Modeling & Simulation Assignment

Modeling & Simulation Assignment

Include your MATLAB script as part of the assignment.

A radar drone surveillance system is desired with the following range window requirements:

1. (tracking) range window length m
2. range window sample interval m
3. number of range cells

and the drones are assumed to have the following properties:

1. length of 1.5 m
2. well modeled by discrete scatterers with sample spacing of m with random amplitude values within the interval  and random phase values within

and the radar has the following receive window (time domain) parameters:

1. receive window sample interval ns
2. number of receive window time samples
3. receive window duration ns

and the following frequency domain properties:

1. double-sided bandwidth rad/sec (1 GHz)
2. single-sided bandwidth rad/sec (0.5 GHz)
3. number of frequency samples
4. frequency bin size rad/sec (10 MHz)
5. sampling frequency rad/sec (1 GHz)
6. carrier frequency rad/sec (10 GHz)

and the following dependent parameters

1. fast-time sampling interval ns
2. maximum baseband signal frequency rad/sec (0.5 GHz)

Note that the sampling frequency is set to the double-sided signal bandwidth, and that with respect to the carrier frequency, the sampling rate is insufficient to represent the carrier component without aliasing.

The incident waveform is the real sinusoidal signal

Note that the Hilbert transform of the carrier signal is .

Consider

to be a model of the complex passband signal scattered by a drone. Assume  and  are real.

The function

is the down-converted scattering function.

Let  be the Fourier transform of . Let  be the Fourier transform of . We want to be sure in our models and analysis not to make  and  a Hilbert transform pair by having  be an equal, but odd version of . If you do, then  would have a single-sided spectrum and would be an analytic signal. We are seeking to show that  may be arbitrarily complex.

Let  with  and .

Do the following using MATLAB:

1. Model the amplitude and phase components of the drone model as specified on page 1. Place the drone somewhere in the range window. Plot this in MATLAB. Hint: For each of 10 samples (1.5/0.15 = 10), provide random amplitude and phase values within the specified intervals
2. Convert the drone model from the spatial domain to the temporal domain. Plot this result in MATLAB. This process will change the “range window” to a “receive window”. Hint: Scale all axis by 2/c from spatial (x) to temporal (t) domain – all amplitude/phase values remain the same.
3. With the results of Tasks a) and b), model the real received signal scattered by the drone over the entire range window by creating and plotting

Now consider the following:

1. Consider a drone surveillance system with a range of concern (called the “instrumented range”) that extends from 300m to 3,000m.
2. Consider a radar that has a receive noise level that corresponds to 290 degrees K.
3. Consider a radar that requires 5dB SNR of sensitivity to detect drones at the range of 3,000m.

Do the following using MATLAB:

4. Utilize your model of a drone above and place the drone near the far edge of the (300m-3,000m) range window and plot the range window (with the drone included).
5. Utilize the temporal sampling frequencies on page 1, plot the receive window (with the drone included).
6. Use a random Gaussian model for noise and plot a noise-only receive window signal that corresponds to 290 degrees K.
7. Determine the peak transmit power required to provide a 5dB SNR at a range of 3,000m. Scale the amplitude of the drone-in-receive window signal (of step 5) to match this peak transmit power level. Combine and plot the noise-only and scaled signal-only receive windows to form a model of the received radar signal.
8. Note, the steps above do not involve a waveform. So next, assume the use of a pulse waveform that has a duration of 100 samples. Model and plot the received echo signal (including noise), where this waveform illuminates the drone.
9. Design and apply a pulse compression matched filter to this receive window signal and plot the result.
10. Verify that matched filtered signal has an SNR gain corresponding to the use of a simple pulse with a duration of 100 samples.