Introduction to Radar System Design with MATLAB and Simulink

TOPIC #1 (Introduction)

Hello, all. My name is Tony Azar. I am an application engineer at The MathWorks. My expertise includes RF, radar, and antenna design, as well as teaching professional and college courses. We will spend the next 45 minutes going over some design aspects of radar systems. So thank you for attending, and I hope you will leave this presentation with valuable information that you can apply in your job.

TOPIC #2 (Agenda)

The objective of this webinar is to give an overview of radar system design, using MATLAB and Simulink. We will approach this by going over one of our documentation examples from specifications to detection. Along the way, we will demo tools and apps that make the process simple and fast. The agenda will cover:

• An overview of a generic radar block diagram. Here we will run the simulation of the example and show the final results.
• Then, we'll go over the specifications and start by designing the Waveform.
• Next, we'll cover RF design options for transmitter and receiver.
• Then, we'll move to demo our two popular tools on antenna and array design.
• Next, we'll show options for modeling environmental effects, targets, and interference.
• And finally, we'll finish with the signal processing techniques leading to detection and visualization.
• When all is done, we'll navigate the Help menu and show how to pick and access examples from over 120 examples in our documentation menu. These examples can often be used as a starter to most practical applications.

TOPIC #3 (Radar Block Diagram)

The most elementary functions of a radar system start with

• Generating a Waveform.
• Feeding it into the transmitter to amplify it.
• Transmit the signal through an array.
• As the signal propagates, it experiences different environmental effects, like rain and fog.
• It hits the target and comes back to the radar.
• Along with desired signal, we might have interference and return from unwanted objects.
• The return signal is collected at the receive antenna. In our case, we have a mono-static radar. So the transmit and the receive are the same.
• It gets amplified by the receiver.
• and then onto the signal processor. Here different signal processing techniques separate the desired from the undesired signals and gets displayed using a variety of visual aid tools.

TOPIC #4 (Example Scenario)

The scenario of the example that we will discuss is as shown in this slide. We have the radar moving in the y-direction at this speed, 224 m/s. It is about 1 km above ground level. Directly opposite to it, at 2 km away, there's a jammer. On ground level, there's a target moving away from it. The target is at 1.7 km  from the radar. The target moves through a wooded area. The wooded area is modeled with a gamma clutter of -15 dB.

The appropriate Simulink file will be shown next. It is to note that a MATLAB program can be written that does the exact same thing.

TOPIC #5 (Simulink Block Diagram)

Here's the file. I have a Waveform, Transmitter, Transmit Array, free space channel, this is how we model the propagation in free space. The target, this is where we can change the velocity and position of the target. Here's the jammer. This is the free space channel for the jammer, and this is how we model the clutter. They all go into the receiver, and then onto the signal processing unit. From the signal processing unit, they go into the visualizations box.

Now let's look at these and get an overview of what all of these blocks do. Rectangular Waveform. If I click on it, I see the parameters that I can change. Among them are the pulse widths, number of pulses, and so on. By the way, we will cover all of these in details later on in this webinar.

This is a Transmitter. This particular Transmitter is a linear Transmitter. So it doesn't have all the options available for RF impairments, but we will show that later. All of them are pretty much the same, except for the signal processing unit. If I click on it, there's more into it. So this is the raw signal. The raw signal goes into four different paths. One of them is the raw signal itself, and three are processed using the appropriate signal processing algorithms.

Now from the signal processing unit, it goes into Visualization. We have four outputs. Here they are. If I click on it, number one is the raw data. Number three is the processed data. Two and four are the Angle-Doppler responses of before and after. So this is it. Now if I click on Run, I see the results. Now I already have the results in my file, in my Power Point presentation. So I'm going to show my results instead.

TOPIC #6 (Simulink Output Data)

OK, here is the scenario, and here are the four different outputs. This is the raw signal. If I look at the raw signal, I see this is the theoretical location of the target. This is 1.7 km. As it is clearly shown, it's buried in noise, and what is seen here is the clutter due to the area immediately below the radar. That's 1,000 meters, 1,000. Now after we process it, we see that we can filter out the clutter, and the target is visible is clearly visible at 1.7 km.

