doc.: ieee 802.11-04/0016r0 submission january 2004 yang-seok choi et al., vivatoslide 1 layered...

January 2004

Yang-Seok Choi et al., ViVATO

Slide 1

doc.: IEEE 802.11-04/0016r0

Submission

Layered Processing for MIMO OFDM

Yang-Seok Choi, [email protected]

Siavash M. Alamouti, [email protected]

January 2004


Slide 2

doc.: IEEE 802.11-04/0016r0

Submission

Assumptions Block Fading Channel

– Channel is invariant over a frame– Channel is independent from frame to

frame CSI is available to Rx only

– Perfect CSI at RX– No feedback channel

Gaussian codebook

January 2004


Slide 3

doc.: IEEE 802.11-04/0016r0

Submission

Motivations … To fully exploit Space- and Frequency-diversity in MIMO

OFDM– Each information bit should undergo all possible space- and

frequency-selectivity – Subcarriers should be considered as antennas

(Space and frequency should be treated equally)– Apply Space-Time code (STC) over all antennas and subcarriers

STC – STC encoder generates multiple streams– Large dimension STC decoding is prohibitively complex in MIMO

OFDM– Not only decoding, but also “designing good code” is complex

19248,4 Ex. KnNKn TT

dEncoder Information

bits

Symbols

STC

January 2004


Slide 4

doc.: IEEE 802.11-04/0016r0

Submission

Motivations (cont’d)… Serial coding : Use Single stream code and apply

Turbo-code style detection/decoding– Serial code generates single stream (convolutional code,

LDPC, Turbo-code,..)– MAP, ML or simplified ML with iterative decoding is

complicated in MIMO OFDM (calculating LLR, large interleaver size,…)

Is there any efficient way of maximizing both Space- and Frequency-diversity while achieving the capacity?– Use existing code (No need of finding new large dimension

STC)– Reduce decoding complexity of ML or MAP (linearly increase

in the number of subcarriers and antennas)

Information bits dS/P

SymbolsEncoder

Serial Coding

January 2004


Slide 5

doc.: IEEE 802.11-04/0016r0

Submission

Parallel Coding Parallel coding : Multiple Encoders

– Encoder generates single stream – Each layer carries independent information bit stream– In order to reduce decoding complexity, equalizer can

be adopted

Parallel Coding

Information bits dS/P

Symbols

Encoder

Encoder

Encoder

January 2004


Slide 6

doc.: IEEE 802.11-04/0016r0

Submission

System Model

dH

w

y

)()()( nnn wHdy

. . ,/:

,)()(th vector winoise 1:)(

,)()(th vector widata 1:)(

1,),(h Matrix wit channel :

vector,received 1:)(

2

2

2

NPPowerTxTotalPSNR

nnEMn

PnnENn

lkHENM

Mn

MH

NH

Iwww

Iddd

H

y

where

January 2004


Slide 7

doc.: IEEE 802.11-04/0016r0

Submission

Linear Equalizers (LE)

MF : LS (or ZF) : MMSE :

wGHdGyGz HHH

1111

M

HHHN

HH IHHHHIHHG

HHH HHHG 1)(

HH HG

dH

w

yzHG

Equalizer

January 2004


Slide 8

doc.: IEEE 802.11-04/0016r0

Submission

Layered Processing (LP)

LP– Loop– Choose a layer whose SINR (post MMSE) is

highest among undecoded layers– Apply MMSE equalizer– Decode the layer– Re-encode and subtract its contribution from

received vector– Go to Loop until all layers are processed

dH

w

yzLP

January 2004


Slide 9

doc.: IEEE 802.11-04/0016r0

Submission

“Instantaneous” Capacity Capacity under given realization of channel

matrix with perfect knowledge of channel at Rx

from this point on for convenience the conditioning on H will be omitted

If transmitted frames have spectral efficiency less than above capacity, with arbitrarily large codeword, FER will be arbitrarily small

If transmitted frames have spectral efficiency greater than above capacity, with arbitrarily large codeword, FER will approach 100%.

