Early Verification of RADAR Front Ends with Model-Based Design

All right, my name is Leif Hille. I am an industry manager here at The MathWorks. And my colleague here, Giorgia Zucchelli, is a product manager of our suite of RF and microwave design tools. Together, Giorgia and I are going to talk about applying model-based design techniques to RF and radar component development and we're going to frame the work we're going to show you in the context of mission engineering flowing down to component design. So effectively, our components will be part of a larger system.

And we're going to show how you can use MATLAB and Simulink tools to do detailed component design and then flow those design models back into a system-level model for system-level verification activities.

So a quick summary of the things I'm going to talk about here. I mentioned I'm going to talk about mission engineering and showing how that can be flown-- how the requirements for mission engineering can be flowed and models can be pass down all the way down to component engineering. Then I will put on my hat as if I were a system engineer designing a radar to support a broader effort.

And I will talk about specifying a radar and doing an architectural design. And then I will pass it off to Giorgia, who will be actually walking through the meat of the matter here for this webinar, which will be an RF component design, which will be compliant to a bunch of specs that we will derive in the earlier phases.

And once we've designed the-- or she's designed the RF components, those will be reintegrated and then reassembled as a system-level design. And we will operate those components together in a system-level simulation and show that they are performant as a system-- an assembly of systems, all while staying within the design team design space.

I mentioned that I would be talking about our design efforts here at the component level at the very bottom of this pyramid in a mission engineering context. So as a contractor for many decades, I appreciated understanding where the requirements of the thing I was designing or implementing came from. And they come from somewhere, those things. It's usually a mission commander or a policymaker that has an event that occurs occasionally that requires a capability they don't have.

And the understanding of what is needed to solve that problem is often handled with a simulation, a mission simulation, at the very top level. And that mission simulation would tend to result in a system design that might specify a few systems that are required to answer that shortcoming of that need. And the job of the program, office, or integrator is to decide which of the systems should be bought off the shelf or used existing assets and which of the systems should be newly designed.

In the case of today's discussion, we're going to pretend that the radar is a piece that needs a new design, and we're going to basically set up as if we were being told to build a radar. And again, a radar has also different simulations that are conducted both at the system level and the subsystem level and the component level. And all of these levels of aggregation and fidelity up and down this chain all demand an input, a design, a simulation.

And there's often paper exchange or electronic exchange of some sort of requirements between all these models, which adds friction between the layers. So today we're going to discuss how in model-based engineering techniques and model-based system engineering, how you reduce the friction for the handoff between these layers, and it facilitates your overall design efforts.

So let's put ourselves now in the role of the radar design organization. We have been handed a specification by a government team or organization that provides, that procures hardware. And we have to go through the three design steps I've laid out here-- there are actually more design steps, but I'm just focusing on these three-- to basically take a specification, turn it into a component specification, and then reintegrate it to perform integration test.

And the objective of model-based techniques, of course, is to do all of this at lower risk and cost by doing early integration and tests as much as possible. And one of the things that the historical approaches to doing radar design add is a friction layer between each step. Specs are handed off by paper or even as documents.

But the bottom line is you're rebuilding a model or rebuilding an analysis at every stage. And you may not be able to benefit from tools built in the previous stage or tools used in the previous stage to do the next stage. And that results in a cost increase or a chance of error.

And so these three phases, specify, design, and integrate, are kind of sideways activities in historical workflows. And then obviously the model-based design approach, the idea is to reduce the friction between these layers and do as much early integration and testing through simulation as possible.

So each of the three layers defined, or steps, rather, defined in the last slide also have a person or a group of people who perform the activities in that area and then also different kinds of information they specify or produce. And for today's exercise, I'm going to be the system engineer. And my objective is to provide a system engineering spec and a top-level component spec for the designer, in this case, the RF designer, antenna designer.

And Giorgia, since that's her area of expertise, will be the RF designer. And she will actually then perform the third step as well, which will be acting as the integration and test engineer who will integrate the RF components that she's designed in the previous step, using the design models that she's created in the previous step to perform a full system-level simulation, complete with targets and environments and where we can do verification activities or early decision making about the design, success of the design.

