January 2004
doc.: IEEE 802.11-04/0016r2
Layered Processing
for MIMO OFDM
Yang-Seok Choi, [email protected]
Siavash M. Alamouti, [email protected]
Submission
Slide 1
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 2
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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) jointly over all antennas
and subcarriers
Ex. nT  4, K  48  N  nT K  192
Submission
Slide 3
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
STC
 STC
– STC encoder generates multiple streams
– Large dimension STC decoding is prohibitively complex in MIMO
OFDM
• STTC - Conventional techniques such as space-time trellis coding are
very complex
• STBC - Simpler techniques such as space-time block codes are
limited in dimension (2x2 for Alamouti code)
– Not only decoding, but also “designing good code” is complex
Symbols
Information
bits
Encoder

d
STC
Submission
Slide 4
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Serial Coding
 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,…)
Information
bits
Encoder
Symbols
S/P

d
Serial Coding
Submission
Slide 5
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Question?
 Is there any efficient way of maximizing both
Space- and Frequency-diversity while achieving
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)
Submission
Slide 6
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Encoder
Information
bits
Symbols
Encoder
S/P

d
Encoder
Parallel Coding
Submission
Slide 7
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
System Model
w
d
y
H
y (n)  Hd (n)  w (n)

where y (n) : M 1 received vector,

H : M  N channel Matrix wit h E H (k , l )

2

 1,
d (n) : N 1 data vector wi th E d (n)d (n) H  PI N ,


w (n) : M 1 noise vector wi th E w (n) w (n) H   2 I M ,
SNR :   P /  2 , Total Tx. Power  NP.
Submission
Slide 8
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Linear Equalizers (LE)

z  G H y  G H Hd  G H w
w
d
Equalizer
y
H
GH
z
GH  H H
 MF :
H
H
1
H
G

(
H
H
)
H
 LS (or ZF) :
1
1
 H

1 
1
H
H
H
H
 MMSE :
G   H H  I N  H  H  HH  I M 

Submission

Slide 9



Yang-Seok Choi et al., ViVATO

January 2004
doc.: IEEE 802.11-04/0016r2
Layered Processing (LP)
w
d
y
LP
H
z
 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
Submission
Slide 10
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
“Instantaneous” Capacity
 Capacity under given realization of channel
matrix with perfect knowledge of channel at Rx
C  max I (d ; y | H  H )
 log 2 I M  HH H  log 2 I N  H H H
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%.
Submission
Slide 11
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Mutual Information in LE
 Theorem 1 (LE)
For any linear equalizer N  M G H
( A)
C  I (d ; y)  I (d ; z )
( B) N

– Equality (A) holds
k 1
I (d k ; zk )
if rank (G )  M


iff rank (G )  M

if rank (G )  N and G H  AH H

when N  M
when N  M
when N  M
where A is a non-singular matrix
– Equality (B) holds iff G H H and G H G are diagonal
Proof : See [1]
Submission
Slide 12
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Mutual Information in LE (cont’d)
 In general equality (A) can be met in most practical systems.
 In general the equality (B) is not met.
N
C  I (d ; y )  I (d ; z )   I ( d k ; z k )
k 1
 In most cases, the sum of mutual information in LE is strictly less
than the capacity
 There is a loss of information when zk is used as the decision
statistics for d k
 This means that zk only is not sufficient for detecting d k since
the information about d k is smeared to z1 ,, zk 1 , zk 1 , , z N
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
Submission
Slide 13
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Mutual Information in LP
 Theorem 2 (LP)
In LP
(use MMSE at each layer)
N
N
C  I (d ; y )   I (d k ; z k )   log 2 (1  SINR ( k ) )
where SINR
k 1
(k )
k 1
is the SINR (post MMSE) at k-th layer
Proof : See [1]
w
d
y
z
LP
H
LP is an optimum equalizer !!!
Submission
Slide 14
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Mutual Information in LP (cont’d)
 Chain rule says :
N
C  I (d ; y )   I (d k ; y | d k 1 ,, d1 )
k 1
 Note
I (d k ; y | d k 1 , , d1 )  I (d k ; y ( k ) )
where y
is the modified received vector at k-th
stage in LP
(k )
Chain
Rule

I
(
d
;
y
)  I (d k ; zk )  Theorem 2

k
– Decoder complexity can be reduced in LP
– In LP, according to Theorem 2, MMSE equalizer
output scalar zk is enough for decoding d k while the
chain rule shows that vector y (k )is required
(k )
Submission
Slide 15
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Mutual Information in LP (cont’d)