HHIHHI

HydH

NH

M

HIC

22 loglog

)|;(max

January 2004


Slide 10

doc.: IEEE 802.11-04/0016r0

Submission

Mutual Information in LE Theorem 1 (LE)

For any linear equalizer

– Equality (A) holds

where A is a non-singular matrix

– Equality (B) holds iff and are diagonal

Proof : See [1]

);();()(

zdyd IICA

HMN G

);(1

)(

kk

N

k

B

zdI

MNwhenandNrankif

MNwhenMrankiff

MNwhenMrankif

HH )(

)(

)(

AHGG

G

G

HG H GG H

January 2004


Slide 11

doc.: IEEE 802.11-04/0016r0

Submission

Mutual Information in LE (cont’d) In general equality (A) can be met in most practical

systems. In general the equality (B) is hard to be met.

In most cases, the sum of mutual information in LE is strictly less than the capacity

There is a loss of information when is used as the decision statistics for

This means that only is not sufficient for detecting since the information about is smeared to as a form of interference.

Hence, we need joint detection/decoding such as MLSE across not only time but all layers as well.– However, MLSE can be applied prior to equalization No

need for an equalizer

kdkz

N

kkk zdIIIC

1

);();();( zdyd

kz kdkd Nkk zzzz ,,,,, 111

January 2004


Slide 12

doc.: IEEE 802.11-04/0016r0

Submission

Mutual Information in LP Theorem 2 (LP)

In LP (use MMSE at each layer)

where is the SINR (post MMSE) at k-th layer

Proof : See [1]

N

k

kkk

N

k

SINRzdIIC1

)(2

1

)1(log);();( yd

dH

w

yzLP

LP is an optimum equalizer !!!

)(kSINR

January 2004


Slide 13

doc.: IEEE 802.11-04/0016r0

Submission

Mutual Information in LP (cont’d) Chain rule says :

Note

where is the modified received vector at k-th stage in LP

– Decoder complexity can be reduced in LP– In LP, according to Theorem 2, MMSE equalizer

output scalar is enough for decoding while the chain rule shows that vector is required

),,;();( 111

dddIIC kk

N

k

|yyd

);(),,;( )(11

kkkk dIdddI y|y

)(ky

2 );();( )( TheoremzdIdIRuleChain kkk

k y

kz kd)(ky

January 2004


Slide 14

doc.: IEEE 802.11-04/0016r0

Submission

Mutual Information in LP (cont’d) There is no loss of information in LP Perfect

Equalizer is a perfect decision statistic for The received vector y is ideally equalized through

LP Hence, through “parallel ideal code”, k-th layer

can transfer without error

In LP it is natural that the coding should be done not across layers but across time (parallel coding)

Don’t need to design large dimension Space-Time code

ontransmissilayerbitsSINRC kk // )1(log )(

2

kz kd

January 2004


Slide 15

doc.: IEEE 802.11-04/0016r0

Submission

Practical Constraints Error propagation problem

– No ideal code yet

Layer capacity is not constant– Even if the sum of layer capacity is equal to

the channel capacity, individual layer capacity is variant over layers

– Unless CSI is available to Tx and adaptive modulation is employed, we cannot achieve the capacity

Optimum decoding order– SINR calculations: determinant calculations– One of bottlenecks in LP

January 2004


Slide 16

doc.: IEEE 802.11-04/0016r0

Submission

Solutions Error propagation problem

– Iterative Interference cancellation• Ordered Serial Iterative Interference Cancellation/Decoding (OSI-ICD)• Minimize error propagation and the number of iterations

Layer capacity is not constant– Spreading at Tx :

Spread each layer’s data over all layers Regulate Received Signal power

– Ordered detection/decoding at Rx :Serial Detection/Decoding No loss of information rate

– GroupingIncrease Layer size

– Layer Interleaver– Minimize variance of SINR over layers Maximize Diversity

Gain Decoding Order

– Layer Interleaver and Spreading :Less sensitive to decoding order

January 2004


Slide 17

doc.: IEEE 802.11-04/0016r0

Submission

Spreading Without Spreading

– Received Signal power for :

With Spreading

where T is a unitary matrix– is carried by which is a linear

combination of – Received Signal power for :

wHdy

wdHwHTdy ˆ

kd2

kk PS h

kd

nmknkm

nm

N

m

N

n

N

mmkmkk ttPtPPS hhhh ,ˆ

,*

,1 11

22

,

2

kd

kk Hth ˆ

Nhh ,,1

January 2004


Slide 18

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for Orthogonal channel Assume that channel vectors are

orthogonal each other– Example : Single antenna OFDM under time-

invariant multipath -- The channel matrix is diagonal

(OFDM w/ Spreading called MC-CDMA[2])

