06 - Wireless Signal Processing - Mimo

8/6/2019 06 - Wireless Signal Processing - Mimo

1/55

1

PROCESAMIENTO DE SEAL

EN SISTEMASINALMBRICOS

MAESTRIA EN INGENIERAREA TELECOMUNICACIONESUniversidad Pontificia Bolivariana

Leonardo Betancur [email protected]


2/55

2

Contenido

Sistemas MIMO

Modelado de canales MIMO Desvanecimiento rpido en canales MIMO

Desvanecimiento lento en canales MIMO

Arquitecturas de receptores Arquitectura V-BLAST

Arquitectura D-BLAST

Multiplexacin y diversidad

Enlaces en sistemas MIMO

Evaluacin de capacidad en sistemas MIMO


3/55

3

Canal con desvanecimiento plano

(Bcoh>> 1/ Tsymb) Canal con slow fading (Tcoh>> Tsymb)

nr receptores y nt transmisores (antenas)

Sistema de ruido limitado (no CCI)

Los receptores estiman perfectamente elcanal

Solo se considera diversidad espacial

Suposiciones Generales


4/55

4

Sistema MIMO en General


5/55

5


y = Hs + n

User data stream

.

.

User data stream

.

.

.

.Channel

Matrix H

s1

s2

sM

s

y1

y2

yM

yTransmitted vector Received vector

.

.

h11

h12

Where H =

h11 h21 .. hM1h12 h22 .. hM2

h1M

h2M

.. hMM

. . .. .

MT

MR

hij is a Complex Gaussianrandom variable that models

fading gain between the ith

transmit and jth receive

antenna


6/55

6


Ambiente de Radio propagacin


7/55

7

Ventajas de Sistemas MIMO

Incrementa la eficiencia espectral de un

sistema inalmbrico significativamente.

Permite generar diversidad de ganancia para

mitigar los efectos de desvanecimiento delcanal.

Codificacin de Canal puede incorporar un

mejor desempeo del sistema


8/55

8

H11

H21

= log2[1+(PT/2

)|H|2

] [bit/(Hzs)]

H = [ H11 H21]Capacity increases logarithmicallywith number of receive antennas...

Diversidad en recepcin tpica

+= *22

detlog HHIt

T

n

PC


9/55

9

Diversidad de transmisin /

Beamforming

H11

H12

Cdiversity = log2(1+(PT/22)|H|2) [bit/(Hzs)]

Cbeamforming = log2(1 +(PT/2

)|H|

2

) [bit/(Hzs)]

3 dB SNR increase if transmitter knows H Capacity increases logarithmically with nt


10/55

10

Multiple Input Multiple Output

H11

H22

H12H21

=

2221

1211

HH

HHH

Cdiversity = log2det[I +(PT/22 )HH]=

++

+= 222122 21log

21log

TT PP

Where the i are theeigenvalues to HH

1

2m=min(nr, nt) parallel channels, equal power allocated to each pipe

Interpretation:ReceiverTransmitter


11/55

11

Tipos de Canal


12/55

12

Canales con Desvanecimiento

Fadingrefers to changes in signal amplitude and phase caused by thechannel as it makes its way to the receiver

Define Tspread to be the time at which the last reflection arrives and Tsym tobe the symbol time period Time-spread of signal

Frequency-selective Frequency-flat

Tsym

Tspread

time

freq

1/TsymOccurs for wideband signals (small Tsym)

TOUGH TO DEAL IT!

Tsym

Tspread

time

freq

1/TsymOccurs for narrowband signals (large Tsym)

EASIER! Fading gain is complex Gaussian

Multipaths NOT resolvable


13/55

13

Matriz del Canal H

In addition, assumeslow fading

MIMO Channel Response

Taking into account slow fading, the MIMO channel impulse response is constructed as,

Time-spread

Channel Time-variance

Because of flat fading, it becomes,

a and b are transmit and

receive array factor vectors

respectively. S is the

complex gain that is

dependant on direction and

delay. g(t) is the transmit

and receive pulse shaping

impulse response With suitable choices of array geometry and antenna element patterns,

H( ) = H which is an MR x MT matrix with complex Gaussian i. i. d random variables

Accurate for NLOS rich-scattering environments, with sufficient antenna spacing attransmitter and receiver with all elements identically polarized