Now that we've laid out the three steps in our abbreviated design process workflow, we're going to begin with step one, the system engineering, where we'll begin addressing the radar and component specifications.

Here are the four areas which we'll cover in the system engineering section of the demonstration here. And it'll begin obviously with modeling our system through an assembly of architectural elements and interfaces and interconnections. Then we'll take the customer-provided specification and apply those and allocate requirements to elements of that architecture.

And then we'll begin using design and analysis tools to derive the preliminary RF features of our radar system, which could be things like pulse shape, waveform selection, repetition frequency, number of pulses, signal processing parameters, et cetera. And then in that same tool, we will determine what RF parameters we need to use to achieve the waveforms and features of the RF emissions and receptions that we derived in section C.

We're going to dive into the first three substeps of the system engineering section here. And these three substeps are architectural modeling, allocation of specifications, and initial RF parameter selection for our RF front end. So

I've got three insets here of three tools that we're going to talk about. The first two are for the architecture and requirements piece of this design. And we're going to use two tools. One is called System Composer, and the other one is called Requirements Toolbox. The former is a graphical modeling language for developing architectural models.

And it's integrated with our Requirements Toolbox, which is a requirements management tool which can import requirements from text documents, common requirements databases, and document formats from most providers. And it lets you allocate the requirements to elements of the architecture through the graphical interface. And then, also, if you are working on subsystems of that architecture, you can allocate requirements to subelements of that architecture as well.

Now, the tool on the right is the Radar Designer in our Radar Toolbox, and this is our first stab at the power level design analysis of our radar performance. And what we would do in that-- we're going to go into that more in detail in a bit here, but that would be where you would begin to put your targets and your environments in and start selecting waveform parameters that would be suitable for meeting your performance specification. And your requirements, by the way, would be at the bottom there of that little inset on the right.

And if you have a-- if you meet the performance requirement with that waveform, then it'll be red, and if you-- sorry, green. And if you don't meet it, it'll be yellow or red. And those levels are explained.

So we're going to continue working in our Radar Designer app to finalize our radar hardware requirements to pass to the RF Designer, which is where Giorgia will take off from here. And this tool lets you basically trade performance parameters between hardware, signal processing, and other elements of executing a radar mission.

And you have already put in your performance requirements for your target and your environment, and you are basically trading off between elements of your design to make sure that you have a clean understanding of what the RF Designer should be building their hardware to. So in this example-- for example, I've got a max range of 40 kilometers, probably a detection of 10-- sorry, 90%, an RCS of 10 square meters, and a center frequency of 2.4 gigahertz.

And the output of this design effort in this phase is that we need a peak power of 53 dBm, a receive noise figure of 4 dB, an antenna gain of 7 dBi, and an array size of 8 by 8, and so on. And we are going to now pass this set of requirements to our RF designer, and they'll take it off from here.

So now one question that comes up is, how do we pass the requirements to our RF Designer? Well, the good news is that this suite of tools, in fact MathWorks entirely, all the MATLAB tools and Simulink tools, operate with modern process tools like Source Control, Report Generation, and those kinds of tools that make passing your design to another team or person in your design workflow. And so they can stay in the MathWorks design environment, which is what Giorgia is going to illustrate in the next set of slides.

Thank you, Leif. This is going to be our starting point. From these high-level specifications, we will derive the specification of the RF component. Before we get started with the design, I would like to spend a few words about the methodology that we will follow. We will systematically repeat two steps. First, we will perform analysis to derive the specifications. Then we will use a simulation model to verify that our design meets the specification.

So why two steps? With the analysis that is static, you determine the specifications. Then we use a simulation model that effectively works as a verification test bench. So the first thing that I'm going to do now is I'm going to build a simulation model of the radar system and verify that the specification that Leif just derived allowing it to detect the targets as expected.