– Assume

– Then, the received signal power is constant

– SINR after MMSE is constant as well

nandmforN

t nm 12

,

kforN

PPS

N

mmkk

ˆ1

22

hh

January 2004


Slide 19

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for Orthogonal channel (cont’d) : SINR of after MMSE equalizer with

Spreading matrix

Constant SINR over k regardless of choice of T Constant Received Signal Power, SINR and

Layer Capacity Maximum diversity gain Note is a harmonic mean of

Hence,

kkH

NH

kk

HN

MMSESPkSINR

THHITHHI11

, 1

ˆˆ

11

N

lMMSElSINRN 1 1

111

MMSESPkSINR ,

MMSEk

MMSESPk SINRSINR min,

MMSESPkSINR ,1 MMSE

kSINR1

kd

January 2004


Slide 20

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for Orthogonal channel (cont’d) Although constant layer capacity is

achieved, layer capacity is less than the mean layer capacity from Jensen’s inequality or Theorem 1

Spreading destroys orthogonality of the channel matrix Inter-layer interference

N

lMMSEl

MMSESPkk SINRN

SINRC1

2,

2 1

11log)1(log

N

CSINR

NMMSEl

N

l

)1(log1

21

January 2004


Slide 21

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for iid MIMO channel There is no benefit when spreading is

applied to iid MIMO channel– Since the spreading matrix is a unitary matrix,

the channel matrix elements after the spreading are iid Gaussian

– Spreading may provide some gain in Correlated MIMO channel (when the layer size is smaller than number of Tx antennas)

January 2004


Slide 22

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for Block Diagonal Channel MIMO OFDM : Block Diagonal channel

matrix

Spreading Matrix– : Spreading over Space– : Spreading over Frequency

KH00

0

0H0

00H

H

2

1

TT ~T

T~T

January 2004


Slide 23

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for Block Diagonal Channel (cont’d) New channel matrix

where

Assume Then SINR at k-th subcarrier and n-th antenna

where is the SINR when (No spreading over frequency)

– Again,

K

lMMSESP

nl

MMSESPnk

INRSK

SINR

1,

,

,,

ˆ1

111

1

THH kk ˆ

KKKKKKK

K

K

ttt

ttt

ttt

HHH

HHH

HHH

H

ˆ~ˆ~ˆ~

ˆ~ˆ~ˆ~ˆ~ˆ~ˆ~

,2,1,

2,222,221,2

1,112,111,1

TH

MMSESPnlINRS ,

,ˆ

KIT ~

MMSESPnl

l

MMSESPnk INRSSINR ,

,,

,ˆmin

nandmforK

t nm 1~ 2

,

January 2004


Slide 24

doc.: IEEE 802.11-04/0016r0

Submission

Spreading for Block Diagonal Channel (cont’d)

Spreading regulates received signal power and SINR at the output of the MMSE equalizer, and hence maximizes diversity

Inverse matrix size for MMSE is nT instead of nT K because the channel matrix is a block diagonal matrix and the spreading matrix is unitary

Spreading increases interference power since it destroys orthogonality

January 2004


Slide 25

doc.: IEEE 802.11-04/0016r0

Submission

Ordered Decoding at RX Corollary 1

In LP, different ordering does not change the sum of layer capacity which is equal to channel capacity.

Proof : Clear from the proof of Theorem 2 Thus, even random ordering does not

reduce the information rate.– However, different ordering changes individual

layer capacity and yields different variance.

Hence, optimum ordering is required to maximize minimum layer capacity

January 2004


Slide 26

doc.: IEEE 802.11-04/0016r0

Submission

Ordered Decoding at RX (cont’d) Assume that channel vectors are orthogonal Without Spreading the layer capacity is

where the decoding order is assumed to be k

With Spreading (see [1] for proof)

–

–

MMSEk

MMSEk

LPk CSINRC )1(log2

MMSESPk

N

lMMSEl

LPSPLPSPl

lC

SINRNCC ,

12

,1

,

1

11logmin

N

l

MMSEl

LPSPN

LPSPl

lSINR

NCC

12

,, 11logmax

capacitylayertheimprovesLPlkforCC

capacitylayertheofregulationtheyieldsSpreading

CCCC

LPSPk

MMSESPl

LPl

l

LPSPl

l

LPSPl

l

LPl

l

,

maxmax,minmin

,,

,,

January 2004


Slide 27

doc.: IEEE 802.11-04/0016r0

Submission

Grouping A simple way of reducing layer capacity

variance is to reduce the number of layers by grouping (i.e. increasing layer dimension)– Namely, coding over several antennas or

subcarriers

N element data vector d is decomposed to subgroups (or layers)

In general, each layer may have a different size

N~

TTN

T~1 ddd

N~1 HHH

January 2004


Slide 28

doc.: IEEE 802.11-04/0016r0

Submission

Grouping (cont’d) Is there an equalizer which reduces

decoder complexity without losing information rate?

