Design of 5G mmWave Beamforming Systems
Overview
5G and 6G communication systems will employ mm-Wave frequencies. This has made the development of highly integrated antenna arrays and RF front ends a standard practice. Engineers need to integrate RF, electromagnetic analysis, and digital signal processing algorithms within their system-level models.
In this webinar, we provide practical examples of RF design and simulation techniques for MIMO transceivers to enhance the overall performance and reduce costly re-spins. For RF transmitters, you will learn how to model power amplifiers and their interaction with antenna arrays and beamforming algorithms. This includes quantifying their spectral regrowth, measuring metrics such as EVM and ACLR and developing linearization techniques such as digital predistortion. For RF receivers, we showcase how you can develop equalization strategies, anticipate the impact of in-band and out-of-band interfering signals and develop interference mitigation strategies based on filtering or null steering. Finally, we will develop new architectures and algorithms using data sheet specifications, component measurements, electromagnetic analyses and ray tracing methods.
Highlights
- Design and simulation of mmWave transceivers for 5G
- Integration of antenna arrays and RF front ends
- Linearization of mmWave transmitters
- Anticipating the impact of interfering signals on RF receivers
- Integration of RF modeling, EM analysis, and ray tracing algorithms for scenario modeling
About the Presenter
Giorgia Zucchelli is the product manager for RF and mixed-signal at MathWorks. Before moving to this role in 2013, she was an application engineer focusing on signal processing and communications systems and specializing in analog simulation. Before joining MathWorks in 2009, Giorgia worked at NXP Semiconductors on mixed-signal verification methodologies and at Philips Research developing system-level models for innovative communications systems. Giorgia has a master’s degree in electrical engineering and a doctorate in electronics for telecommunications from the University of Bologna.
Recorded: 23 Jul 2024
Hello. Today we are going to talk about the design of 5G millimeter wave beamforming systems. My name is Giorgia Zucchelli, and I'm product manager at MathWorks for the RF mixed signal area.
The topic of today is really close to my heart, because this is where I started my career many years ago. And the topic of designing millimeter wave systems is getting a revival, driven by the need of applications such as 5G and 6G to support higher and higher data rates.
And one way to support such high data rates is to use larger bandwidth, or to utilize bandwidth more efficiently, often together. And one way to accommodate large bandwidth is to move to higher frequencies, above 10 gigahertz or in the millimeter wave range.
We see this with the opening of new bands, such as FR2, and more recently, FR3, around 10 gigahertz, but also with the interest of researching sub terahertz bandwidth. And we also see it with the usage of carrier aggregation to enhance the spectrum utilization.
But at these high frequencies, the losses of the channel are not negligible, which means that we need to use a MIMO architecture or beamforming systems, both on the transmitter and the receiver side, often using a large number of antennas moving towards a massive MIMO.
Last, but not least, we also see the trend of using multiple wireless technologies, to both support higher data rates and also to increase the quality of service. And we see this, for example, with the usage of both cellular and satellite networks for non-terrestrial applications.
So these are the trends that we see today that drive the move towards millimeter wave frequencies. Unfortunately, however, designing millimeter wave systems is not easy, and is not easy because there are many impairments that need to be estimated and mitigated.
For example, antennas need to be packed tightly together, and this might lead to coupling. So a different element might leak, leading to an overall reduction of diversity. As a designer, you can decide, for example, to increase the spacing, or to use defective ground structures, or to put parasitic structure to reduce the effects of coupling, but all these mitigation strategies come with a cost.
Maybe grating lobes may be a larger area. Costs need to be taken into account. Similarly, at millimeter wave, power is key. It's hard to generate and transmit power, which means that the losses are our enemy.
And losses might be coming from impedance mismatches-- dispersions in between the different elements. Especially when we operate on very large bandwidth, the characteristics of the components are not flat over frequency, which means that this needs to be mitigated using, for example, equalization algorithms or calibration algorithms.