14/55

14

Valores propios del Canal

Orthogonal channels HH =I, 1= 2= = m= 1

)/1(log),min(1log 221

22 tTrt

m

i

i

t

T nPnnn

PC

+=

+= =

diversity

Capacity increases linearly with min( nr , nt ) An equal amount of power PT/nt is allocated

to each pipe

Transmitter Receiver


15/55

15

Capacidad de Canales MIMO

=

+=

=

+=m

i

i

t

T

t

T

n

P

HHn

P

IC

122

*

22

1log

detlog

H unknown at TX H known at TX

=

+=

m

i

iip

C1

22 1log

Where the power distribution overpipes are given by a water fillingsolution

= =

+

==

m

i

m

i i

iT pP1 1

1

1

234

p1

p2

p3

p4

),min( tr nnm =


16/55

16

Capacidad de Canales MIMO

y = Hs + n Let the transmitted vector s be a random vector to be very general and n is normalized noise.

Let the total transmitted power available per symbol period be P. Then,

C = log 2 (IM + HQHH) b/s/Hz

where Q = E{ssH} and trace(Q) < P according to our power constraint

Consider specific case when we have users transmitting at equal power over the channel andthe users are uncorrelated(no feedback available). Then,

CEP = log 2 [IM + (P/MT)HHH] b/s/Hz

Telatar showed that this is the optimal choice for blindtransmission

Foschini and Telatar both demonstrated that as MT and MR grow,

CEP = min (MT,MR) log 2 (P/MT) + constant b/s/HzNote: When feedback is available, the Waterfillingsolution is yields maximum capacity but converges to equal power capacity athigh SNRs


17/55

17

Capacidad (continuacion)

The capacity expression presented was over one realization of the channel.Capacity is a random variable and has to be averaged over infinite realizations to

obtain the true ergodic capacity. Outage capacity is another metric that is used tocapture this

So MIMO promises enormous rates theoretically! Can we exploit thispractically?


18/55

18

Modelos de Canal y limitaciones por

Retardo In stochastic channels,

the channel capacity becomes a random

variable

Define : Outage probability Pout = Pr{ C < R }

Define : Outage capacity R0 given a outageprobability Pout = Pr{ C < R0 }, this is the delaylimited capacity.

Outage probability approximates theWord error probability for coding blocks of approx length100


19/55

19

Ejemplo : Canal Rayleigh

Hij CN (0,1)

nr=1nr= nt

Ordered eigenvalue

distribution fornr= nt = 4 case.


20/55

20

Criterios de Diseo

MIMO Systems can provide two types of gain

Spatial Multiplexing Gain Diversity Gain

Maximize transmission rate

(optimistic approach)

Use rich scattering/fading toyour advantage

Minimize Pe (conservative

approach)

Go for Reliability / QoS etc

Combat fading

System designs are based on trying to achieve either goal or alittle of both

If only I could have both! As expected, there is a tradeoff


21/55

21

Diversidad

Each pair of transmit-receive antennas provides a signal pathfrom transmitter to receiver. By sending the SAME

information through different paths, multiple independently-faded replicas of the data symbol can be obtained at thereceiver end. Hence, more reliable reception is achieved

A diversity gain dimplies that in the high SNR region, my Pedecays at a rate of 1/SNRd as opposed to 1/SNR for a SISO

system The maximal diversity gain dmaxis the total number of

independent signal paths that exist between the transmitterand receiver

For an (MR,MT) system, the total number of signal paths isMRMT1 d dmax= MRMT

The higher my diversity gain, the lower my Pe


22/55

22

Multiplexacin Espacial

y = Hs + n y = Ds + n (through SVD on H)where D is a diagonal matrix that contains the eigenvalues of HHH

Viewing the MIMO received vector in a different but equivalentway,

CEP = log 2 [IM + (P/MT)DDH] = log 2 [1 + (P/MT)i] b/s/Hz

Equivalent form tells us that an (MT,MR) MIMO channel opensupm = min (MT,MR) independent SISO channels between the

transmitter and the receiver

So, intuitively, I can send a maximum of m different informationsymbols over the channel at any given time

=

m

i 1


23/55

23

Sistemas Prcticos

Redundancy in time

Coding rate = rc Space- time redundancy over T

symbol periods

Spatial multiplexing gain = rs

1

2

MT

Channel

coding

Symbol

mapping

Space-

TimeCoding

.

.