There is no loss of information in LP  Perfect Equalizer
zk is a perfect decision statistic for d k
The received vector y is ideally equalized through LP
Hence, through “parallel ideal code”, k-th layer can
transfer without error
Ck  log 2 (1  SINR ( k ) ) bits / layer / transmission
 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
Submission
Slide 16
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 17
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
– Grouping
Increase Layer size
– Layer Interleaver
– Minimize variance of SINR over layers  Maximize Diversity Gain
 Decoding Order
– Layer Interleaver and Spreading :
Less sensitive to decoding order
Submission
Slide 18
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Spreading
 Without Spreading
y  Hd  w
– Received Signal power for d k : S k  P hk
2
 With Spreading
y  HTd  w  Hˆ d  w
where T is a unitary matrix
– d k is carried by hˆk  Ht k which is a linear
combination of h1 ,, hN
– Received Signal power for d k :
S k  P hˆk
Submission
2
N
 P t m,k
m 1
2
N
N
hm  P  tm* ,k tn,k hm , hn
2
m 1 n 1
m n
Slide 19
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
1
tm,n 
for  m and n
N
– Then, the received signal power is constant
N
2
P
2
ˆ
S k  P hk   hm for k
N m 1
2
– SINR after MMSE is also constant
Submission
Slide 20
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Spreading for Orthogonal channel (cont’d)

: SINR of d k after MMSE equalizer with
Spreading matrix
SINRkSP, MMSE
1  SINR
SP, MMSE
k
1
1


1
H
H
H
 I  Hˆ Hˆ 
T
I


H
H
N
 N
 kk
1

1 N
1

N l 1 1  SINRlMMSE





1
T

kk
 Constant SINR over k regardless of choice of T
 Constant Received Signal Power, SINR and Layer
Capacity Maximum diversity gain
 Note 1 SINRkSP,MMSE is a harmonic mean of 1  SINRkMMSE
 Hence, SINRkSP,MMSE  min SINRkMMSE
Submission
Slide 21
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
1 N

1


Ck  log 2 (1  SINR
)   log 2  
MMSE 
N l 1 1  SINRl


N
1
C
  log 2 (1  SINRlMMSE ) 
N l 1
N
SP, MMSE
k
 Spreading destroys orthogonality of the channel
matrix  Inter-layer interference
Submission
Slide 22
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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)
Submission
Slide 23
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Spreading for Block Diagonal Channel
 MIMO OFDM : Block Diagonal channel matrix
 H1
0
H 
 

0
 Spreading Matrix
0 
0  
 0 

0 HK 

0
H2


~
T  T T
– T : Spreading over Space
~
– T : Spreading over Frequency
Submission
Slide 24
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Spreading for Block Diagonal Channel (cont’d)
 New channel matrix
where
~
t1,1 Hˆ 1
~ ˆ
t H
H  HT   2,1 2
 
~
 tK ,1 Hˆ K
Hˆ k  H kT
~ ˆ
t1, 2 H1
~ ˆ
t2, 2 H 2

~ ˆ
tK , 2 H K
~ ˆ 
t1, K H1
~ ˆ 
 t2, K H 2 

 
~ ˆ 
 tK , K H K 

2
1
~
tm ,n 
for  m and n
K
 Assume
Then SINR at k-th subcarrier and n-th antenna
1
1  SINRkSP,n, MMSE 
1
K
K
1

SP , MMSE
ˆ
l 1 1  SINRl , n
~
, MMSE
where SˆINRlSP
is the SINR when T  I K (No spreading
,n
over frequency)
– Again,
, MMSE
SINRkSP,n, MMSE  min SˆINRlSP
,n
l
Submission
Slide 25
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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 n instead of n K
because the channel matrix is a block diagonal
matrix and the spreading matrix is unitary
T
T
 Spreading increases interference power since it
destroys orthogonality
Submission
Slide 26
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 27
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Ordered Decoding at RX (cont’d)
 Assume that channel vectors are orthogonal
 Without Spreading the layer capacity is
CkLP  log 2 (1  SINRkMMSE )  CkMMSE
where the decoding order is assumed to be k
 With Spreading (see [1] for proof)
–
1 N