Staying on the topic of power, on the transmit side, to have maximum efficiency, we need to have a power amplifier that often operate close to saturation, which means that non-linearity become a limiting factor, causing distortion and spectral regrowth. So typical mitigation strategy include the linearization technique, such as digital pre-distortion envelope tracking, or sometimes, just backing off the operating point for the power amplifier.
Moving to the receiver side, as we operate on large simulation bandwidth, interfering signals might become critical, and if interfering signals have high power, that might cause desensitization on the receiver side. So typical mitigation strategies might include filtering-- filtering either through filters or beamforming-- gain control, or even moving towards digital receiver architectures to perform the interference mitigation on the digital domain.
Last, but not least, when we stitch together transmitter and receivers, we need to take into account what happens in between. That is to say, the channel. This might have a multipath. It might be affected by fading. Again, losses, polarization, diversity.
And to mitigate the impact of the channel and the losses, we might have to use beamforming strategies-- beamforming algorithms-- or using equalization and a stronger diversity on the antenna side.
Today. We are going to explore these five classes of impairments one by one, and we are going to discuss how modeling and simulation helps you understand the causes of the impairments, and also different ways to mitigate the impairments to make sure that your transmitter and your receiver works preferably well before you build the costly lab prototypes. So let's get started with our first impairment and see how we can estimate the impact of antenna coupling on beamforming algorithms.
Let's start with the basics. What is antenna coupling? An intuitive way to understand it is by separating its effect in the near and in the far field. Let's assume that we have a transmitter made of eight parallel chains, feeding into an antenna array made out of eight antennas. In this case, they're circular patches.
Because the antennas are closely spaced together, they will couple. Near-field effects can be modeled through port analysis, and in particular, through scattering parameters of S parameters, as parameters represent both the impedance of the elements as well as the coupling in between the different elements, and elements that are close to each other will be more tightly coupled than the elements that are further apart. One way of thinking about it is that when I feed element one through the ground, part of that excitation may lead to antenna two, and three, and four, and so forth, in a progressively smaller value.
But coupling also affects the far field radiation pattern. Think that if we excite only one antenna of the array, and we do not excite all the remaining elements, the pattern of that antenna element, when embedded within an array, will be different from the pattern of the antenna when positioned in free space.
In other words, the other antenna elements act as addition structure-- parasitic structure-- that change the pattern. So you see here, the embedded element of the first and the eighth antenna are different. And you might wonder, why are they different? Because they should be symmetric.
Well, in this case, the feed point for each of the antennas is not placed in the center of the circular patch. Hence, there is an asymmetry on the array.
Let's understand what is the impact of coupling on this specific example-- an array of eight circular patches. First, we compute the pattern of the array without coupling. How do we do that? We use the Antenna Toolbox in this case to compute the far field radiation pattern of a single patch located in free space, and then we use pattern superposition of the array factor to compute the pattern of the entire array.
We see a big lobe pointing up and 90 degrees elevation, with a directivity of 16.8 dBi. We also see several side lobes with very defined, well-defined lobes and nulls. Then we compute the same pattern using a full wave electromagnetic analysis of the entire array. And again, we use the Antenna Toolbox.
We see, again, a big lobe pointing up at 90 degrees of elevation with a directivity of 16.3 dBi, but we also see that the side lobes are a little bit larger-- a little bit less defined-- with nulls that don't go as deep. You might argue that the difference of half a dB in directivity is not worth the additional cost of performing a full wave electromagnetic analysis on a much larger structure than a single patch.
But to really understand the impact of coupling, let's look at a different example. Let's assume that we have a desired signal coming in towards our array at 15 degrees from boresight, and that we have an interfering signal coming in at 45 degrees from boresight.
So in this example, we want to steer the beam towards our desired signal and we want to steer a null towards our interfering signal. We compute the weights with the phased array System Toolbox, and then we apply the weights to our array. First, we compute the pattern of the array without coupling.