Generalized Layered Processing (GLP)– Assuming a decoding order to be k, at the k-th

layer, the received vector can be written as

where– MMSE Equalizer (L is the layer size)

– Let MMSE equalizer output

wdHy )()()( ~~ kkk

Nk

k~

)(~HHH TT

NTk

k~

)(~ddd

)(kHk yGz

Hk

-

kHk

-

HkkHk

H HIHHIHHHG LN

1

)()(

1

)()( 11

January 2004


Slide 29

doc.: IEEE 802.11-04/0016r0

Submission

Grouping (cont’d) Theorem 3 (GLP)

GLP does not lose information rate when is full rank and MMSE equalizer is applied

Proof : See [1]

At each layer, MMSE equalized vector is used instead of for the decoding

Under certain conditions [1]

kH

N

kkkIIC

~

1

);();( zdyd

kz)(ky

capacitylayertheimprovesGLPlkforCC GLPSPk

MMSESPl , ,,

January 2004


Slide 30

doc.: IEEE 802.11-04/0016r0

Submission

Layer Interleaving (LI) Layer Interleaving provide Layer diversity

– Doesn’t require memory and doesn’t introduce any delay– Doesn’t require synchronization– Diversity gain is less significant than spreading

LayerInterleaver

….

….

)(nxN

)(1 nx )(1 ny

)(nyN

)(1 nx

)(2 nx

Time, n

)(nxN

Inputstreamsto Layer

Interleaver

….

)1(1x )2(1x )3(1x

)1(2x )2(2x )3(2x

….

….

….

….

)1(Nx )2(Nx )3(Nx ….

….

….

)(1 ny

)(2 ny

Time, n

)(nyN

Outputstreams

after LayerInterleaver

….

)1(1x

)2(1x

)3(1x

)1(2x

)2(2x

)3(2x

….

….

….

….

)1(Nx

)2(Nx

)3(Nx

….

….

….

)2(1Nx

)1(3x

)2(3x

)3(1Nx

)3(2Nx

)1(4x

L=1 case

January 2004


Slide 31

doc.: IEEE 802.11-04/0016r0

Submission

Numerical Experiments General Tx Structure

Simulation Conditions– Without Interleaver– 2-by-2 MIMO OFDM, K=32 subcarriers N=64– iid MIMO channel– Maximum delay spread is ¼ of symbol duration– rms delay spread is ¼ of Maximum delay spread– Exponential delay profile– Decoding order is based on maximum layer capacity– 32-by-32 Walsh-Hadamard code for frequency

spreading – No spreading over space

S/PInformation

bits

Encoder SymbolInterleaver

Encoder SymbolInterleaver

LayerInterleaver

Spreading

….

….

…...

…...

... ...

... ...

January 2004


Slide 32

doc.: IEEE 802.11-04/0016r0

Submission

Numerical Experiments (cont’d) CDF of normalized layer capacity in MIMO OFDM, L=1

– Spreading yields steeper curve Diversity– LP improves Outage Capacity– Recall by Theorem 1&2

k

MMSESPk

k

MMSEk

k

LPSPk

k

LPk CCCCCCC ,, ,,

January 2004


Slide 33

doc.: IEEE 802.11-04/0016r0

Submission

Numerical Experiments (cont’d) CDF in MIMO OFDM, L=2(Grouped over antennas, )

– Grouping can significantly improve outage capacity– Unless Best grouping is employed, GLP has less outage capacity than LP– Spreading is still useful in reducing the variance of the layer capacity– Recall

MMSELP CC

lkforCC GLPSPk

MMSESPl , ,,

January 2004


Slide 34

doc.: IEEE 802.11-04/0016r0

Submission

Numerical Experiments (cont’d) Effect of Layer size and Spreading in LP and GLP

– w/o Spreading : distance of grouped subcarriers is maximized – w/ Spreading : neighboring subcarriers are grouped