So we go to MATLAB, and we start from our Radar Designer app session. So we have on the left-hand side our high-level specification. We know that this radar that operates around 2.4 gigahertz with 1 megahertz of pulse bandwidth, 1 microseconds of pulse width, and a pulse repetition frequency of half a kilohertz. We also see some of the specifications that are important for the TR module, such as a 53 dBm of peak power that approximately corresponds to 200 watts per TR module.

We also see that the noise figure of the receiver should be 4 dB. And we also have the specifications for the target. So we assume here a target with the radar construction of approximately 10 square meters. And with this specifications, we see that we should be able to detect a target at the distance of approximately 40 kilometers.

From this static analysis environment, I want to build a simulation model to verify that indeed it can detect this target. So let me go to MATLAB. And because I want to maintain some programmability-- so if my specification change, I still want to have the ability to adapt my design in an agile way.

So I created here a script where I repeat essentially the same specification that we used in the Radar Designer app. So the operating frequency, the size of the array, the array, the antenna directivity, the maximum range, the number of integration pulses on the digital signal processing side, all of these become variables that, as I execute the script, populate the MATLAB workspace.

We also integrate four targets, one at 10 kilometers, one at 24 kilometers, one at 39 kilometers, so just within our range, and one at 47 kilometers. The last target is just outside our range. And these numbers are just essentially not exact, precise numbers so that they allow us to play a little bit with the targets as well. In terms of receiver parameters, we have parameters for the match filter and time varying gain as well as 10 coherent integrated pulses.

So let's see where these variables are used. We created a simulation model in Simulink where we can simulate our target and verify that indeed when we perform the simulation, all our four targets get detected. So you see here 10 kilometers, 24 kilometers, 39 kilometers, just within range, and in this case we are lucky enough that we still detected the target that is farther away, though, if we run the simulation, we will see that the last target is actually the one that is closest to the noise floor.

Let's look at the model. So let's start from the linear FM waveform. Here we generate a pulse-modulated linear waveform using the variables that we defined in the MATLAB workspace. This linear waveform gets scaled here to have an input power of 3 dBm. And this input power will be multiplied times the transmitter gain of approximately 50 dB to achieve a transmitter peak power of 53 dBm.

We also use the absolute value of the linear FM waveform to control the switches that decide when to transmit and when to receive. This is a very interesting block where, essentially, we repeat 64 times each TR module by 64 because we decided to have an antenna array that is made by 8 by 8 antenna elements.

So these 64 blocks are executed in parallel. This is also the reason for these two blocks here that effectively perform a scalar expansion of our input waveform. In other words, we have here 64 control signals and 64 input signals that are all identical and feed each of the TR modules.

Let's look at the placeholder for our TR module now. It's extremely simple. What do we have? A placeholder for the transmitter, where essentially we model the gain of our transmitter. So we have 3 dBm of input signal and 53 dBm of peak power at the output. And we also have a placeholder for the receiver, where the most important parameter in this case is the noise figure. And this noise figure of 4 dB, as we specified in the Radar Designer app.

We also have a couple of switches that control when to transmit and where to receive. So if you remember, the control signal is the absolute value of our pulse waveform. When the pulse waveform is greater than the threshold, in this case at 0.5, just to give a number, then the first input passes. This means that when there is an input signal pretty much we transmit the signal. Otherwise, we transmit 0.

Similarly, on the receive side, we use the opposite logic. So when there is an input signal, we don't receive. And when there is no input signal, then we receive our signal. If you go one level up, what's next? We have placeholders for the antenna gain. So this represents the directivity of our antenna, 7 dBi. And we also have placeholders for our arrays. So in this case, we use narrowband transmit and narrowband receive arrays that represent a N by N, so 64 URAs, Uniform Rectangular Arrays, of isotropic antennas.

And just for convenience, we place the array normal on the z plane, which means that our arrays are pointing up. But it really doesn't matter the direction of point where we point.

We have the models of the targets, our four targets. So we have the transmit signal that impinges on the targets and gets sent back to our receiver array. We have the 64 receiver signals that get passed to our receive modules. We assume that we will perform beamforming, and we'll talk a little bit later about it, in the analog domain.