R bits/symbol

rs : number of different

symbols N transmitted

in T symbol periods

rs = N/T

Spectral efficiency = (R*rc info bits/symbol)(rs)(Rs symbols/sec)

w

= Rrcrs bits/s/Hz assuming Rs = w

rs is the parameter that we are concerned about: 0 rs MT

** If rs = MT, we are in spatial multiplexing mode (max transmission

rate)

**If rs 1, we are in diversity mode

Non-redundantportion of symbols


24/55

24

Aprovechando un Canal MIMO

Time

s0

s0

s0

s0

s0

s0

s1

s1

s1

s1

s1

s2

s2

s2

s2

V-BLAST

D-BLAST

An

tenna s1 s1 s1 s1 s1 s1

s2 s2 s2 s2 s2 s2

s3 s3 s3 s3 s3 s3

nr nt required

Symbol by symbol detection.Using nulling and symbolcancellation V-BLAST implemented -98

by Bell Labs (40 bps/Hz) If one pipe is bad in BLASTwe get errors ...

Bell Labs Layered

Space Time Architecture


25/55

25

V-BLAST

This is the only architecture that goes all out for maximum rate.

.

.

s1

s2

sM

s

User data

stream .

.

User data

stream.

.

y1

y2

yM

y

.

.

HV-BLAST

Processing

Split data into MT streamsmaps to symbols send Assume receiver knows H

Uses old technique ofordered successive cancellation to recoversignals

Sensitive to estimation errors in H

rs = MT because in one symbol period, you are sending MT differentsymbols

MT MR


26/55

26

V-BLAST

The prototype in an indoor environment was operated at a carrier frequency of1.9 GHz, and a symbol rate of 24.3 ksymbols/sec, in a bandwidth of 30 kHz withMT = 8 and MR = 12

Results shown on Block-Error-Rate Vs average SNR (at one received antenna

element); Block = 100 symbols ; 20 symbols for training

Each of the eight substreams utilized uncoded16-QAM, i.e. 4 b/symb/trans

Spec eff = (8 xmtr) ( 4 b/sym/xmtr )(24.3 ksym/s)30 kHz

= 25. 9 bps/Hz

In 30 kHz of bandwidth, I can push across 621Kbps of data!! Wirelessspectral efficiencies of this magnitude are unprecedented, and are

furthermore unattainable using traditional techniques


27/55

27

Receptores Alternantes

Can replace OSUC by other front-ends; MMSE, SUC,ML for instance

OSUC

ML


28/55

28

D-BLAST

In D-BLAST, the input data stream is divided into sub streams whichare coded, each of which is transmitted on different antennas timeslots in a diagonal fashion

For example, in a (2,2) system

receiver first estimates x2(1) and then

estimates x1(1) by treating x2

(1) as

interference and nulling it out

The estimates of x2(1) and x1

(1) are fed to a

joint decoder to decode the first substream

After decoding the first substream, the receiver cancels

the contribution of this substream from the received signals

and starts to decode the next substream, etc.

Here, an overhead is required to start the detection process;corresponding to the 0 symbol in the above example

Receiver complexity high

MT MR


29/55

29

Alamouti

Transmission/reception scheme easy to implement Space diversity because of antenna transmission. Time diversity

because of transmission over 2 symbol periods Consider (2, MR) system

Receiver uses combining and ML detection rs = 1

V-BLAST SUC

Alamouti

If you are working with a (2,2)system, stick with Alamouti!

Widely used scheme: CDMA2000, WCDMA and IEEE 802.16-

2004 OFDM-256


30/55

30

Comparaciones

LOW

MODERATE

HIGH

Pe

LOW

HIGH

LOW

ImplementationComplexity

ALAMOUTI

D-BLAST

V-BLAST

Scheme

LOW

MODERATE

HIGH

SpectralEfficiency


31/55

31

MIMO y Beamforming

Requires that channel H is known at the transmitter

Is the capacity-optimal transmission strategy if

Cbeamforming = log2(1+SNR1) [bit/(Hzs)]

SNR12

11

Which is often true for line of sight (LOS) channels

Only one pipe is used


32/55

32

Capacidad de Sistemas MIMO

La capacidad con Energa constante:

+= H

TN

NC

RHHIH

detlogE 2

antennasRXofnumbertheisantennasTXofnumbertheis

antennaRXeachatsesignal/noitheis

matrixchannelcomplextheis

R

T

NN

H


33/55

33

Receptor BLAST

Las antenas detectan por turnos, usando

cancelacin de interferencia donde sea posible.

