Transcript Channel Estimation for OFDM Systems

Channel Estimation
for OFDM Systems
Xianghao YU
20/11/2014
Outline
 Channel Estimation Techniques
 Pilot Symbol Aided Estimation
 Compressive Sensing Based Estimation
 Conclusion
Outline
 Channel Estimation Techniques
 Pilot Symbol Aided Estimation
 Compressive Sensing Based Estimation
 Conclusion
Channel Estimation Techniques
• Decision-Directed Estimation
─ Transmit at least one known OFDM symbol to obtain the Channel
State Information (CSI) of all sub-carriers at a specific time
─ The current CSI should be estimated by the data decisions from
previous symbols by using channel correlation
• Pilot symbol aided Estimation
─ Decide the pilot symbol positions and estimate the channel values
at these positions
─ CSI at other subcarriers and times can be estimated by
performing 2-D interpolation
─ Accurate, fast, widely used and more of research interest
Outline
 Channel Estimation Techniques
 Pilot Symbol Aided Estimation
 Compressive Sensing Based Estimation
 Conclusion
Pilot Symbol Aided Estimation
• OFDM System Model
─ Assume the CP yield perfect orthogonality, the input/output
relation of the system
y k ,l  hk ,l x k ,l  n k ,l
─ k is the subcarrier index, l is the time / symbol index
─ Considering the channel is constant during an OFDM symbol
h  f ;t  
1
M
M
 exp  j  
n 1
k
h k , l  h  ; lT
T
n

 2 f Dn t  2 f  n 

N

Doppler
,
T

 TC P

frequency
W

Delay of
nth path
Pilot Symbol Aided Estimation
─ To fulfill the sampling theorem
M
Mt 
f
N

W TC P
1
W TC P 

2 1 
 f D , rel
N 

─ Define the per-symbol SNR as
E
SN R 

x k ,l
 
E
n 
2
E
2
hk ,l

2
k ,l

1
SN R loss   10 log 10  1 

M tM

f




Pilot Symbol Aided Estimation
• Ideal Case——2-D Estimator
─ If the system allows full complexity with high multiplications, 2Destimator is used, which is optimal in terms of MSE
─ The estimated tone (X) is a
linear combination of the 7 pilot
tones (■)
─ If the estimator use the K
closest pilots to estimate, the #
of multiplications is K
Pilot Symbol Aided Estimation
• Practical Case——Separate Estimator
─ The outer product of two 1-D estimator can give a good trade-off
between performance and complexity
─ First a 1-D filter is applied in
the frequency direction and
thereafter another 1-D filter is
applied in the time direction
─ If the estimator use the Kf and
Kt length Wiener filters, the # of
𝐾
multiplications is 𝑁𝑓 + 𝐾𝑡
𝑡
Pilot Symbol Aided Estimation
• Comparisons between Different Estimators
Estimator
Structure
# mult. / att.
# of
pilots
2-D
Use the 𝐾𝑝 closest pilots
𝐾𝑝
𝐾𝑝
Separable
Separable FIR filter with
𝐾𝑓 and 𝐾𝑡 taps
𝐾𝑓
+ 𝐾𝑡
𝑁𝑡
𝐾𝑓𝐾𝑡
Low-rank 2-D
Estimates 𝐾ℎ attenuations
using the 𝐾𝑝 pilots and a
rank of 𝑟
Low-rank
separable
Estimates 𝐾ℎ attenuations
using the 𝐾𝑝 pilots and a
rank of 𝑟 (frequency) and
𝐾𝑡 taps FIR filter (time)
𝑟(1 +
𝐾𝑝
)
𝑁ℎ
𝐾𝑝
𝑟
1+
+ 𝐾𝑡
𝑁𝑡
𝑁ℎ
𝐾𝑝
𝐾𝑝 𝐾𝑡
Pilot Symbol Aided Estimation
• Analysis
─ For ideal 2-D estimator, the linear 2-D wiener filter can be
expressed as
h k , l  W p  R hp R
where 𝐩 =
𝑦𝑘,𝑙
𝑥𝑘,𝑙
1
pp
p
is the observation vector and 𝐑 ℎ𝑝 and 𝐑 𝑝𝑝 are the
correlation matrices
─ Hence, MSE becomes

2
k ,l
2
H

 h  W R hp
 2
H
H
H
  h  W R hp  W R pp W  R hp W
ideal case
practical case
Pilot Symbol Aided Estimation
• Simulation Results
─ W=5MHz, N=1024, T=215μs, uncoded 16QAM at SNR=15dB
Using 31*11 and 10 pilots, both achieve the minimal SER 0.19 and 0.22
at Mt=3 and Mf=5, 93% data with SNR loss 0.30dB
Outline
 Channel Estimation Techniques
 Pilot Symbol Aided Estimation
 Compressive Sensing Based Estimation
 Conclusion
Compressive Sensing Based Estimation
• Baseband OFDM System
X
N
x
N
z  x h
Y
M
y
M
Compressive Sensing Based Estimation
• Channel Sparsity
─ We assume the channel response comprises P propagation paths
P
hn 

p
  n   p T s  , n  1, 2,
,N
n 1
0   p T s  TG  sym bol duration
h   h1 , h 2 , h3 ,
, h N , 0,
, 0 
• Compressive Sensing
─ Allows sparse signals to be recovered from very few
measurements, which often translate to fewer samples
M  N
Compressive Sensing Based Estimation
• Compressive Sensing Based Estimation
─ Because convolution is a circulant linear operator
y  P z  P  x  h     P  C h      P C  h   
Full circulant matrix
determined by x
Uniform down-sampling
from N to M points
─ To design the sensing matrix C, we can generate the pilots X by setting
the real and imaginary parts of X(k) from standard Gaussian distribution
xh  F
y  P F
1
1
 diag  X  F  h  
 diag  X  F  h     
Compressive Sensing Based Estimation
• An intuitive explanation
Information of h spread
over all its elements
y  P F
1
sparse
 diag  X  F  h     
non-sparse
The challenges are to
avoid 𝐹 −1 diag 𝐗 𝐹 ℎ
from de-spreading 𝐹 ℎ
Random phase of X
“scramble” the components of
𝐹 ℎ break the “delicate
relations” among the elements
Since 𝐹 −1 diag 𝐗 𝐹 ℎ is not sparse at all, every sample will contain the
information of the nonzero parts of h so that we can recover it with relatively
small samples
Compressive Sensing Based Estimation
• Simulation Results
─ Proposed compressive
sensing based estimation
further improves the
performance by half of a
magnitude
Outline
 Channel Estimation Techniques
 Pilot Symbol Aided Estimation
 Compressive Sensing Based Estimation
 Conclusion
Conclusion
• Performance VS Complexity
─ Performance loss caused by pilot symbols
─ Low complexity consideration
• Sparsity of OFDM Channel
─ Utilizing the sparsity of OFDM channel