Our main beam has a directivity of 16.3 dBi, and our null has a deep attenuation of 51.6 dB, which means that overall, we reduce the impact of the interfering signal by almost 68 dB. Now, we perform the same analysis, taking into account coupling-- so, with full wave electromagnetic analysis.
In this case, the directivity is 16.2 dBi-- only 1.1 dB of difference-- but the null is 16.8 dB, which means that we attenuate our interfering signal only by 33 dB. This is a big difference and can make the difference between a receiver that works versus a receiver that does not work.
Let's now see this example in practice. I'm now opening MATLAB and launching the Array Designer app. I'm going to design our array of eight elements-- our linear array of eight elements-- and I'm going to use a circular patch as an antenna element. And I'm going to design it to operate at 27ghz, for example. This is just an example.
We design our array, which means that the elements are spaced approximately at alpha lambda at a given frequency, and we are now going to analyze our array with and without coupling. You can see here the spacing in between the elements, and you can see how close together these patches are. You could also see what I was describing before, how the feedpoint is not exactly in the center of our circle.
We can now compute the 3D far field radiation pattern from our array, taking into account coupling. We can verify the directivity, as well as taking a cut at 0 degrees of elevation. And we can also visualize the antenna matrix and confirm, again, the main lobe, as well as the zero-- the null-- locations.
We can then perform the same analysis, neglecting coupling, and we can reproduce, essentially, what we were seeing before. We can see how the pattern is now different, and in particular, how the nulls are much, much deeper.
Don't be fooled here, because the scale for the two plots are slightly different without coupling and with coupling. But even just by looking at the images, you can see that there is a difference in the two scenarios, as we would expect. No big surprise here.
We're going to write a script here so that we can perform more exploration of this antenna array. So you can see here in MATLAB how we can design our microstrip circular antenna, put it in an array, and reproduce the results that we just computed with the Antenna Designer app. This is just a way to automate the analysis of your system when you want to perform multiple analysis, or, for example, more easily share these results, or document these results.
Good, so we analyze our structure with the full wave results, taking into account coupling on the right-hand side, and without coupling on the left-hand side. And we also forced the scale to be the same, so we can see how, without coupling, results are much, much-- the nulls are much, much deeper.
Let's now compute the weight to do the exercise that we were mentioning before-- so, to steer the beam towards a certain direction, and a null in a different direction from which the interference signal might be coming from.
To do that, I'm going to actually open up the MATLAB documentation, and find an example for null steering. This is a very convenient way for me. Every time that I'm looking for a new example, I just search the documentation and some of the shipping example make life a lot easier.
And we see here a section of code that uses the function, steervec, to steer the beam in our direction, but also to steer the null. And this allows me to point out how great MATLAB is for developing beamforming algorithms, because all these functions that are provided by the Phased Array System Toolbox are actually wide box. You can see what is the algorithm that they use, and if you like, you can modify it and enhance it with your secret recipe.
So I'm going to copy the code, paste it in my script, and essentially, you can see how now we apply these weights to our array. We are going to look in the direction of 15 degrees for our main beam, and to 45 degrees for our null, to reduce or filter out the interfering signal.
We can verify with an ideal array, essentially, that we are indeed computing the right weights, so that our calculation is correct, which is in the direction of where we were wanted to go. And now we can just apply the weights directly to our array in amplitude and phase, without considering coupling, but simply using pattern array multiplication-- the array factor, or pattern multiply function-- and by performing full wave electromagnetic analysis.
And just like before, we force the scale of the graphs to be the same so that indeed, we can verify that our beam is steered in the right direction, but also that our null is indeed happening at 45 degrees from both side. So here we are just adding-- let me just add a cursor here. It's exactly 135 degrees, so 90 degrees plus 45 from the boresight.
And you can see how without coupling, the null is much deeper compared than with the coupling. So like I was saying before, this can really make a difference between a receiver that really seems to be working in presence of an interferer, versus a receiver that once it gets deployed in the field, will not work, because it doesn't attenuate the interfering enough-- sufficiently hard.