T b C difi i Di d


34/55

34

Turbo Codificacin y Diseo de

ReceptoresLog likelihood ratio (LLR)

Combining LLRs

outputsoftprioriaextrinsic

SAEXTMAP

++=

++=

( ))1Pr(

1Pr

log)( =+=

= xx

x


35/55

35

Combinacin Mutua de Informacin

Combining LLRs

Optimum weights

[ ]

( )+=

=

=

)+(=

T

T

w

w

ww

MAP

MAP

S

ASAMAP

SAMAPEXT

)iiTw

iopt wIw ,maxarg, =


36/55

36

Ejemplo MIMO en HSPDA

Objective: Increase DL user data-rates through a combination of code re-use

across transmit antennas and high-order modulation schemes.

Code re-use results in high levels of interference, even in non-dispersive

channel conditions. This can be particularly disruptive when using high-

order modulation schemes such as 16- and 64-QAM.

4x4 MIMO radio link


37/55

37

Receptor No Iterativo para MIMO

No iterations occur between the detector and decoder. Both the detector and decoder can be iterative or non-iterative.

Space-Time channel equalization for orthogonalization of the received signatures in

dispersive channel conditions is optional.


38/55

38

Receptores Iterativos para MIMO

Iterations occur between the detector and decoder (and possibly equalizer).

Both the detector and decoder can be iterative or non-iterative.

The more reliable decoder soft-outputs (LLRs or Extrinsic Information) are used to

improve the detection (or optionally also the equalization) in an iterative process.

Space-Time channel equalization is again optional for dispersive channels.


39/55

39

Receptores Iterativos

The complex APP detector is replaced by alow-complexitySuccessive InterferenceCanceller based on matched filter (rake) detection units (MF-SIC). High performance isachieved via iterations with a turbo-decoder in conjunction withsoft-output combining.

With soft-output combining, soft-outputs computed in the current iteration are combinedwith those from the previous iteration. This suppresses convergence instabilitiescaused by incorrect cancellations. Combining weights are computed off-line in order tomaximize the Mutual Information[Cla-03a] [Cla-03c] after each combining operation.[Cla-02] H.Claussen, H.R.Karimi, B.Mulgrew, A Low Complexity Iterative Receiver based on Successive Cancellation for MIMO,

Personal Wireless Communications 2002, October 2002, Singapore.

[Cla-03a] H.Claussen, H.R.Karimi, B.Mulgrew, Layered Encoding for 16- and 64-QAM iterative MIMO Receivers,

5th European Personal Mobile Communications Conference, April 2003, Glasgow, UK

[Cla-03c] H.Claussen, H.R.Karimi, B.Mulgrew, Improved Max-Log MAP Turbo-Decoding using Maximum Mutual Information Combining,

September 2003, PIMRC 2003, Bejing, 2003


40/55

40

Receptore Iterativos

The received signal observed over thetth symbol epoch may be

written as

Iteration1: Order symbolsaccording to highest reliability (e.g. signature energies) at each symbol

epoch.

Performsymbol-level MF-SICat each symbol epoch:

Use rake to derive hard- and soft-estimates for most reliable symbol.

Subtract its contribution from the received signal.

Repeat for next most reliable symbol.

De-interleave MF-SIC soft-outputs (LLRs), decode, re-interleave and finally re-apply to

MF-SIC for next iteration.

( 1) 1

1 1( ) ( ) ( ) ISI ( ) C

T

R

N Kn N Q W n

k kn kr t a t x t v t

+

= == + +

H( ) ( ) ( )nn

k ky t a t r t =

{ } { }{ }( ) ( ) ( ) sgn Re[ ( )] sgn Im[ ( )]n n nk k kr t r t a t y t j y t = +


41/55

41

Receptores Iterativos

Order bitsaccording to highest reliability (decoder LLRs fromprevious iteration) at each symbol epoch.

Performbit-level MF-SICat each symbol epoch:

Use rake to derive hard- and soft-estimates for most reliable bit.

Subtract its influence (based on decoder LLR from previous iteration) fromreceived signal.

wherei= 0 or 1, dependent on whether the bit of interest forms the real orimaginary part of the 4-QAM symbol

Repeat for next most reliable bit.

Combine MF-SIC soft-outputs (LLRs) according to theMaximum Mutual Information(MMI) principle, de-interleave, decode, combine decoder soft-outputs (MMI principle), re-interleave and finally re-apply to MF-SIC for next iteration (q+1).