Now the Angle-Doppler responses before and after, let's start with the after first. I see a blue line at 60 degrees. Blue line is low RF energy, and I see a blue line going from minus 90 all the way to 90. Now the one at 60 degrees is the jammer itself. If I look at the jammer, this is 60 degrees. So the processing did its job, which means it nulled the jammer and the clutter. And this is the clutter going from minus 90 all the way to 90 across all the doppler frequencies.

This is the location of the target. It's that 0.22 normalized Doppler and 45-degree angle. This is 45 degrees over here. Now this is before. If I look at before processing, the area at 60 degrees and the area where the blue clutter line is, is all yellow. Yellow is high RF energy. So it's buried. That's why the signal here cannot be seen, but here it can be seen easily.

TOPIC #7 (Case Study: Specs & Reqs.  Pt 1)

Now let's move on to the radar design procedure. These are the specs of the radar. Operating frequency of 10 GHz, max range of 5 km, range resolution of 50 meters, probability of detection of 0.9, probability of false alarm of 10 to the minus 6, minimum detectable RCS of 1, and the number of pulses that can be integrated is 10.

So what do we need for this example? We need to find a bandwidth, the pulse width, the PRF, signal to noise ratio, and the peak transmitting power. We also need the antenna and the array layout and the clutter and interference-removal algorithm, the appropriate one. And because we are in the digital domain, we need to choose the proper sampling frequency.

We chose a rectangular waveform for this example. We did have one slide on showing how to choose the proper waveform. We compared the Rectangular to LFM, but we had to skip it due to time constraints. So again, the choice is the Rectangular waveform. So for Rectangular waveform, the bandwidth is speed of light divided by 2 range resolution. That's 3 MHz.

The pulse width is 1 over the bandwidth. That's 0.334 microsecond. The PRF is the speed of light divided by 2 Max_Range, which is 30 kHz. The sampling frequency is twice the bandwidth. That's 6 MHz, and the samples per frame is the sampling frequency divided by the PRF, which is 200.                                             

TOPIC #8  (Case Study: Specs & Reqs.  Pt 2)

Now I'm going to approach this as a textbook example. For any of you who's had a radar course, will probably be familiar with this technique. First we start with the detection charts. This particular chart shows the probability of false alarm from 10 to the minus 4 to the 10 to the minus ten. The blue lines are probability of false alarm. The y-axis is the probability of detection, and the x-axis is the signal-to-noise ratio in dB for one pulse. In my case, I have 10 to the minus 6 for probability of false alarm. So I go to 10 to the minus 6. It's this blue line, and I find where it intersects the probability of detection on 0.9. This is the point. I drop down to the x-axis, and I see 13.1 dB. So the minimum signal-to-noise ratio required for this example, if I were to use just one pulse, would be 13.1 dB. But I have 10 pulses that I can integrate. So I'm going to use the Improvement Factor.

So the Improvement Factor, this is a cleaned-up figure. I only plotted a few lines for the 10 to the minus 10 part of the false alarm, or 10 to the minus 6 probability of false alarms to keep it clean. We have three lines for each. Probability of detection 0.5, 0.7, 0.9. So If I go to 10 to the minus 6 and 0.9, I follow this to 10 pulses, and I see that it's 8.1 dB.

So now I have 8.1 dB improvement. So my signal-to-noise ratio is 13.1 minus 8.1. It's 5 dB. Now luckily to us, MATLAB has the Albersheim function. You can populate it easily. All you need is the probability of detection, probability of false alarm, and the number of samples. I'm sorry, the number of pulses, and you get the 5 dB.

Next is the peak power. We can find the peak power by using the Radar Equation Calculator. We had a plan on demoing this particular app, but we skipped it does the time constraints. But instead of doing this, we can also use the following MATLAB function. All we have to do is populate it correctly and get the peak transmitter power of 5.234 kW.

TOPIC #9 (Waveform Generation)

So we designed the radar. Next, we're going to show what the Phased Array Toolbox offers for these particular blocks that are shown in this radar diagram. We start with the Waveform Generator.

Waveforms are critical components in modelling and radar systems. The Toolbox includes some of the most commonly used waveforms.

On the pulse side, there is the LFM, Phase-coded, Rectangular, and Stepped FM. Each has a number of settable parameters, including pulse duration and bandwidth.

On the continuous side, you can choose between FMCW and MFSK.

Again in the spirit of providing tools to visualize your design, the toolbox includes the ambiguity function to analyze waveforms.

