Transcript Channel Estimation for Wired MIMO Communication Systems Final Presentation Daifeng Wang

05/05/2005
Channel Estimation for Wired MIMO
Communication Systems
Final Presentation
Daifeng Wang
Dept. of Electrical and Computer Engineering
The University of Texas at Austin
[email protected]
Introduction
• Review
– Wired MIMO Communication Systems
– Multicarrier Modulation
– Training-Based Channel Estimation
• Today
–
–
–
–
Which channel estimation strategy for wired communication systems?
How to design the training sequence?
What is the channel model?
How to estimate
mirror
Multiadd
D/A +
the wired MIMO Bits S/P Modulation
data
cyclic
P/S
transmit
and
prefix
filter
Encoder
N-IFFT
channel?
TRANSMITTER
Data Transmission for ADSL, a wired communication system
RECEIVER
N/2 subchannels
N real samples
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P/S
decoder
freq.
domain
equalizer
(invert
channel)
N-FFT
and
remove
mirrored
data
delete
S/P cyclic
prefix
time
domain
equalizer
(FIR filter)
channel
receive
filter
+
A/D
Training-Based Channel Estimation Strategy
• Block-Type
–
–
–
–
All subcarriers + Period
Least Square (LS), Minimum Mean-Square (MMSE)
Slow Fading/Varying Channels
Decision Feedback Equalizer
Tradeoff between
performance and
• Comb-Type
complexity
– Selective subcarriers + Interpolation
– LS, MMSE, Least Mean-Square (LMS)
– Fast Fading/Varying Channels
– Interpolation
•
•
•
•
•
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Linear
Second order
Low-pass
Spline Cubic
Time domain
Training Sequences
• y=Sh+n
– h: L-tap channel
– S: transmitted N x L Toeplitz matrix made up of N training symbols
– n: AWGN
Domain
Method
Time
Periodic
Minimum Complexity
MSE
Optimal
Sequence*
Yes
High(2N)
Yes
No
Medium(N2)
Yes
Almost
Low(Nlog2N)
Sometimes
No
Low(Nlog2N)
Sometimes
[Chen & Mitra, 2000]
Aperiodic
[Tella, Guo & Barton, 1998]
L-Perfect (MIMO)
[Fragouli, Dhahir & Turin, 2003]
Frequency
Periodic
[Tella, Guo & Barton, 1999]
* impulse-like autocorrelation and zero crosscorrelation
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Training-Based MIMO Channel Model
•
2 X 2 MIMO Model
TX 1
RX 1
h11
TX 2
h12
h21
RX 2
h22
y 
 h ( L)
y   1   Sh  z  [ S1 ( L, N t ) S 2 ( L, N t )]  11
 y2 
 h21 ( L )
where y and z are of 2( N t  L  1)  1
T
hij ( L )  
hij ( L  1) 
 hij (0)
 , i or j  1, 2
si (0)
 si ( L  1)

 s ( L)

s
(1)
i
i
 , i  1, 2
S i ( L, N t )  


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

s
(
N

1)
s
(
N

L
)


t
i
t
 i

h12 ( L ) 
z

h22 ( L ) 
Training-Based Channel Estimation for MIMO
• Least Square (LS)
– Assumes S has full column rank
 hˆ11
ĥ= 
 hˆ21
hˆ12 
H
-1 H
 =(S S) S y
hˆ22 
• Mean-Square (MSE)
H
2
– zero-mean and white Gaussian noise: R z  E  zz   2 I Nt - L 1
H
–
2
H
-1

ˆ
ˆ 

  h  h   2 Tr((S S) )
MSE  E h  h

2 2 L
–
H
H


S
S
S
1
1
2 S1
H
MMSE =
, iff S S=  H
  ( Nt  L  1)I 2 L
H
Nt  L  1
S1 S2 S2 S2 
– Sequences satisfy above are optimal sequences
– Optimal sequences: impulse-like autocorrelation and zero
crosscorrelation
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