Here, we sum up all the signals, and we pass it to our signal processing elements that is made of a match filter, a time varying gain, a coherent integration of time pulses. And as we perform the simulation, we can verify that all our four targets are actually detectable.

But now let's go into the step of RF component design. Step by step, we will first design the transmitter and identify the common path or the common component shared by the transmitter and the receiver. Then we will design the receiver and use the same common components that we identified at the previous parts-- for the previous part.

Then we will also design a single dual polarized antenna and look at the directivity, design matching network to integrate the antenna in our module and maximize power transfer, and then we will integrate together transmitter, receiver, and antenna and use this as a baseline for what will be later integrated in our verification radar model.

Let's start breaking down the specifications of the components that are part of our transmitter branch in our TR module. What you see here is the budget analysis of the transmitter side. So what do we know about the transmitter? We know that the operating frequency is 2.4 gigahertz. And we know that for an input available power of 3 dBm, we want to have an output power of approximately 53 dBm or a gain of approximately 50 dB.

So we decided to break down this 50 dB of gain pretty much in three amplification stages, a common gain amplifier with gain of 12 dB, a driver amplifier with a gain of 25 dB, and a power amplifier with a gain of 13 dB. If you look at the chain, we see a number of components. We see three switches.

You remember that we initially had two switches to enable and disable the transmitter and the receiver. So these are TR_Switch1 and TR_Switch3. They represent exactly those two switches that we have seen before. But we also need to consider a third switch, in this case TR_Switch2, that allows us to share some common components between transmitter and receiver.

What are these common components where a common amplification stage? The phase shifter, because we will be able to steer the beam of the transmitter and the receiver in the same direction, and the programmable attenuator. In terms of each of the components, what you see here are the specifications provided primarily in terms of gain. Right now, although we provided the noise figure for the gain common amplifier, noise figure of 5, everything else is ideal, as well as the nonlinearity is ideal.

We will see that as we refine these components using a real-life specification, some of the nonlinearity parameters will be added as well next step in the design process.

We also included an antenna array. So in this case, we included the antenna model that is just an isotropic model as a placeholder with gain of 43 dBi. Why 43 dBi? Well, because consider an antenna with 7 dBi of directivity plus an array gain of 20 log 10 of 64 that is 36 dB. If you sum the two, you obtain a total gain of 43 dBi. Essentially, we are summing up the outputs of the 64 transmitter in the air.

This model provides us with a first floor planning of our transmitter. And from here, we can actually generate a model for simulation. So you see here the model of the transmitter branch of the TR module with the programmable switches. And with an input power of 3 DBM, we achieve the expected EIRP of 96 dB.

We repeat the same design process and the same budget analysis for the receiver. So here what we see is the chain, the cascade representing our receiver, starting with an antenna with 7 dBi of gain, followed by gain, three amplification stages, and three switches, and the common path with the common amplification gain, the phase shifter, and the attenuator.

Focus on the budget analysis of the receiver is primarily on the gain and noise figure because that is what the term means, the signal-to-noise ratio. And because we also provide the signal bandwidth in terms of specification, we can also verify the overall signal-to-noise ratio is consistent with what required by the Radar Designer app to detect a target at 40 kilometers.

Notice that in this case the LNA is the first block in the chain pretty much that adds noise. And that is really the most impactful in terms of signal-to-noise ratio. We know that the first components in the chain are the ones that are more important because every other contribution gets divided by the overall gain of the previous elements in the chain.

So what we see actually at this level the budget is very favorable with the total noise figure of 2.2 that is not really realistic because we don't consider any losses between the antenna and the LNA. We will see later how this budget will get updated. Again, from here, we can generate a simulation model.

And once we run the simulation, we can verify that for a nominal input power that is representative of the transmitter EIRP plus the path loss, we receive an output power of minus 66 dBm, considering the same architecture that we already identified for the transmitter in terms of common path.