Let's now look at the second class of impairments that affect millimeter wave system-- frequency dispersion-- and see how we can mitigate dispersion with gain calibration and equalization algorithms. But before we start, let's understand what are the possible sources of dispersion and impedance mismatches. And we use our example, the eight channel transmitter.
For example, we have a feed network that splits the input signal over the eight channels. In this case, we have used a Wilkinson splitter, a corporate divider implemented on a PCB. This is a distributed structure, and when we analyze its S parameters through electromagnetic analysis, we see that this behavior is not flat over frequency-- is not perfectly matched at low frequencies, and there are possible leakages also in between the branches, by the way.
A similar analysis could also be performed on the filters and other passive structure that are in general not perfectly flat, and not perfectly matched at all frequency of operations. Similarly, active devices, such as amplifier, can be affected by dispersion. Here, we see the S parameters of an amplifier. We see the gain as well as the S1 1 and the SO 2 on the Smith chart.
And this indicates that the gain is not perfectly flat, as well as the impedance is not perfectly matched. Power amplifier are another source of dispersion, or a possible source of dispersion, because they can be affected by memory effects. What does it mean? That the output signal of the amplifier depends not only on the instantaneous value of the input signal, but also on its previous values, and this has particular impacts when we use a modulated waveform.
And last, but not least, we have seen that the antennas are affected by dispersion, both in terms of impedance as well as pattern. When we put all these effects together, what we find out is that when we stream a signal that is modulated over a large simulation bandwidth-- maybe 100 MHz, 400 MHz, 1 GHz, you name it-- the behavior of the transmitter is not flat, and the impedance mismatch is-- and the impedance matching is not perfect at all frequencies.
As an example, we feed our transmitter with a 4 GHz bandwidth white noise signal, indicated here in the Spectrum Analyzer with a yellow waveform. When we inspect the output that is the blue waveform on the Spectrum Analyzer, we see that the output is not flat over frequency. It has notches. It has ripples. This is a factor of dispersion and impedance mismatches.
Even if the transmitter is perfectly linear, the output will be distorted. Additionally, dispersion does not only change the amplitude of the output signal, but also the phase, and this can have a very important impact when using modulated waveforms, or waveforms that have complex modulations.
For example, here, we are seeing an OFDM signal with 100 MHz bandwidth and 124 carriers with 120 KHz spacing. On the left-hand side, you see the result of the received constellation without an equalizer. The constellation is distorted due to the dispersive effect introduced by our eight element transmitter.
If, in our baseband receiver, we include an automatic gain control and a static phase equalizer, we can, on the contrary, recover the constellation quite clearly. This is actually one of the reasons why reference receivers that are standard compliant are often appreciated, because they include the channel equalization algorithms. Channel equalization algorithms equalize the impact of the channel, but they also equalize the impact of dispersion introduced by transmitter and receivers up from tens.
Let's now look at a practical example that can help us understand the impact of dispersion. In this case, we start from the budget analysis of the single chain that is part of our transmitter. The first element represents the Wilkinson splitter, with a loss of 10 dB representing the splitting between the input and the eight ports.
This is followed by a filter centered around 4 GHz, because the input central frequency is 4 GHz intermediate frequency, with a relatively small attenuation at the central frequency. Followed by an amplifier, specified by its S parameters and its output referred IP3, followed by a modulator with a local oscillator frequency of 23 GHz that performs up conversion to 27 GHz at the output, followed by a power amplifier with this nonlinear characteristic and our circular patch antenna to transmit.
On the bottom we see the budget, and we can also plot the S parameters of the chain. So we can look at S1 1, S2 2. But if you look at the gain in terms of magnitude and phase, we can really see the effect of dispersion throughout the chain.
From here, we can generate a model for simulation-- so moving from analysis to actually streaming a modulated signal. But before that, I want to take a little bit of more of a look into the splitter.
