matched filter detection

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