matched filter detection
DESCRIPTION
MATCHED FILTER DETACTION USING LABVIEW BY:M.SURYADEEPAKTRANSCRIPT
Matched Filter DetectionUsing lab view
Objectives(Tasks)
Generation of chrip signal
Generation of noisy
wave form
Matched filter
detection
• Generation of chirp signal
• Generation of noisy wave form
• Matched filter detection
2
Matched Filter
• Detection of pulse in presence of additive noiseReceiver knows what pulse shape it is looking for
Channel memory ignored (assumed compensated by other means, e.g. channel equalizer in receiver)
Additive white Gaussian noise (AWGN) with zero mean and
variance N0 /2
g(t)
Pulse signal
w(t)
x(t)h(t)
y(t)
t = T
y(T)
Matched filter
)()(
)(*)()(*)()(
0 tntg
thtwthtgty
T is pulse period
13 - 4
Matched Filter• Given transmitter pulse shape g(t) of duration T, matched filter
is given by hopt(t) = k g*(T-t) for all kDuration and shape of impulse response of the optimal filter is
determined by pulse shape g(t)
hopt(t) is scaled, time-reversed, and shifted version of g(t)
• Optimal filter maximizes peak pulse SNR
Does not depend on pulse shape g(t)
Proportional to signal energy (energy per bit) Eb
Inversely proportional to power spectral density of noise
SNR2
|)(| 2
|)(| 2
0
2
0
2
0
max
N
Edttg
NdffG
N
b
Typical Application: Radar
][ns
n
Send a Pulse…
][ny
n
0n
… and receive it back with noise, distortion …N
Problem: estimate the time delay , ie detect when we receive it.0n
Use Inner Product
“Slide” the pulse s[n] over the received signal and see when the inner product is maximum:
][s
][y
0n
N
n
1
0
* ][][][N
ys snynr
0 if ,0][ nnnrys
Use Inner Product
][s
“Slide” the pulse x[n] over the received signal and see when the inner product is maximum:
][y
N
0n
if 0nn MAXsnynrN
ys
1
0
* ][][][
Matched Filter
Take the expression
][]0[]1[]1[...]1[]1[
][][][
***
1
0
*
nysnysNnyNs
snynrN
n
ys
Then
]1[]1[]1[]1[...][]0[][̂ NnyNhnyhnyhnr
][ny ][nh
1,...,0 ],1[][ * NnnNsnh
]1[][ˆ Nnrnr ys
Compare this, with the output of the following FIR Filter
Matched Filter
This Filter is called a Matched Filter
The output is maximum when
][ny ][ˆ nr
][nh
1,...,0 ],1[][ * NnnNsnh
]1[][ˆ Nnrnr ys
01 nNn
10 Nnni.e.
Example
0 2 4 6 8 10 12 14 16 18 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
][ns
0 20 40 60 80 100 120 140 160 180 200-6
-4
-2
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160 180-2
-1.5
-1
-0.5
0
0.5
1
1.5
][ny
][ny ][ˆ nr
][nh
1,...,0 ],1[][ * NnnNsnh
1,...,0],[ NnnsWe transmit the pulse shown below, with length 20N
Received signal:
Max at n=1191001201190 n
Example: Chirp
49,...,49],[ nnrss49,...,0],[ nns
0 5 10 15 20 25 30 35 40 45 50-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-50 -40 -30 -20 -10 0 10 20 30 40 50-10
-5
0
5
10
15
20
25
30
s=chirp(0:49,0,49,0.1)
Example
Transmit a Chirp of length N=50 samples, with SNR=0dB
0 50 100 150 200 250 300-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 200 400 600 800 1000 1200-15
-10
-5
0
5
10
15
20
25
30
Transmitted Detected with
Matched Filter
Example
Transmit a Chirp of length N=100 samples, with SNR=0dB
0 50 100 150 200 250 300-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 200 400 600 800 1000 1200-20
-10
0
10
20
30
40
50
Transmitted Detected with
Matched Filter