So the splitter has been designed with a rough PCB Toolbox. It's implemented on a PCB substrate-- on a Teflon substrate-- and you can see that this is a corporate divider that splits an input signal on eight parallel paths. Using the method of moments, we have computed these S parameters, represented by the variable sw, and we can see here the S parameters of the splitter, indicating the input matching condition as well as the coupling in between the different ports, and of course, the losses from the input port to the output ports.
We generated a model from the budget. We copied the chains eight times, and we connected it together with the Wilkinson splitter as well as our antenna array. We can now perform simulation using a modulated signal. The Wilkinson splitter is represented by its S parameters.
We can verify the S1 1. The component is decently matched at the input. We can also verify if the S2 1 that represents the insertion loss between the input and the first chain, just to make an example. And the loss is around a slightly larger-- minus 10 dB-- which is reasonable, because we are expecting a 10 log 10 of 8 loss, which is a minimum of 9 dB in ideal condition.
This is the filter. We can inspect the filter, center it around 4 GHz, both in the amplitude and phase. We can inspect the parameters of our amplifier. We can visualize, for example, on the Smith chart, both the S1 1 and the S2 2, and see how the matching condition changes throughout the frequencies over which the amplifier is defined.
This also allows me to point out how great MATLAB and RF Toolbox are for managing S parameters. Importing, visualizing, cascading, the embedding, transforming, you name it-- RF Toolbox provides you with the function to do it. But back to our design.
We also have a phase shifter that introduce a dispersion, in this case, which is interesting. When we run the simulation, in this case, we combine all the effects of dispersion and dispedance mismatches across all the elements and all the chains. Additionally, we also take into account coupling introduced by the splitter and the antenna array.
Here, we use a 4 GHz white noise signal at the input, indicated in yellow, and in blue, we probe the output of our transmitter-- the output of the antenna-- and we clearly see the effects of dispersion on the amplitude with the different notches and the different gain.
This is very useful, because it means that not only we have statically analyzed our chain, but we can actually simulate it, which means that now we can stream modulated signals through the chain and take into account the effects of dispersion.
Let's talk about the third class of impairments for today that primarily affects transmitters-- that is to say, the non-linearity of power amplifiers-- and see how we can use digital pre-distortion to mitigate this phenomenon. In power amplifiers, the output power of the signal increases linearly as a function of the power of the input signal and proportionally to the gain, until the amplifier enters in compression.
At that point, the output power saturates, and this means that we have a spectral regrowth and distortion, which are in general undesirable, because they decrease the quality of the transmitted signal. At the same time, operating in compression is desirable, because it maximizes efficiency. So we have two contrasting requirements.
So one way to keep the characteristics of the amplifier as linear as possible, and the quality of the signal high, is to implement digital pre-distortion. Digital pre-distortion implements the opposite characteristics of the amplifier so that when we cascade it due to the overall behavior, is linear.
This is the theory and is relatively easy to understand. The practice is a little bit more complicated. This is because the power amplifier is affected by memory, which means that the output of the power amplifier at a specific point in time not only depends on the input at that specific instant, but also on the previous values of the input signal.
And this has large consequences when you deal with modulated signals. Second power amplifiers operate in the RF domain. Digital pre-distortion operates in the baseband domain, which means that we need to take into account upconversion, downconversion, and timing effects that might cause instability when closing the feedback loop.
Lastly, there is an effect of antenna loading that can be extremely complicated when you have transmitters with multiple antennas, like we have seen. To study and to develop digital pre-distortion algorithm, the first thing that is needed is a model of the power amplifier.
In RF Blockset, you find a generalized memory polynomial for the power amplifier, and a fitting procedure that can be applied to your measured data. The generalized memory polynomial allows to model the memory with by looking back a certain number of samples. I/Q samples in the time domain are what are used to identify the model, as well as models the non-linearity by using a certain number of orders in the polynomial series.