Next, we're going to move into antenna design. We're going to design a microstrip PCB antenna with two orthogonal feeds, as shown in the image here on this slide, that guarantee dual polarization. We're going to use the PCB Antenna Designer app. Let's see it in action.

So let's look at our PCB antenna. First of all, we work with the square board shape. And we see that this board shape has different layers. The top layer is a dielectric material. It could be any of the material that you are indicated here in our catalog or, for example, a custom material, as it is in this case with a dielectric constant of 3.38 at a certain thickness.

We have three actually dielectric, D1 at the top, D1 as well at the bottom with the same characteristic, and D2 that is actually a foam material that is sandwiched in between. In between these three dielectric material, we actually have different metal layers. The top layer is a patch. This represents our radiating element. It's a rectangular patch. And you can see that it's actually a rectangle with a certain length and width and, in this case, is a fixed dimension.

This second metal layer in between D2 and D1 dielectric is a ground plane with a couple of slots. You see it here also indicated in a 3D view. And this is interesting because our ground plane is all created using a Boolean operation applied to geometric shapes. And each of these geometric shapes are actually defined by the use of design variables.

In this way, if we wanted to scale up or down the antenna or slightly change some of the characteristics, this can be easily done. The bottom layer is made of the two orthogonal fields that excite the antenna. Now that we have designed the antenna and defined its geometric properties, we can perform the full wave electromagnetic analysis using the method of moments.

We can see here the 3D volumetric mesh of our antenna with approximately 11,000 elements. And then we can perform a simulation. We can compute, for example, the S-parameters. And we can, for example, highlight the S11 and the S22 that indicate the matching. We can also inspect the impedance of each of the two elements as well as verify the far field radiation pattern.

And the good news is that our antenna achieves directivity of 8.75 dBi, which is more than what we were initially required. And you might wonder, what if you want to further optimize this antenna?

Well, what is very interesting is that, from here, you can actually use the surrogate optimization method that comes with the Antenna Toolbox that allows you to actually automatically optimize the design for different metrics, like increase, optimize the gain or the bandwidth, by changing any of the design variables within certain bounds and by forcing specific constraints.

So this is one way in which you can better explore the design space or even further improve the specifications of your design. So now that we have designed our antenna, let's design this matching network to improve the power transfer.

So I'm going to use now the Matching Network Designer here. I've already imported the S11, in this case, of the antenna, which means the input impedance of the first termination of the antenna. And I can choose between different topologies for matching the antenna to 50 ohm. In this case, I use a L topology. And you can see here that I automatically get four different matching network that bring the impedance of the antenna that is fairly mismatched, you see it here, straight in the middle of the Smith chart, through a series of-- so a couple of transformation using lumped components.

You can go through the different options and decide whether to use one or the other. In this case, I use the first matching network that is provided because it's the one with the best choice in terms of lumped component values. And of course, if we do this for the S11 of the antenna as well as the S22, which means the input impedance of the second network as well.

So now that we have designed our antenna and its two matching networks, what's next? We're going to integrate the antenna into our transmitter model. So we will add the Wilkinson splitter to feed the two matching networks. And we will integrate our antenna model into the antenna block. We will do the work for the transmitter antenna, for the receiver antenna as well.

In this case, the Wilkinson splitter actually works as a combiner of the same two matching networks. And then we will take it a step further. We will put together both transmitter and receiver and the antenna and the matching network into a single model. Let's inspect our TR module model. So where do we start? We start from here.

This is the switch that control the operating mode. Now we are in transmit mode. When we are in transmit mode, the input power is 3 dBm for a CW signal. So that is just a constant signal with constant power at 3 dBm coming into our transmitter through a circulator. This switch here also control the controllable switches.

So now we are in transmit mode, which means that the output of the circulator is directly connected to the common path. So the signal gets through the common path amplifier, the phase shifter that is just currently a placeholder. We will use it later for beamforming. A programmable attenuator, and then out to the driver amplifier, the power amplifier, again through the circulator, through our Wilkinson splitter, the two matching network, and the antenna block.