TOPIC #10 (Radar Waveform Analyzer app)

The best way to initialize the waveform design is to start with the Radar Waveform Analyzer app. It's a neat app. I will show you how to use it, and by the end when we're done, you'll see how powerful it is. The best way to open this app is to go to the MATLAB main window. And from the MATLAB main window, go to the Apps tab. Click down. Go to Signal Processing & Communication, and find the Radar Waveform Analyzer. Click on it, and start it.

I've already started it. So I was just going to go to the one that I already loaded. Here we go. This is it. This is the default view. On the right side, I see the choice of waveforms. I can choose between Linear, Rectangular, Stepped FM, Phase-coded, FMCW. I'm going to choose Rectangular. The PRF for our radar example is 30 kHz. 1, 2, 3. We have only one pulse. The pulse width is 0.334 microsecond, but I'm going to put the exact value, which is 1 over 3 MHz. 1, 2, 3, 1, 2, 3. Propagation speed is already there. There's no frequency offset. The spectrum window is none, but I can choose between Hamming, Chebyshev, Hann, Kaiser, or Taylor. On the left side, I have to enter the sample frequency. In our case, it's 6 MHz. And I'll click “accept”. OK, here's my Spectrum, and this is the pulse in time domain. It's hard to see. But if I should say 3 pulses, I can see it easily. Pulse one, pulse two, pulse three. Let me we go back to pulse one. Here's pulse one. Down at the bottom, I have some of the characteristics of this waveform. The Range Resolution is 0.05 km, or 50 meters. The Unambiguous Range is-- sorry, the Max Unambiguous Range is 5 km. And the duty cycle is 1%. So this waveform satisfies the specs of this radar.

Now let's see what else I can plot. If I go to the Plotting tab, down here at the bottom there's the Ambiguity plots. If I choose contour, this shows me the-- let me just make this a little bit wider. See if I can make it wider. I guess I can. And a little bit bigger over here. OK, let me zoom in on the area of interest. OK, so here's my Doppler-Delay Ambiguity plot. This in in 2D. But it can also plot the 1D Ambiguity. This is the Delay cut. This is the cut at zero, which means I can plot one without the Delay 0 and 1 with the Doppler zero. So this is the cut of 0 microsecond. And I can see being the first nulls at 3 MHz. Those are important for waveform designers. This is how you can determine both the max speed and max range. (Sorry, Nulls are related to the Range & velocity Resolutions)

And here's the other one. Doppler cut, same thing. When you zoom in on it, if I zoom in, I can see that my nulls are 0.334 microseconds. We did have a one slide to show the difference between LFM and Rectangular waveform, but we had to omit it due to time constraints. But this is what we use to determine which waveform is the better waveform.

Once I'm done, once I decide on my waveform, I can export. I can generate a Simulink model, or I can export it. I can export it into several formats. One of them is the MATLAB script. If I click on Generate MATLAB script, here we go, now I see the model. This code now plots the exact same plots or generates that same waveform. I can run it, or I can modify it, or I can include it into a larger code. This is it in terms of the app. I think we're going to stop and move on to the next topic.

TOPIC # 11 (Transmitter & receiver – Phased Array Toolbox)

Before we move on to our next topic, let me show you this slide, which will be included in your PDF file. But we won't have time to go over. This is just a comparison of the Rectangular waveform and LFM waveform. It's available for those of you who already know the Ambiguity function. They probably can make some sense out of it.

Next is transmitter and receiver. For transmitter and receiver, the MATLAB can offer linear models and nonlinear models. Linear models are available in the Phased Array Toolbox, and the nonlinear models are available in the Blockset toolbox.

Let's start with the Linear model first. So we have a Waveform, Transmitter, Radiation, and Environment. For the Transmitter, the Transmitter basically is a simple function. It's a Phased.Transmitter. All you have to do is include several parameters, like the RF Peak Power, Gain, and some other parameters also. But it's simple. By the way phase, Phased.Transmitter means that it's a function out of the Phased Array Toolbox. The proper name that we use at MATLAB at MathWorks is not the function. But for those of you who are not familiar with it, we're going to use that term. It's a simpler term. It's basically like the old fashion subroutine; it’s something you call, you populate it, and it gives you a response. So probably the generic name is as a subroutine. This is the Simulink block for it. Simple, just one Simulink block. We saw that when we demoed the Simulink file.