Like I was saying before, using I/Q time domain wideband measurement data, you can extract a matrix of complex values that represents the model of the power amplifier. And the model actually reproduces fairly well the behavior of the power amplifier, given that the waveform has a realistic dynamic range peak to average power ratio and bandwidth. By the way, in RF Blockset, you also find an extension of the generalized memory polynomial model that also includes lead and lag terms, for which is provided a causal implementation.
Now, let's say that we have a model of a power amplifier that we have identified using this procedure. There are many ways in which you can linearize a transmitter with multiple chains. So you need to perform-- you might have to perform an architectural exploration among the different options.
For example, you could use an Over The Air approach, in which the observer path is based on the information provided by an antenna placed in the near field compared to the transmitter array. An equivalent implementation positioned the observer antenna in the far field, always feeding a single digital I/Q chain.
Another on chip or on board architecture could consist in probing the output of the power amplifier of one or a limited subset of the power amplifiers of the MIMO transmitter, under the assumption that all the power amplifiers are essentially very similar or behaving in a similar way. Another option-- more complex-- is to combine all the outputs of the power amplifiers of the MIMO translimiter with the channel emulation block that provides the information to the observer path for the digital pre-distortion algorithm.
Or alternatively, we could think of a structure that is timeshared with a switch that toggles in between the different outputs of the power amplifiers. These are architectural choices that you can explore with the use of a model of the power amplifiers plus a simulations environment where you can model all the additional control logic, digital signal processing algorithm, as well as low power electronics.
But to test a digital pre-distortion algorithm and to verify if it works, you need to use modulated waveforms. We left before with a white noise signal to test the dispersion. Now, we're going to close this gap and use a fully standard, compliant 3 GPP waveform to test our RF transmitter.
We can use any arbitrary waveform for FR2, FR1, test model 1.1, or 3.1-- different options are possible depending on the type of system that you are keen to test. And by the way, if you don't use a 5G but you use wireless LAN, or satellite communication waveforms, such as dvb-s2, other options are also possible in MATLAB.
This gives me the opportunity to mention how great Matlab is for waveform generation-- custom or standard. And if you wonder where you can start, the Wireless Waveform generation app is a great place. Here, you find the standard signals, custom signals, 5G, LTE, wireless LAN-- even radar signals. And you can customize the waveform generation, and verify its spectrum and its resource grid as you go along.
But back to our example. Here, we generate a waveform. We stream it through our RF receiver, and then at the output, we measure the standard compliant SCLR, as well as EVM. We perform the simulation twice, with and without digital pre-distortion, and we verify that the DPD algorithm can indeed improve both the EVM as well as the ACPR.
So what we have here is MATLAB script. First of all, we set up some global variables, like the input frequency, the output frequency, the local oscillator frequency, and we loaded the designs of the antenna that we performed before. Then we generate a 3 GPPP waveform.
We can generate-- use any standard channel. In this case, we use a test model 3.1 with 100 MHz of bandwidth and a frequency division multiplexing. We generate a waveform-- it's fairly straightforward-- and then we scale it. We scale the input power so that we know that the input signal within it will be within the dynamic range of our transmitter.
We also visualize here the input power as well the peak to average power ratio, and then we stream our input freeform through an object that is called BFIC_TX. This BFIC_TX is an RF system. Is nothing else but a wrapper of a Simulink model-- the Simulink model that is, in this case, called BFIC_TX_Model.
And you see here the properties of the input frequency and the output frequency of this model for the circuit envelope simulation. If we open up the model, behind the scene, when we run this command, essentially, there is a Simulink model that now represents our transmitter, plus the digital pre-distortion algorithm.
So you see the input signal from the input port, to the splitter, through the chain, to the antenna array, the theta and phi polarization component. The output, we probe the theta component. We have a Spectrum Analyzer. We sense the output with a far field antenna-- in this case, it's just a simple dipole with feedback with the digital pre-distortion algorithm, and a switch that we can toggle on and off to enable or disable the linearization of our transmitter.
