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PROCESAMIENTO DE SEAL
EN SISTEMASINALMBRICOS
MAESTRIA EN INGENIERAREA TELECOMUNICACIONESUniversidad Pontificia Bolivariana
Leonardo Betancur [email protected]
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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
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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
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Sistema MIMO en General
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Sistema MIMO en General
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
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Sistema MIMO en General
Ambiente de Radio propagacin
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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
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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
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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
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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
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Tipos de Canal
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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
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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
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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
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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 =
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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
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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?
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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
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Ejemplo : Canal Rayleigh
Hij CN (0,1)
nr=1nr= nt
Ordered eigenvalue
distribution fornr= nt = 4 case.
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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
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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
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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
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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
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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
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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
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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
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Receptores Alternantes
Can replace OSUC by other front-ends; MMSE, SUC,ML for instance
OSUC
ML
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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
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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
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Comparaciones
LOW
MODERATE
HIGH
Pe
LOW
HIGH
LOW
ImplementationComplexity
ALAMOUTI
D-BLAST
V-BLAST
Scheme
LOW
MODERATE
HIGH
SpectralEfficiency
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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
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Capacidad de Sistemas MIMO
La capacidad con Energa constante:
+= H
TN
NC
RHHIH
detlogE 2
antennasRXofnumbertheisantennasTXofnumbertheis
antennaRXeachatsesignal/noitheis
matrixchannelcomplextheis
R
T
NN
H
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Receptor BLAST
Las antenas detectan por turnos, usando
cancelacin de interferencia donde sea posible.
T b C difi i Di d
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Turbo Codificacin y Diseo de
ReceptoresLog likelihood ratio (LLR)
Combining LLRs
outputsoftprioriaextrinsic
SAEXTMAP
++=
++=
( ))1Pr(
1Pr
log)( =+=
= xx
x
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Combinacin Mutua de Informacin
Combining LLRs
Optimum weights
[ ]
( )+=
=
=
)+(=
T
T
w
w
ww
MAP
MAP
S
ASAMAP
SAMAPEXT
)iiTw
iopt wIw ,maxarg, =
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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
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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.
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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.
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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
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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 = +
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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
= +
= +
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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.
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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.
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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
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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
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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
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Receptor Multistage Partial PIC
Prewhitened statistic
Difference equation
( )
++=
+=
xx
xw
R
R
( ){ }xwx =+ R11
R M l i P i l PIC
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Receptor Multistage Partial PIC
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
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Receptor Multistage Partial PIC
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
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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
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-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
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-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
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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
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Preguntas
Preguntas y Sugerencias
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