Next is Radiation. In MATLAB, Radiation is kind of divided, the act of radiation is divided into two. First, you have to set the geometry of the antenna, and then you have to do the radiation. So basically, the array is designed, and we use the function Phased.Radiator to point to the array, and then radiate the signal. So again, simple, just one-line function, and in Simulink, it's simple, just one block.

Now on the way back, we have the Collector, Receiver, and Signal processing. Same thing, it's almost the reverse. We first collect the signal, you point to the array, collect the signal, we populated with the proper parameters; on the Simulink block, It's a simple block. And then for the Receiver, we use the Phased.ReceiverPreamp. And again, you just populate a few blocks, like Gain and NoiseFigure. And on the Simulink side, all you need is this block.

TOPIC #12 (Transmitter & receiver – RF Blockset)

For the nonlinear model, I am going to show-- instead of showing my files, my slides, I'm going to show one of our examples that uses nonlinear models. This is an example. It's a simple example. It's an example of an automotive radar. If I click on Transmitter, now I see what's inside the Transmitter. And if I click on Directional Coupler, I see what the directional coupler-- what you can change in the Directional Coupler tab.

First, you can decide what coupler you need. OK, they're listed. You populate the Coupling value, Directivity , and Insertion Loss, Return Loss, and Reference Impedance.

And here's the PA, if I double click on the PA. I see the Main tab. The Main tab, you can specify the Gain that you want. You can specify Power Gain or Voltage Gain. The amount of Gain, the Input Impedance, the Output Impedance, the non-linearity. You can specify the IP3, 1-dB Compression Power, Output Saturation Power, Gain Compression at Saturation. Now if you choose Even and Odd, you get to do IP2 and IP3. Noise, you get to choose the type of noise and the noise distribution.

So let's exit Transmitter and go to the receiver. For the Receiver, we have a similar box. If I click on the IQ Demodulator and click on Mask-- here's mask-- and look under Mask, I see what it is made of. Mixers, Phase Shifters, and other parameter, other components. But if I double click on it, I see what I can change. On the Main tab, I can change the Available Power Gain, Local Oscillator frequency, LO frequency, Input Impedance, Output Impedance, if I go to Impairments. I can change the IQ Gain & Phase mismatch, isolation between LO and RF, and the noise figure. I can also add phase noise and specify the phase noise is. On the non-linearity side, it's kind of similar to the amplifier. You can change the-- choose the IP2 and IP3, or you can choose compression points just like we showed on the amplifier slide. The amp is the same, same as the other amp. So this in terms of non-linearity, it's kind of comprehensive.

And let's see now what we have on our list.

TOPIC #13 (Antennas and Arrays)

So next is a transmit Antenna, transmit and receive Array and Antenna elements. For transmit and receive Arrays, we'll start by giving a brief overview of the capability of a Phase Array toolbox. Then we will demo our Sensor Array or array designer app. It's an easy way to design the array, and then move to MATLAB to finish the design. And then we'll demo our antenna designer app. Again, it's an easy app to start the design and then move on to MATLAB or exported to MATLAB to finish the design.

Topic #14 (Arrays)

With MATLAB, you can model most array shapes. Among the available ones are the most commonly used, linear, rectangular, and conformal arrays. In terms of element layout and weighing, rectangular and triangle lattices can be easily set up. Array tapering and array thinning are also easily done. The blue line is a Taylor array, and the orange circles are thinned arrays. These were done with a generic algorithm. All the circles represent elements that are turned ON, and all the ones down here at zero elements are turned OFF. Custom elements can be used, which means the elements do not have to be designed in MATLAB. They can be designed in any other software and imported into MATLAB to be used. And also more than one element can be used in one array, which is important for array designers.

Subarrays: toolbox supports overlapped subbarrays. Here's an overlapped subarray. Just to give you a quick overview of what it does, an overlapped subarray is useful for limited field-of-view applications. This subarray is seven elements, but two of the elements are shared with the adjacent array, and on both sides. So the orange one has seven elements. The white ones are shared with the blue, with the purple, and these are shared with the red. And same as all of them, except the last two arrays. They're not shared. They're not actually used. This is again, useful for limited field-of-view applications.

