Synchronization in WLAN

Time Domain Channel Estimation
• The channel impulse response is estimated
X
r = h∗ x + w The received time domain signal during the two long training symbols
1, n n 1, n
⎡ x1 x64 x63 … x64− L+
2⎤
⎢
x2 x1 x64 x
⎥
⎢
64− L+
2 ⎥
= ⎢ ⎥
⎢ ⎥
⎢x63 x62 x64−L
⎥
⎢
⎣x64 x63 x ⎥
64− L+
1 ⎦
The circular convolution
matrix of the training
symbols, L the max length
of impulse response that
can be estimated
2
= ⎢h
⎥
3
⎢ ⎥
WLAN Synchronization 16.3.2004 © Hafeth Hourani 34
h
⎡ h1
⎤
⎢
h
⎥
⎢ ⎥
⎢ ⎥
⎢
⎣h
⎥
L ⎦
ˆ 1 −1
h= X ( r1, n
+ r2,
n)
2
1 −1
= X ( Xh + w1+ Xh + w2)
2
−1 1 −1
= X Xh+ X ( w1+
w2)
2
1 −1
= h+ X ( w1+
w2)
2
The channel
impulse response
vector