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# Matched filter detection

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MATCHED FILTER DETACTION USING LABVIEW
BY:M.SURYADEEPAK

Published in: Education
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### Matched filter detection

1. 1. Matched Filter Detection Using lab view
2. 2. 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
3. 3. 2 Matched Filter • Detection of pulse in presence of additive noise Receiver 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 y t g t h t w t h t ( )  ( )* ( )  ( )* ( ) 0 g t n t   ( ) ( ) T is pulse period
4. 4. 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 k Duration 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 SNR 2   E b  g t dt G f df     | ( ) |   max 2 | ( ) | 2 0 2 N  0 2 0  N N Does not depend on pulse shape g(t) Proportional to signal energy (energy per bit) Eb Inversely proportional to power spectral density of noise
5. 5. Typical Application: Radar Send a Pulse… ] [ns n … and receive it back with noise, distortion … ] [ny n 0 n N Problem: estimate the time delay , ie detect when we receive it. 0 n
6. 6. Use Inner Product “Slide” the pulse s[n] over the received signal and see when the inner product is maximum: s[] [ ]  [  ] * [ ]  y[]  0 n N n    1 0 N ys r n y n s    0 r [n] 0, if n n ys  
7. 7. Use Inner Product “Slide” the pulse x[n] over the received signal and see when the inner product is maximum:  * [ ] [ ] [ ] if 0 nnMAX s n y n r 0 n   s[]  y[]  N N ys     1 0   
8. 8. Matched Filter Take the expression  1 *     r n y n s [ ] [ ] [ ] 0  * * * s N y n N s y n s y n [ 1] [ 1] ... [1] [ 1] [0] [ ] N n ys         Compare this, with the output of the following FIR Filter rˆ[n]  h[0]y[n]... h[1]y[n 1] h[N 1]y[n  N 1] Then y[n] h[n] rˆ[n]  r [n  N 1] ys [ ] [ 1 ], 0,..., 1 * h n  s N   n n  N 
9. 9. Matched Filter This Filter is called a Matched Filter y[n] rˆ[n] ] [nh [ ] [ 1 ], 0,..., 1 * h n  s N   n n  N  The output is maximum when rˆ[n]  r [n  N 1] ys 0 n  N 1 n 1 0 i.e. n  n  N 
10. 10. Example We transmit the pulse s [ n ] , n  0 , . . . , N  1 shown below, with length N  20 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 12 10 8 6 4 2 0 -2 -4 -6 1.5 ] [ny 1 0.5 0 -0.5 -1 -1.5 0 20 40 60 80 100 120 140 160 180 -2 y[n] rˆ[n] h[n] [ ] [ 1 ], 0,..., 1 * h n  s N   n n  N  Received signal: Max at n=119 119 20 1 100 0 n    
11. 11. Example: Chirp r [n], n  49,...,49 ss 0 5 10 15 20 25 30 35 40 45 50 s[n],n  0,...,49 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 30 25 20 15 10 5 0 -5 -10 -50 -40 -30 -20 -10 0 10 20 30 40 50 s=chirp(0:49,0,49,0.1)
12. 12. 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 30 25 20 15 10 5 0 -5 -10 -15 Transmitted Detected with Matched Filter
13. 13. 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 50 40 30 20 10 0 -10 -20 Transmitted Detected with Matched Filter