Support for subarray steering phase or time delay is available. For large array design, replicated arrays can be also designed. So basically, you can design a smaller array, and then replicate the array to get a larger array. There are many advantages to having subarray or tiles. One of them basically is that it's cost effective. You design a small tile, and then you just replicate the tile. Of course, there are many other reasons for replicated arrays. Subarray steering can be done at both the array and the subarray level.

This is how easy it is to steer an array, basically just one function. And this is how easy it is to get the time delay. Here's the time delay. And same as Gain and E-field response.

In terms of visualization, 3D plots are available both in phi-theta space and in U-V space. Geometry of the array can be plotted easily. 2D plots Az an Elevation and also Axial Ratio. This is the Axial Ratio of a Crossed Dipole. Basically, the zero Elevation and zero Az is the center of radiation. That's where the Axial Ratio is one, and as you move away from it, it deteriorates.

TOPIC #15 (Sensor Array Analyzer App)

Next, we will demo how to get started with array design, and this is the easiest way to get started with array redesign. It's through using the Sensor Array app. I could open this app similar to the way I opened the Waveform Analyzer app, but I'm going to open it differently since we already have a Simulink file that uses this particular array. I can go to the Simulink file, go to the Transmit Array, double click on it, click on Sensor Array. And then if I click on Analyze, I load the app.

Now I've already loaded it. So I'm just going to use the one that I loaded, and here it is. What I have is a 6-element array laying on the y-axis. Here's the y, x and z, z is vertical; spaced at halfwave apart. I can choose Lambda or meter. This is the array axis, and this is the taper. I used none, which means uniform, but I could choose Hamming, Chebyshev, and other ones, Taylor, and so on. This is the propagation speed, 3 times 10 to the eighth, and the frequency, 10 GHz. I'm going to use back baffled. I'll show what back baffled means in a second. And then after that, click Apply. Now, I could have chosen a different layout. Here are the layouts that are available in this particular app. There's the Rectangular array, Circular, and the rest. I am not going to name them all, but there are more than just the typical three Rectangular, Linear, and Circular.

In terms of element, I chose Isotropic, but I could have chosen other elements, as listed here. I could choose custom waveforms, which is important. Custom waveform is that I can-- I'm sorry, not custom waveform, but I could choose custom element, which means an element that's designed in any other software. Could be designed in the Antenna toolbox in MATLAB, or in any other software, or even measured in the lab.

Once I choose these, then I can start plotting my functions. First one is the most important I guess, the 3D pattern. Here's the 3D pattern. Back baffled means that it's radiating in one direction. Now if unclick Back Baffled, you can see what happens. That's all the way around. Let me go back to back baffled. Of course, the directivity changes when you do back baffling.

These are the characteristics of the array on the right side. Array Directivity, Array Span, Number of Elements, Half Power Beam Width (HPBW), First Null Beam Width (FNBW), and Side Lobe Level (SLL). I can also plot the 2D patterns, like Azimuth, for example. Here's the Azimuth pattern. And I can also steer the array. Now, let's suppose I want to steer is to 45-degree Azimuth and 0-degree elevation. Let's see what happens. OK, here we go. Now my main beam is at 45 degrees. Now suppose now I want to compare steering, as a reference, steering analog and steering digitally. So suppose I'm using a digital phase shifter with 3-bit quantization levels. I chose three bits to make the difference visible. Here's the difference. Orange is the reference, and blue is the quantized beam. You can easily see the difference between the two. This is very important to array designers, and they do like to know what happens when they use digital phase shifters.

Now once I'm done, of course, there are other things I can use. But once I'm done, I can again, either export it into several forms. One of them is MATLAB. If I export into MATLAB, I get the same thing as before. And I can modify the array or fine tweak it. There is more room to modify the array in MATLAB.

The good thing about the Sensor is it gets you started in a very easy and quick fashion. Once you get started and you know where you are, then you can export it and then do fine tweaking. Among what I can do is generate a report. Here's the report now that I can generate. This is a little bit different than just generating a MATLAB script.

TOPIC #16 (Antenna Designer app)                               

Now on to our next topic. An important part of the radar array is the antenna element itself. As we saw in the Sensor Array app, it allows for custom elements to be used. Custom elements can be designed in any software, including the MATLAB Antenna Toolbox. MATLAB Antenna toolbox has an app called Antenna Designer, which allows for the design of large variety of different antennas. So I will demo the use of this neat app.