Notice that the antenna block uses the PCB antenna that we just designed, our dual polarized antenna. You see that it has two inputs, each representing the feed of each of the two antennas, and that it operates at 2.4 gigahertz, both for the incident wave as well as the radiated carrier. And we are looking at 90 degrees of elevation because we consider that our patch antenna is positioned horizontally on the ground.

We perform frequency domain modeling, by the way, both for the antenna impedance as well as the vector effective length, which means that both the impedance and the far field radiating characteristics are frequency dependent in the antenna block.

Again, we follow the transmit path, we have a placeholder for the array gain, and we verify that our EIRP is very, very close to what we expected. It's 97 dBm. And it is 97, slightly higher, because, if you remember, the directivity of our antenna was slightly better than what we had in the initial specifications.

The antenna block also receives an incident plane wave with an input power of minus 113 dBm proportional to the transmitted EIRP and the path loss. So let's see what happens when we toggle our switch and we make our TR module operate in receive mode.

And when we toggle the switch to receive mode, the transmit power goes to minus 200. So we stop transmitting the signal, and the received signal gets through our antenna, our matching networks, through the Wilkinson that effectively works as a combiner, through the circulator, the LNA, the additional gain block, and through again our common path because the switches got toggled to pass the other input.

We go again through the common path, out to the circulator, and we receive a power of approximately minus 67 dBm. And we can also use the spectrum analyzer to verify the SNR and verify that it's consistent with what previously predicted by the budget analysis as well as the radar analysis. It's interesting also to observe that you see now I'm receiving 67 dBm of power when I am in receive mode.

But when I am in transmit mode due to a leakage through the circulator and through the switches, I actually receive minus 50 dBm. So this is the model that, essentially, we use as a blueprint for our TR module and for the integration with the antenna array, taking into account all effects like coupling and impedance mismatches. And we are going to evolve this model further to take into account more realistic characteristics for the amplifiers and some of the RF components.

So we are now marching through our design. We designed the transmitter, the receiver using nominal specifications. We performed budget analysis. We created a simulation model. We analyzed the antenna, and then we created a simulation model of the antenna integrated with the transmitter and receiver model. And we put everything together into a single TR module.

Our next step will consist in elaborating this model in such a way that for some of the components we can use datasheet specifications or RF measurements. So let's say that, for example, for some of the components you have S-parameters attached on files either coming from measurements or coming from simulation tools or coming from datasheets or vendors.

And this you could have, for example, characteristics for some of the amplifiers, such as AM-AM, AM-PM power curves. We're going to integrate this into our TR module simulation and see how it performs in terms of results.

So for some of the components, we're going to use datasheet specifications. But for some other components, we're going to actually use measurements. So in this case, first of all, I'm going to import and inspect the AM-AM, AM-PM curves that will represent the power amplifier. So you see here how we get a gain of, if you look here in linear region, approximately 17 dB in the linear region and that we model the compression of the gain as the input power increases as well as increase distortion on the phase.

Similarly, we import the touchstone file, a three-port touchstone file for the circulator. And let's plot this to inspect the data as well. So what we see here are the different-- let's look at the S11, S22, and S33 that represents the matching conditions. So the circulators are decently matched at 2.4 gigahertz.

Then we can expect to inspect, for example, the S21 path. It's one of the path. And then if you plot the S12, you will see that it's not symmetric, providing isolation between the different ports. So these are going to be the data we're going to use.

By the way, you notice here we are extracting two port equivalence circulator for some of the connected ports so that we can use this data directly into the budget analysis. So let's look at our updated budget. So here we have the updated budget for the transmitter. You can see that in place of what we before had the placeholders for the circulators, we actually have the actual losses with the touchstone file representing the circulator both here, and towards the end, just before the antenna.

Similarly, for the power amplifier, we use the AM-AM, AM-PM characteristics. And we can visualize them and verify that they are correct. And also, for the common path amplifier, we specified the output-referred IP3 so more nonlinearity.