1
SP, MMSE

min C
C
  log 2  

C
k
MMSE 
l
 N l 1 1  SINRl

1 N


SP, LP
SP, LP
max Cl
 CN
 log 2 1   SINRlMMSE 
l
 N l 1

–
min ClLP  min ClSP, LP , max ClSP, LP  max ClLP
SP, LP
l
l
SP, LP
1
l
l
l
 Spreading yields the regulation of the layer capacity
ClSP, MMSE  CkSP, LP for k , l  LP improves the layer capacity
Submission
Slide 28
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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)

d  d1T
 d NT~
~
N

T
H  H1  H N~ 
 In general, each layer may have a different size
Submission
Slide 29
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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 H~ ( k )
~ ~
y (k )  H (k )d (k )  w
~(k )
T
 H k  H N~ d  d k



 d

T T
~
N
– MMSE Equalizer (L is the layer size)
-1
-1

 (k ) H (k ) 1 
1
H
H
(k )
(k ) H


G  Hk  H H
 I N    H
H  I L  H kH
  
 

– Let MMSE equalizer output
Submission
Slide 30
z k  G H y (k )
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Grouping (cont’d)
 Theorem 3 (GLP)
GLP does not lose information rate when H k is
full rank and MMSE
equalizer is applied
~
N
C  I (d ; y)   I (d k ; zk )
Proof : See [1]
k 1
 At each layer, MMSE equalized vector zk is used
(k )
y
instead of
for the decoding
 Under certain conditions [1]
ClSP, MMSE  CkSP,GLP for k , l  GLP improves the layer capacity
Submission
Slide 31
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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 especially in diagonal
or block diagonal channel matrix
y1 (n)
x1 (n)
x N (n)
y N (n)
x4 (1) x3 (2) x2 (3)
….
….
….
x N (n) x N (1) x N (2) x N (3) ….
y N (n) x N (1) xN 1 (2)xN 2 (3) ….
Time, n
Submission
y1 (n) x1 (1) x N (2) xN 1 (3) ….
y2 (n) x2 (1) x1 (2) x N (3) ….
x3 (1) x2 (2) x1 (3) ….
….
Output
streams
after Layer
Interleaver
….
….
….
….
Input
streams
to Layer
Interleaver
x1 (n) x1 (1) x1 (2) x1 (3) ….
x2 (n) x2 (1) x2 (2) x2 (3) ….
….
….
….
Layer
Interleaver
Time, n
Slide 32
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Numerical Experiments
 General Tx Structure
...
Spreading
…...
Symbol
Interleaver
…...
Layer
Interleaver
...
...
Encoder
Symbol
Interleaver
….
….
Information
S/P
bits
...
Encoder
 Simulation Conditions
–
–
–
–
–
–
–
–
–
Without Symbol/Layer Interleaver (unless otherwise mentioned)
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
Submission
Slide 33
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Numerical Experiments (cont’d)
 CDF of normalized layer capacity in MIMO OFDM, L=1
– Spreading yields steeper curve  Diversity
– LP improves Outage Capacity
– Recall C   CkLP   CkSP,LP , C   CkMMSE , C   CkSP,MMSE by Theorem 1&2
k
Submission
k
k
k
Slide 34
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Numerical Experiments (cont’d)
 CDF in MIMO OFDM, L=2(Grouped over antennas, C LP  C MMSE )
–
–
–
–
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 C SP, MMSE  C SP,GLP for k , l
Submission
l
k
Slide 35
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 36
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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)
32 32 WH
ST
Encoding
1
S/P


Spreading

IFFT

IFFT
S/P

IFFT
ST
Encoding

ST
Encoding
32

Spreading

IFFT
Serial STC w/o Spreading
Parallel STC
Submission
S/P
Slide 37
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Numerical Experiments (cont’d)
 GLP of Parallel STC w/ SP has the best performance
 Serial STC has less frequency diversity gain
Ideal 2-by-2
STC w/ GLP
& w/o SP
2.1 dB Gain
Ideal N-by-N
STC
3.5 dB Gain
Ideal 2-by-2
STC w/ SP&GLP
Submission
Loss due to
non-ideal 2-by-2 STC
Slide 38
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 39
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
~
T  TSF  I K / SF
TSF : SF  SF spreading matrix
– The partial spreading matrix is useful when K is not a
multiple of 4
Submission
Slide 40
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 41
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 42
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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
Submission
Slide 43
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
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.126133, Dec. 1997
Submission
Slide 44
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Thank you for your attention!!
Questions?
Submission
Slide 45
Yang-Seok Choi et al., ViVATO
January 2004
doc.: IEEE 802.11-04/0016r2
Back-up
 Different Spreading Matrix
Submission
Slide 46
Yang-Seok Choi et al., ViVATO