Now the Antenna Designer app can be open similar to the other apps. I'm not going to show you again how to do it. So I've already opened it. I'm just going to go to the one that I opened. This is the first window that you see. It says, click on New to begin a new design. Here is New.

The default is a dipole antenna, but I do not have to choose dipole. I can choose any of the following antennas here. If I go back all the way down, I see the family of Spirals, family of Patches, Vivaldi, Slot, Yagi-Uda, Log Periodic, Monopole family, or a bunch of different variation of Monopoles, a family of Loops, Helices, Fractals, Dipoles, Cones, and Horns or Apertures.

Now once I choose the antenna, in my case, I chose the Dipole, because it's a simpler antenna to analyze. This is a method of moments app. So it takes a little bit of time to run, a little bit more than the other ones. But it's actually very fast compared to other tools in the market. I can choose backing. If I choose circular backing, now it looks just like a panel antenna or an FM panel antenna if any of you has done broadcast antenna design in the past. Or I can choose Corner Reflector, and now I have a Corner Reflector. Or I can choose Parabolic. With a Parabolic, now I have a Dish. Here's the Feed point. Red is Feed, and yellow is metal. And then you go back to none. OK, I'm going to enter my frequency. Let's see, 10, 1, 2, 3. This is 10 GHz, and Accept. So the default values are those of a resonant antenna. So here is the length and the width, I can tilt the Dipole. This is how I can tilt it, and I can offset the feed.

Now let me compute the Impedance. If I compute the Impedance at the default values, I see that at 10 GHz, I have zero reactance, which is resonance, and a 72 Ohm resistance. For the S-parameters, I have a return loss of about minus 15 dB. That's good.

Let’s Look at the 3D pattern. Here's a 3D pattern. With a 3D pattern, I can see it. It's kind of a typical, simple pattern. But there is an option of showing the antenna on the side or over-laying the antenna. So now the antenna is inside. This is a neat option. Or I can hide it at all. But if I export this into MATLAB, I get the choice of adding something called Transparency to the pattern. This way I can choose. I can see the pattern with respect to the antenna. Now, I've already plotted two for a Helix just because it shows the antenna. You can see the difference between when you have a pattern and an antenna overlaid. This shows you the pattern with respect to the physical location and the physical orientation of the antenna itself. I chose Helix, because it's a lot more visible than a Dipole. This is with the Transparency of 0.3. This is with the Transparency of one, which means that it's all hidden. Now, if this had a little bit different pattern, it could hide the whole antenna. By adding the Transparency, you can see the antenna inside. It’s a neat option, again.

I can do Az pattern, and then I can normalize. Here we go. In addition to this, I can optimize. With optimization, I get the choice of optimizing for Gain, for Area or Bandwidth. And once I decide to optimize, I get the Optimization panel. This is how I can choose my constraints for the optimization. I'm not going to optimize. It takes a little bit longer to run, again. So I'm not going to do this, Cancel.

Once I'm, done similar to the other ones, I can export this. Once I export it, I can modify the design or fine tune it. Let's see, what else do I have on this? This is it. I'm not going to show you how to export it. We've already done this, but we can see how easy this antenna, this tool is.

Again, you get started with the Antenna Designer app, and then you export to MATLAB. With MATLAB, you can do a lot more. You can just fine tune the design, basically. And that's it in terms of antenna design. Let's move on to the next topic.

TOPIC #17 (Environment, Targets, and Interference)

Next is Environment Targets and Interference. Question that one would ask is, what happens to the signal from the time it leaves the Transmit array until it's received by the Receive array. Several factors play a role at this point. We're going to discuss three factors. Environment, Targets, and Interference.

TOPIC #17a (Environment)

On the environment side, the signal experiences different kinds of attenuation. These can be classified as attenuation due to free space, rainfall, fog and cloud, and atmospheric gases.

• Free space is the loss that the wave experiences as it spreads over distance. This happens in clear, dry weather where the propagation velocity is very close to the speed of light in vacuum.
• Rainfall adds to the loss due to free space. The rain rate can be specified from light rain to extreme rain. Light rain is about 0.25 millimeters per hour, and extreme rain is over 50 millimeters per hour. Since rain loss is polarization dependent, the polarization ellipse tilt angle Tau-- right here-- can be specified, which can describe any possible wave polarization.
• Same as rainfall, attenuation due to fog is an additional loss term in the overall propagation loss. Fog is measured by its water content, and it ranges from thin fog to dense fog. Visibility of thin fog is about 1 km, and visibility for dense fog is less than 50 meters.
• Even when there is no fog or rain, the atmosphere is full of gases that still affect the signal propagation. Atmospheric gas attenuation is a function of both dry air pressure and water density, P and density.