{ }H H,0

4 1( ) ( ) ( ) + ( 1) ( ) ( ) {0,1}

2

n nn i

k i k k iy t a t r t r t a t i

N j=

{ },( ) ( ) ( )sgn ( )ni n

k k ir t r t j a t t =

, , ,

, , ,

( ) [ ] : ( ) [ ] (1 ) ( ) [ 1]

( ) [ ] : ( ) [ ] (1 ) ( ) [ 1]

n n n

k i k i k i

n n n

k i k i k i

y t q y t q y t q

t q t q t q

= +

= +


42/55

42

Receptor APP

Full APP joint-detection implies search over a trellis of states for2M-QAMand ISI extending overL symbols. For no dispersion (L=0) and re-use ofKorthogonalcodes, number of states reduces to a more manageable .

As a result, space-time equalizationis performed first to eliminate dispersion.The equalizer output is then de-spread for each of the codesc1 cK , resulting insufficient statisticsz

1z

Kfor each symbol epoch.

The pre-whitened APP algorithm is applied tozkat each symbol epoch, forjoint-detection of bits transmitted from all antennas via thekthspreading code.This is repeated fork=1K.


43/55


44/55

44

Receptor APP

Pre-whitened APP detection:

Considering only theNT rows of the equalized and de-spread signalzkwhichcorrespond to thetth symbol epoch, we have

2 1

( )

( ) ( ) ( ) C and 1...TN

k k k k

ku t

z t c x t t v k K = + =T

The optimum maximum a posteriori probability (MAP) soft outputs in the form of

log-likelihood ratiosfor each transmitted bitbk,in(t) withn=1NT andi{0,1}

( )( )

( )

12

,

12

,

2

( )

( )| ( ) 1 0

,2

( )( )| ( ) 1 0

1exp ( ) ( ) ln P{ ( )}

( ) ln1

exp ( ) ( ) ln P{ ( )}

knk ik

knk ik

ku t k k k

x t b t n

k i

ku t k k k x t b t

z t c x t x t N

y b t

z t c x t x t N

=+

=

+

=

+

R

R

whereuk(t)=Tk(t)v andRuk(t)=E{uk(t)uk(t)H}=N0Tk(t)Tk(t)

H.


45/55

45

Receptor APP

Thea posteriori probability (APP) detector, is derived by using themax-logapproximationto give

( ) ( )

( )

12

,

12

,

22

, ( )( )| ( ) 1

22

( )( )| ( ) 1

( ) min ( ) ( ) ln P{ ( )}

min ( ) ( ) ln P{ ( )}

n kk ik

n k

k ik

n

kk i u t k k k x t b t

ku t k k k x t b t

y b t z t c x t x t

z t c x t x t

=

=+

R

R

Theapproximation makes the APP detector sub-optimal. While the performancedifference may be insignificant at high SNRs, for low SNRs (range of interest) thiscan no longer be ignored


46/55

46

Receptor M PIC

Proposed receiver (Option 1):

As in the reference receiver, space-time equalizationis performed first to eliminatedispersion. The equalizer output is then de-spread for each of the codesc1 cK ,resulting in sufficient statisticsz1zK for each symbol epoch.

The de-spread symbol outputs are processed by a pre-whitened MS-PPIC detector(=Recursive Neural Network) in order to suppress the interference from the othertransmitter antennas[Cla-03b].

[Cla-03b] H.Claussen, H.R.Karimi, B. Mulgrew, High Performance MIMO Receivers based on Multi-Stage Partial

Parallel Interference Cancellation. VTC 2003 Fall, 2003

C


47/55

47

Receptor M PIC

Iterative Calculation of MS-PPIC (NNet) outputs:

Considering only the theNTrows of the equalized and despread signalzkcorresponding to thetth symbol epoch, we have

2 1

( )

( ) ( ) ( ) C and 1...TNk k k k

ku t

z t c x t t v k K = + =T

Deriving a pre-whitened statistic

12

( ) ( )

H1

H

( ) ( ) ( ) ( ) C where E{ ( ) ( )}

and E{ ( ) ( )}

T

k t k t

N

kk u k u k k k

k k

w t z t x t t u t u t

t t

= = + =

=

R R R

I

The derived statistic wk(t) will be used as input to the MS-PPIC, which is equivalentto the bias of the Neural Network and may be written as wk,[0](t).

R M l i P i l PIC


48/55

48

Receptor Multistage Partial PIC

Prewhitened statistic

Difference equation

( )

++=

+=

xx

xw

R

R

( ){ }xwx =+ R11

R M l i P i l PIC


49/55

49


The detector shown is amulti-stagepartial parallel interference cancellationwith decision feedback within each stage[Mos-96].

