Flow Chart for Approach of Range
| Range Analysis Block Diagram |
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Chirp and Chirp Train Design
First, we design a Linear Frequency Modulated (LFM) chirp for the desired time-bandwidth product amount (TW), oversampling amount p, and sampling frequency (fs) . The MATLAB program "dchirp2" will build up a single pulse while "ctbuild4" will design a burst waveform consisting of L chirps, repeated over a period M.
Example of "dchirp2" MATLAB function call
[s,h,y,T,W,Ts] = dchirp2(TW,p,sampfreq) with outputs:
- s = single LFM chirp set to specified input paramters
- h = match filter impulse response
- y = (used for testing of original code) passing s through match filter
- T = time duration of LFM chirp (units: sec)
- W= swept bandwidth of LFM chirp (units: Hz)
- Ts= sampling period (1/fs)
Example of "ctbuild4" MATLAB function call
[s,ssent,h,y,T,W,Ts] = ctbuild4(TW,p,sampfreq,M,L) with outputs:
- s = single chirp defined by TW,p
- ssent = noise-free burst waveform of L lfm chirps of the same TW, p
- h = match filter impulse response
- y = (used for testing of original code) passing s through match filter
- T = time duration of LFM chirp (units: sec)
- W= swept bandwidth of LFM chirp (units: Hz)
- Ts= sampling period (1/fs)
Simulate radar returns
In order to simulate proper radar returns, we first simulate the noise of a channel. Thus, we add complex white Gaussian nosie, using the "crandn" command in MATLAB, to our complex train of chirps. We perform this opertion in our main MATLAB function called "burst4." Next, we then apply a time delay to our signal. The program accomplishes that by shifting a vector x of length N to the right by amount TD.
Note:
Note:
Defining max range of radar processing
The Maximum Range of our radar system is determiend by two things. First, how large the resting time is between consecutive falling and rising edges of chirps. Secondly, how long our signal is. The reason why these are important is that since this model for range processing is in discrete time, we can not simulate an infinite range for our targets. That would correspond to having to time delay our transmitted signal by a extremely large amount. If shifted by an amount greater than the signal's length, the simulated return would just be a flat line of value zero for the length of the signal. Basically, the signal can be time delayed only up until the first LFM chirp's falling edge. This location corresponds to the last value of the recieved signal to ensure getting a big enough spike in the match filter's output to use in calculating range. Thus, since we define the value for time period (Ts) of our chirp pulse train and the number of pulses, we can define the max range by finding the maximum amount we can shift our signal. Then by plugging in this max Td value into the discrete-time range equation below, the max range value is found.
Equation for Max Time Delay
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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
Note:
Example of "rangecalc" MATLAB function call
[timedelay,range,rsigmatchlocs] = rangecalc(rsig,tsig,h,number,thresh,Ts) with inputs:
- rsig = simulated recieved signal
- tsig = originally transmitted chirp train
- h = match filter impulse resposne
- number = # of pulses you want to be picked out
- thresh = starting point to look for peaks in signal
- Ts = sampling period
- 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:
- x : input data (if complex, operate on mag)
- thresh : reject peaks below this level
- number : max number of peaks to return
- sortem : 'sort' will return list sorted by peak height instead of by index # (the default)
- 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:
- L: number of pulses
- TW: time bandwidth product
- p: oversampling factor
- M: interpulse period
- n: noise factor
- sampfreq: sampling frequency to be used
- TD: The amount the transmitted signal is to be shifted
- 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.
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