TOPIC #17b (Targets)

As for targets, the Phase Array toolbox allows the simulation of point target, statistical targets, backscatter from a bicycle for micro Doppler considerations, and backscatter from a pedestrian, also for micro Doppler considerations.

• Point targets are constant non-fluctuating models.
• Statistical models include swirling I, II, III, and IV. Swirling I and II apply for targets with independent scatters of comparable echo. Swirling III and IV apply for targets that can be modeled as one larger scatter together with many small scatters. Swirling I and III have echoes that are correlated from pulse to pulse, or slow fluctuations. And swirling II and IV have echoes that are correlated from scan-to-scan, or fast fluctuations.
• The backscatter bicyclist function simulates the backscattered radar signal reflected from a moving bicyclist. The bicyclist consists of both the bicycle and its rider. For this model, you have to specify the initial position, the number of spokes on the wheel, initial heading, speed, and the gear transmission ratio. And as an illustration, here is a figure that shows the backscatter from a bicycle.
• Similar to the backscatter from a bicycle, the backscatter from pedestrian simulates the scattered signal from a moving pedestrian. This models the motion of 16 body segments. If you look at these, you have 16 body segments. These are the 16 body segments. They all are modeled to give one model. For this particular model, you have to specify the height of the person, operating frequency, initial position, initial heading and walking speed. As an illustration, this is a figure that shows the arm movement of a pedestrian. Blue is the right arm, and red is the left arm.

TOPIC #17c (Interference)

Now on to interferers and clutter models.

• We can model barrage jamming. This is a white noise source with user-specified power or a custom waveform.
• For modeling land clutter, we can use the constant gamma clutter. Among what you have to specify is the gamma value, the earth model, depression angle, Azimuth angle.
• The Billingsley function calculates the clutter Doppler spectrum due to Intrinsic Clutter Motion, or ICM. ICM arises when wind blows on vegetation and other clutter sources. This model requires the Doppler frequency, the operating frequency, the wind speed, and the propagation of velocity.

TOPIC #18a (Signal Processing - DoA)

Now on to signal processing. Once we receive the signal, we need to know where it came from, either the direction or the position. For this, the Toolbox has several built-in, high-resolution algorithms. To name a few, MUSIC and root-MUSIC. Implementing them is similar to any other phase of array system object or function. Specify the array, number of signals, and other parameters. And for illustration purposes, let's look at the following comparison, MVDR, MUSIC, 2D BeamScan, and MVDR. Here are the targets over here, target one, target two.

TOPIC #18b (Signal Processing - Beamforming)

Once we know the location of the target or the interferer, we need to steer the response of the array toward the proper direction. For this, we can use a number of widely used beamforming algorithms. Again, they're listed in the slide, and there's no need to name them one by one. Each has advantages and disadvantages and have to be selected based on individual scenarios. Again, implementing them is made easy through the use of the corresponding System Object. Here is a random comparison chosen for illustration purposes, LCMV, MVDR, MVDR phase shift, and Virtual array and Physical array.

TOPIC #18c (Signal Processing - Detection)

Detection and filtering. So now we receive the signal with the best possible signal-to-noise ratio. At this point, we need to filter the undesired components out. In our case, we have a jammer and a clutter. So we use one of the Space-Time adaptive processing techniques, namely the Adaptive Displaced Phase Center Array, ADPCA. ADPCA filters the signal in both angular and Doppler domains. Other techniques are available in four different scenarios, like for MTI with a stationary radar, pulse canceler can be used.

CFAR, adaptively estimates the interference power from the data to maintain a constant false-alarm rate. Match filter to maximize the signal to noise ratio, ROC curves to assess detective performance, stretch processing for use with LFM waveforms, and Pulse Integration to increase the signal-to-noise ratio.

TOPIC #19 (Visualization)

And now on to visualizations. Visualizing the data is important, especially if it has multiple dimensions. Being able to spot a problem by simply looking at a graph is extremely valuable. Base MATLAB is extremely rich with plotting 2D and 3D data and any of the commands from base MATLAB can be used.