So now let's look again at the results, our table of results. And what we see here is that we can actually compare results obtained with Friis and with harmonic balance. And if we browse through, we actually see that the output gain is very, very similar. This essentially means that we are not sending our transmitter in saturation.

We also have a similar budget on the receiver side. Again, we have the circulators with the S-parameters for the respective ports. And these circulators have actually a very large impact because they introduce losses, which means that actually now our noise figure is higher than what it was before. We are now around 4 dB. That was actually still in the budget of what we initially had specified in the Radar Designer app and for radar design.

Our SNR is just short of 4 dB, hopefully enough to detect our target. And also in this case, for the common amplifier, we specify no linearity, but we are very far away, effectively, from the power levels that might excite it. So essentially, nonlinearity is not an issue for our receiver, at least in this situation.

Actually, we're also using-- this might be interesting-- S-parameters for the LNA. So the LNA is specified both through its S-parameters as well as the output IP3, as well as the S-parameters of the circulators. With this data, we can now update our TR module model. And now we can see that the circulators have been substituted by their S-parameters, their three port-- using the three-port touchstone file that we used.

For the common path amplifier, we use the gain as well as the nonlinearity characteristics and the noise figure. For the power amplifier, we use the AM-AM, AM-PM table. And for the LNA, we actually use the touchstone file as well as its nonlinear characteristics and its noise figure.

And with this, again, we can verify that when we are in transmit mode with an input power of 3 dBm, we get a slightly worse EIRP than before. Now it has decreased due to the losses of the circulator. And now when we toggle the mode from transmit to receive mode, we actually see the power that on the receive side that also is slightly below what it was before. And more importantly, the noise floor is higher compared to previous values. So we have decreased our budget in terms of SNR.

So let's move towards the concluding part of this presentation. Now that we have a realistic model of the TR module, we are going to integrate it into the radar system and see if with this TR module we can effectively detect the targets, especially the one that is located further away.

Additionally, we will raise the abstraction level of the module model, and we will integrate 64 of these models together with the model of the antenna array, the eight-by-eight antenna array, and enable beamforming.

So this is our first simple integration model. Here we have our top level representing the radar, our test bench. We still have placeholders for the antenna array. We will elaborate more on them in a second. The focus here is on the TR module, and you can see here that is exactly using the same components and the same datasheet specifications and measurements that we just talked about.

Now, when we run the simulation, we can verify whether we detect the targets, yes or no. And as the simulation runs, we actually see that we confidently detect the first two targets, the ones that are closer to us at 10 and 24 kilometers. But actually, for the target that is around 39 kilometers, just in range, then we sometimes miss the detection.

Why is this? Well, we know, because we introduced the circulator, and the losses of the circulators in this case are affecting-- are hitting us on two sides, with the reduced EIRP and we increase the noise floor on the receiver. So for this reason, I'm actually going to stop the simulation, and I'm going to use a different circulator that has lower losses.

So we can see here that the new circulator has better matching, actually. And if you look at the losses on the forward path are much lower than before. So with this new circulator, we can now update our simulation and verify again results. And what we see is indeed that now we can detect our further away target a lot more reliably. This is just a simple example that shows how to iterate back and through the process.

Now, move to the array analysis and integration. We're going to use here the Sensor Array Analyzer. And we have defined an eight-by-eight rectangular array with elements spaced by half lambda. And for each of the elements, we use the amplitude for both horizontal and vertical polarization. Amplitude, and respectively amplitude and phase, is computed with the Antenna Toolbox and the method of moments.

With this data, we can now apply pattern superposition to the antenna pattern and inspect, for example, how the 3D radiation pattern looks like and what is the antenna radar directivity, as well as, for example, we can look at the elevation cut of the pattern itself. We can also apply for-- we can see, for example, that the main lobe points up in 90 degree of elevation and that we have a secondary lobe and that we have a very deep null around 60 degrees from boresight.

We can also apply steering. For example, let's say that we have a target at 60 degrees. Then, if we don't do anything, we will miss the target. But if we steer the beam to 60 degree, then we will see that the main lobe will point towards that direction. And we can also verify what is the updated directivity as 22 dBi as well inspected 3D radiation pattern.

