (LDC) offers aframework to combine spatial multiplexing andtransmit diversity.Code design consists of finding optimumdispersion matrices.
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L AYERED S PACE T IME A RCHITECTURES
Bell Labs Layered Space Time (BLAST) architecture was oneof the first spatial multiplexing systems.
Called also layered space time (LST).Detection originally based on linear and decision feedbackequalization.
Vertical LST (V LST) : Basic scheme with no coding involved Horizontal LST (H LST) : Coding included. Diagonal LST (D LST) : Coding and spatial interleavingincluded and Spatial interleaving to improve performance viaspatial diversity.
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S COPE
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REFERENCES T. M. Cover & J. A. Thomas, Elements of Information Theory. JohnWiley & Sons, 1991. ISBN: 0-471-06259-6G. J. Foschini& M. J. Gans, On limits of wireless communications in afading environment when using multiple antennas. Wireless PersonalCommunications , vol. 6, pp. 311-335, Nov.-Dec. 1999.D. Gesbert, M. Shafi, D. Shiu, P. J. Smith, and A. Naguib , Fromtheory to practice: An overview of MIMO space-time coded wirelesssystems, IEEE J. Select. Areas Commun., vol. 21, no. 3, pp. 281 302,2003.J. C. Liberti. and T. S. Rappaport, Smart Antennas for WirelessCommunications: IS-95 and Third Generation CDMA Applications,Prentice Hall, Upper Saddle River,NJ, 1999.
A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bolcskei , An overviewof MIMO communications A key to gigabit wireless, Proc. IEEE, vol.92, no. 2, pp. 198 218, Feb. 2004.E. Telatar, Capacity of multi-antenna Gaussian channels. EuropeanTransactions on Telecommunications, vol. 10, no. 6, pp. 585-595,Nov.-Dec. 1999.B. Vucetic & J. Yuan, Space Time Coding. John Wiley and Sons,2003. ISBN 0-470-84757-3
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Thank you.