In addition to that, the Phase Array Toolbox has display options specific for radar and antenna applications. The following clip traces the path of 3 targets as the radar scans the area. Let's play the clip and watch what happens. Here's the radar beam, and this is vehicle on the ground, airplane one, airplane two. This has almost a straight path. This is a circular path. And this is a short clip, but it gives you an idea of how effective this tool is.

Another tool is the antenna coverage map. What we're going to play now is assessing basically transmitter site. So what we will see is the site. We have a 7 by 7 element array pointing towards the x-axis, which means parallel to ground level.

The transmitter is placed at the Washington Monument in Washington DC. Here's the transmitter. And there are 5 receivers placed around the transmitter. These are the blue. Blue are the five receivers. And now we vary the beam and then take data. Record the data, and based on the data taken, we can decide on transmitter site and location. This is again, a fast clip, but it shows the effectiveness of this tools.

Other tools that are available, there's the video viewer. I'm not going to show this; it's kind of a peripheral to the Phase Array Toolbox, but it's also a very effective tool. Also the range intensity scope and the Doppler intensity scope can be displayed easily, same as Range-Doppler, Angle-Doppler, and Range-Angle scopes.

We just finished the whole circle, from waveform all the way to signal processing and visualization.

TOPIC #20 (Help Menu)

Now that we've presented an overwhelming amount of information, the question is: how do we access what we need, and the answer is easy. Basically, we go to the examples. The way to get the examples, if we go to the MATLAB main window, and click on Help, and when I click on Help, I get the Help menu. Here's the Help menu. On the left side I see category. I can scroll down all the way to Phase Array System Toolbox. Click on it, and then I see subcategories,

• Targets and Environment
• Detection, Range, and Doppler Estimation
• Beamforming
• Waveform Design
• Phase Array Design

and so on. Up here on Blocks, these are the blocks used in Simulink, and these are the functions used in MATLAB. And here are the examples. There are over 120 examples. Again, I can specify - suppose I want—let me to go back to all, and then click on Applications, for example. And let's say my application is automotive radar. We have six examples of automotive radar. Suppose one of them is of interest to me. Let's say this one is of interest to me. I click on it, and I see a complete description of the example, and the code, and the results. I can open the file by clicking on Open Live Script. And once I open, I see Open Live Script. And here we go. Here's the example. Now I can modify this example. I can do whatever I need to do to it to make it resemble my scenario, and that would be probably the best bet, the best way to access what you need and exactly what you need. Let's go back to our slides.

TOPIC #21 (Summary)

So we're done with the navigation, and finally, our summary and benefits of the Phased Array Toolbox

• OK, rapidly model and simulate phase array systems in either MATLAB or Simulink. Just to give you my own personal experience with MATLAB. When I started using MATLAB, I programmed all of these functions myself. Almost all the functions that we saw in terms of patterns, and arrays, and radars all were programmed by me. When I started working with the MathWorks and saw what they had done with all these functions that are available, it was incredible how much time I could have saved just using the Toolbox. I didn't know about the Toolbox at the time, so I ended up programming them myself. I spent literally months working on programming these models, but now they're available. So that's one of the big benefits that I wish I knew a long time ago.
• Second one is access to a large library of practical radar system examples. That's another one. Almost every practical situation does have a starter, and the starter is one of these examples. You go to the example, you start, and you continue with it. I myself did work on a short-range, low-power radar, and I started all the work myself. Had I had an example like this, it would have been an extreme help for me.
• Second [3rd], interactive development with algorithms and tools, specifically for phased array systems. We saw all the tools that are available in terms of Beamforming, Direction of Arrival, Filtering, and all of these are available as just functions. Do not have to program any of these.
• Explore alternative system architectures and make system level trade-offs. You can easily set up one system against another system and then decide for yourself which system is a better one for you.
• And of course, re-use existing C, MATLAB, and other codes. If you've worked on one project, you already have the C code for it or the MATLAB code. All you have to do is just modify and continue.

And this is just a few of the benefits of the Phased Array Toolbox, but we can end at this point.

TOPIC #22 (Q/A)

Next is the Q&A section. The floor is open for questions. But if you do not have time to ask questions, please jot down my information. Here's my email, my telephone number. You can email me at any time and ask questions. Thank you for attending, and let's start with questions.