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- Ece 301 projects fall 2003
- Radar simulation in matlab
- Approach for range
Basically M multiplied by L is the entire length of the signal and (M-N) is the last value of the first chirp right on the falling edge.
Characterizing match filter
We characterize the match filter impulse response as being h(t)=s*(-t)=exp(-j*W/T*t^2) with t on the range of [-T/2,T/2]. See
"Background" module under the section"Match Filter"for more details.
Range analysis
The approach taken now to analyze the corresponding range of the target for the received signal is the following:
- Process recieved signal through a match filter with impulse response described above and in"Backgrounds"
- Process originally transmitted signal through same match filter
- Pick out the peaks from outputs via setting a threshold value as a starting point
- Compare the location of the first peak from each output
- The difference in locations of the 1st peaks is the time delay (Td) value
- Plug Td into discrete time range equation to get approximate range
The reason why we only need to analyze the first peak is because we are assuming that the object is not moving. Also, for future work, if the range and velocity systems were to be integrated (i.e. can take into account a moving target ) an initial range would be calculated from the first returned pulse. Velocity would be calculated as well from the rest of the recieved signal. Then, a relationship could be found for the object's range as a function of time. More specifically R(t) = Ro - vt where assuming the target is approaching the radar and since the velocity was calculated the simple distance = rate x time relationship can be used ( where x = multiplication). Note, this is all assuming a constant velocity and that the target is still not at an angle to the radar's transmission path.
The matlab function"
rangecalc "does the above stated list and an exampe of how it is called follows. It is interesting to note that the"rangecalc"function calls a subfunction to actually pick out the peaks in the outputs of the matched filters. The subfunction is called"
pkpicker " "and was provided by the"Computer-Based Exerciese for Signal Processing Using MATLAB"book by Burrus [ et al.]. Given the number of peaks to look for, a threshold value to use, and a vector, the function will go through a vector and will output the locations of the highest peaks above the threshold as well as their values.
Example of"Rangecalc"Matlab function call
[timedelay,range,rsigmatchlocs] = rangecalc(rsig,tsig,h,number,thresh,Ts) with inputs:
with outputs:
- timedelay = difference in location of 1st peaks from outputs of both match filters
- range = corresponding real world target range (units: meters)
- rsigmatchlocs = vector containing locations of peaks from output of match filter of recieved signal
Example of"Pkpicker"Matlab function call
[peaks,locs] = pkpicker( x, thresh, number, sortem ) with inputs:
with outputs:
- peaks : peak values
- locs : location of peaks (index within a column)
Putting it all together
The function that we designed to combine all of the previously mentioned functions is called"
burst4 ".
Example of"Burst4"Matlab function call
[noisytestecho,noisyshifttestecho,rsigmatchlocs,timedelay,range,h] = burst4(L,TW,p,M,n,sampfreq,TD) with inputs:
with outputs:
- noisytestecho: noisy burst waveform of L lfm chirps of the same TW,p
- noisyshifttestecho: shifted (i.e. time-delayed) of noisy burst waveform
- rsigmatchlocs: vector containing locations of peaks from output of match filter of recieved signal
- timedelay: difference in location of 1st peaks from outputs of both match filters
- range: real world target range (units: meters)
- h: impulse response for match filter
Method of comparison
Using the"
radar "function provided by"Computer-Based Exerciese for Signal Processing Using MATLAB"by Burrus [ et al.] (see page 328 of book for full explanation of usage) we were able to compare our simulated returned signal.
Range equation
Range equation (continuous time)
Characteristics of continous-time range equation
The equation is designed for continuous time signal where the two parameters are:
- Td = time delay between transmitted signal and recieved signal
- c = speed of light (3 x 10^8 m/s) (where x = multiplication)
Range equation (discrete time)
Characteristics of discrete-time range equation
The equation that matlab will have to use to calculate range and get corresponding real world values from three paramters:
- Td = difference in terms of actual physical location of the same value in 2 vectors
- c = speed of light (3 x 10^8 m/s) (where x = multiplication)
- Ts = 1/sampling frequency (used to create LFM chirp from beginning)
Where to next
Next, look at
"Range Results" as next step.
Source:
OpenStax, Ece 301 projects fall 2003. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10223/1.5
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