• SP is effective when layer size is small•Ideal “single stream code” is better than Ideal “4-by-4 code” !!!•We don’t know optimum spreading matrix structure

January 2004


Slide 35

doc.: IEEE 802.11-04/0016r0

Submission

Numerical Experiments (cont’d) GLP performance with 2-by-2 STC

– 16 state 2 bps/Hz QPSK STTC (1 bps/Hz/antenna)– L=2, 128 symbols per layer– Two iterations (hard decision)

Parallel STC

IFFT

IFFT

STEncoding

S/P

S/P

Serial STC w/o Spreading

IFFT

IFFT

STEncoding

1

STEncoding

32

S/P

WH3232

Spreading

Spreading

January 2004


Slide 36

doc.: IEEE 802.11-04/0016r0

Submission

Numerical Experiments (cont’d) GLP of Parallel STC w/ SP has the best performance Serial STC has less frequency diversity gain

3.5 dB Gain

Loss due to non-ideal 2-by-2 STC

Ideal N-by-N STC

Ideal 2-by-2 STC w/ SP&GLP

Ideal 2-by-2 STC w/ GLP& w/o SP

2.1 dB Gain

January 2004


Slide 37

doc.: IEEE 802.11-04/0016r0

Submission

Comments on Serial code w/ SP Spreading provides diversity gain (steeper

curves) but increases interference Unless ML or Turbo type decoding over

antennas and subcarriers is applied, capacity cannot be achieved– Complexity grows exponentially with the number of

subcarriers and antennas

Partial spreading– The spreading matrix T is unitary but some of

elements are zero– Reduces interference– Reduces ML decoder complexity– Reduces diversity

January 2004


Slide 38

doc.: IEEE 802.11-04/0016r0

Submission

More on Partial Spreading Partial Spreading in MIMO OFDM

– K : number of subcarriers– SF : Spreading factor, number of subcarriers

spread over– SF> Max delay in samples Negligible

frequency diversity loss– Partial spreading over subcarriers

– The partial spreading matrix is useful when K is not a multiple of 4

SFKSF /

~ITT

matrixspreadingSFSFSF : T

January 2004


Slide 39

doc.: IEEE 802.11-04/0016r0

Submission

Versatilities of Parallel coding Allows LDMA (Layer Division Multiple Access)

– Parallel coding can send multiple frames by nature– Different frames can be assigned to different users

(Different spreading code are assigned to different users)

– A convenient form of multiplexing for different users– Control or broadcasting channel can be established

Adaptive modulation– By changing not only modulation order but also the

number of frames

January 2004


Slide 40

doc.: IEEE 802.11-04/0016r0

Submission

MMSE or MF instead of LP MMSE can be used instead of LP at first

iteration in order to reduce latency or complexity– Then, it requires more iteration than LP

because LP provides better SINR.

MF can also be used to reduce complexity. – But it will require more iterations and error

propagation is more severe.

LP requires less number of iterations

January 2004


Slide 41

doc.: IEEE 802.11-04/0016r0

Submission

Conclusions Large dimension STC design/decoding is prohibitively

complex Serial code can have limited diversity gain or the

complexity grows at least cubically with the number of subcarriers and antennas

Use parallel coding, apply SP at Tx and LP at Rx Spreading increases diversity gain when layer size is

small LP does not lose the information rate while LE does SP and Layer interleaver can reduce the sensitivity to

decoding order in LP or GLP Complexity of LP : Linearly increase in the number of

subcarriers and antennas LP needs less number of iterations LP w/ SP is an efficient way of increasing diversity gain

with reduced code design effort and decoding complexity

January 2004


Slide 42

doc.: IEEE 802.11-04/0016r0

Submission

References [1] Yang-Seok Choi, “Optimum Layered

Processing”, Submitted to IEEE Transactions on Information Theory, 2003

[2] Hara et al., “Overview of Multicarrier CDMA”, IEEE Transactions on Commun. Mag., pp.126-133, Dec. 1997

January 2004


Slide 43

doc.: IEEE 802.11-04/0016r0

Submission

Thank you for your attention!!

Questions?

January 2004


Slide 44

doc.: IEEE 802.11-04/0016r0

Submission

Back-up Different Spreading Matrix

doc.: ieee 802.11-04/0016r0 submission january 2004 yang-seok choi et al., vivatoslide 1 layered...

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