And then we can do some fun experiment. For example, let's say add a phantom target at 83 degrees rather than at the boresight then on the main lobe that is 60 degrees. So we can do this type of experiments. So let's go next and integrate this antenna array into our simulation.

So let's look at our model. This should be familiar. We have the same signal source. You remember that we had a 64 TR module with four-each subsystem that allows for their parallelization. We model the antenna array using the narrowband transmit and narrowband receive blocks. If we open up this block, we see that we use a custom pattern to describe the isolated antenna element.

The pattern comes from Antenna Toolbox and has been computed using the full wave electromagnetic analysis. And this block performs a pattern superposition to compute the pattern of the entire array and to model an N-by-N rectangular array. We have a block for the transmitter. We see the transmitted EIRP, as well we have an equivalent block for the narrowband receiver.

We also see that we have an angle that specifies the location of the target, effectively. Here, we are saying that the target at the moment is positioned at boresight, so 0 degrees azimuth and 90 degrees of elevation. We also see a different angle that is the beamforming angle. And currently, we are beamforming also at boresight. And we see here that the angle is passed to a phase shift beamformer and that we use the angles of the weights to directly steer our 64 TR modules.

So we have 64 phase shifts that get handed to each of the element in our TR module. This is exactly the same as we had seen before. So let's look one layer down. And here is where everything happens. So just remember that we have 64 of each of these TR modules that are simulated in parallel.

And one thing that is worth mentioning is that in order to speed up the simulation of this model, we have raised the abstraction level. Now, instead of using circuit envelope, we are actually using an equivalent baseband approach. First of all, you need notice that the signals are indicated with unidirectional arrows. This means that either the impedance mismatch is neglected, or we are assuming that essentially each of the blocks are perfectly matched, or we need to take into account impedance mismatch losses in a different way.

For example, for the circulator, we now use the two-port S-parameters, the same two-port S-parameters that we actually used in the budget analysis when we updated the budgets to use the measured data. For the other blocks, we still use the same characteristics that we used in the previous model. So for example, for the power amplifier block, we still use the AM-AM, AM-PM lookup table.

So let's see what happens with the simulation. We go one level up. Let's look at our target range scope. And what we see is that, as expected, we are detecting all our four targets, which is really cool. Now, let's say that we move our target from boresight, we move it to 60 degrees. That is where our array has a deep null. So we see here that the EIRP has dropped as well as we are losing the targets.

So let's now steer our TR module towards 60 degrees. So what we see is the EIRP going up, increasing back to the levels, as expected. And we're also starting to see the targets being detected. Let's now verify that our TR modules are indeed beamsteering towards the 60 degrees. So now we pause the simulation, and we use the instantaneous excitations to our array to compute the array pattern.

This means that the nonlinearity of the transmitter, as well as other impairments, such as leakage, are effectively taken into account. So what we see here is the 3D radiation pattern that this is gearing towards 60 degrees of elevation. Let's now make a fun experiment and move our target to our secondary lobe, approximately 83 degrees.

Notice that the directivity of our array is now decreased by approximately 10 dB. So now we go back to the simulation, and we change our target angle from 60 to 83 degrees. And we continue the simulation and open up our target range scope. What we see is indeed that the EIRP decreases by 10 dB, as expected, and that slowly our targets disappear.

And if you zoom in, you can actually see that we can barely detect the target that is closest to us at 10 kilometer. Summarizing, we have raised the obstruction level of the model of our TR module, and we have integrated it into the radar simulation. We have verified that the targets get detected. And we also integrated our eight-by-eight transmitter and receiver antenna array.

Last but not least, we have done some really cool experiments. We have positioned our target at the nulls, and we have lost them all. Then we have steered the beam again towards the main null at 60 degrees of elevation, and we have recovered the target. And then we have played around and see how it works when, for example, we have a phantom target, a target that is not where we are steering the beam but maybe a position in one of the adjacent lobes. And that was all from my side. Back to you, Leif.