The detector is equivalent to aRecursiveNeural Networkas proposed for CDMAmulti-user detection in[Kho-99]. The

architecture presented here includes softoutput generation.

Model for a non-linear Neuron:

[Kho-99] H.Khoshbin-Ghomash, Low Complexity Neural Network Structure for Implementing the Optimum ML Multi-User

Receiver in a DS-CDMA Communication System, pp. 643-647, VTC-99, The Netherlands.

[Mos-96] S. Moshavi, Multi-User Detection for DS-CDMA Communications, IEEE Comms Magazine, pp. 124-136, October 1996.

R t M lti t P ti l PIC


50/55

50


Soft output calculation:

After sufficient iterations the detector converges and the soft outputscan be derived:

( ) ,,4

( ) { ( )+ ( 1) ( )}2

n nn n i n

k i k k iy b t w t w t

j=

R

The detector iterations may be described as follows, wherewnk,[m](t) is the nth

element ofwk,[m](t) at iteration m:

( ) ( ){ }

,[ 1]

1 1

,[ ] ,[0] ,

,[ ]

for 1 ... (Iterations)

( )for 1 ... (Antennas)

( ) ( ) tanh Re[ ] j tanh Im[ ]

( )

end

end

where diag( )

k m

Tn n

k m k nn n

k m

m M

u w tn N

w t w t u u

u w t

=

==

= +=

= =

:R

R R R

Si l i


51/55

51

Simulaciones

4x4 MIMO link (NT=NR=4).

Spreading factorQ=16.

K=16 orthogonal spreading codes, reused across all transmit antennas.

Interleaving & coding block size: 1000 blocks x 5114 information bits.

Rayleigh propagations channels:

Flat fading at 3km/h.

Dispersive fading (3 chip-spaced equal-power taps) at 3km/h.

1/3 rate, 8-state turbo encoder (HSDPA specs). Max-log MAP (soft-input, soft-output) decoding algorithm.

6 iterations of the turbo decoder.

6 iterations between MF-SIC and turbo-decoder.

6 iterations of the MS-PPIC (NNet) detector.

Detector has perfect knowledge of the average channel conditions during eachtransmitted block.

4 QAM


52/55

52

-6 -5 -4 -3 -2 -1 0 110

-4

10-3

10-2

10-1

100

Performance comparison for 4-QAM and flat fading

Bit/Frame-ErrorRate

(info-bits)

Eb/No [dB] (Eb=TX-energy/info-bits)

standard APP - BERstandard APP - FERMS-PPIC - BER

MS-PPIC - FERMF-SIC - BERMF-SIC - FER

4-QAM (Flat Fading)

Target

FER

4 QAM i i di


53/55

53

-6 -5 -4 -3 -2 -1 0 110

-4

10-3

10-2

10-1

100

Performance comparison for 4-QAM and dispersive channel

Bit/Frame-Error

Rate

(info-bits)

Eb/No [dB] (Eb=TX-energy/info-bits)

standard APP - BERstandard APP - FERMS-PPIC - BERMS-PPIC - FERMS-PPIC (full) - BER

MS-PPIC (full) - FERMF-SIC - BERMF-SIC - FER

4-QAM (Dispersive Fading)

Target

FER

Bibliografa Sugerida


54/55

54

Bibliografa Sugerida

Mobile Fading Channels. Patzl, Matthias. Wiley. 2002. ISBN0471495492

Space-time Coding. Theory and Practice. Jafarkhani, Hamid. CamridgeUniversity press. 2005. isbn 978-0-521-84291-4

Digital Communications over Fading Channels, K. Simon, Marvin;Alovini Mohamed-slim. Wiley. Isbn 0-471-64953-8

Wireless Communications Principles and Practice. Rappaport, T.Prentice Hall

Theory and Applications of OFDM and CDMA wideband wirelesscommunications. Schulce, Henrik; Luders, Christian.

Space time processing for MIMO communications. Gershman, A.B;Sidiropoulos N.D. Wiley

OFDM and MC CDMA for broadband Multi User communicationsWLANs and Broadcasting. Hanzo, L et al. Wiley.

Digital Beam forming in Wireless Communications. Litva, J.

Preguntas


55/55

55

Preguntas

Preguntas y Sugerencias

Contacto:[email protected]

[email protected]

06 - Wireless Signal Processing - Mimo

Documents

Transcript of 06 - Wireless Signal Processing - Mimo