Talking about the digital pre-distortion gives me the opportunity to mention how you can generate a C and especially synthesizable HDL code for the digital pre-distortion algorithm, including, actually, also, the coefficient estimations. This is a great deal, because this allows you to rapidly prototype your algorithm and test them actually Over The Air. But now back to our model.
So when we run the simulation, you can see here from our MATLAB Test Bench, we just run past the input waveform to our model and we get the output waveform at the output. As we run the simulation, for example, we can inspect the Spectrum Analyzer to see the spectrum of the signal as it gets streamed through our transmitter.
And just as a reminder, we perform circuit envelope simulation-- so multi-carrier simulation-- where essentially, we take into account not only of the dispersion and memory effects of impedance mismatches, but also, the nonlinear effects. We fast forward now. Let's load the simulation results.
So you can see in yellow, the input waveform. In blue, the output waveform. We can now measure the ACPR for a 100 MHz bandwidth signal. Let's look at the two adjacent channels spaced at just 5 MHz away from our reference channel.
And you can see here that due to the non-linearity of our transmitter, the ACPR is -38, -37 DBC. You also see how the spectrum is asymmetrical due to the memory effects introduced by our power amplifier.
We can measure the EVM, again, using the standard compliance 3 GPP functions. We see here the constellation, taking into account the non-linearity, and some of the dispersion introduced by our transmitter.
We can now toggle our switch. So enable digital pre-distortion, rerun the simulation. Here we're going to fast forward and just load the results that we previously computed. We can see compare the spectrum of our output without digital pre-distortion with the -37 DBC of ACPR, and with digital pre-distortion. We can see how we improve the ACPR to -45 DBC, which is a significant amount.
We can also measure the EVM using the same function that we used before, and see how the constellation is now much, much clearer, and how the digital pre-distortion effectively compensated for the non-linearity, but also, for some of the dispersion introduced by our transmitter.
As we are talking about amplifiers and non-linearity in general, I'd be remiss if I wouldn't put transmitter emission in a slightly wider context. So let's make a fun experiment. Still working on our eight channel transmitter, let's focus on the I/Q modulator.
So we have a starting input frequency of 4 GHz, a local oscillator of 23 GHz, and the modulator performs a conversion at 27 GHz. By the way, the local oscillator might be affected by phase noise with different distributions.
Let's also assume that we steer the beam at 15 degrees from boresight. With our simulation model, we can verify what is the effective isotropic radiated power at a given direction, 15 degrees, as well as at a given frequency of 27 GHz.
It's a fun experiment. Let's now assume that our modulator is affected by a low leakage. That is to say, part of the power of the local oscillator leaks to the RF port. This means that we are actually transmitting a signal at 23 GHz of output frequency.
And we can actually verify what is the EIRP and the radiated power at the output emission frequency. So in this case, due, for example, to the dispersion and non-ideality of the chain, what might happen is that the beam points in a complete different direction, or unexpected direction.
So with these simulation models, you can really take into account the spur and spectral emissions, also outside the frequency of interest, thanks to the multi-carrier circuit envelope simulation. So let's see this example in practice.
I'm going back to the Simulink model as we left it, our BFIC_TX, and I'm going to browse down and show plot the pattern, in this case, at the output frequency of 27 GHz. Here, we are probing the instantaneous voltages of the terminals of the antenna, and use these instantaneous voltages, essentially, to feed the electromagnetic solver and look at the pattern as it is.
The good news is that we are steering the beam in the desired direction with the desired EIRP. Let's stop the simulation and change the observation frequency. So rather than looking at 23, 27 GHz, I'm now going to plot the pattern at 23 GHz. So I'm probing the instantaneous voltages at 23 GHz.
This is the characteristics of our modulator with a finite, low isolation, as well as the phase noise. We can also plot the phase noise characteristics, just to show that there is something more than just the CW tone coming out at 23 GHz, just to make an example. And when we plot, we can actually verify where the beam is pointing and what the EIRP is as well.
This is interesting because you will see all dispersive effects, as well the combination of dispersion and non-linearity interacting on your transmitter. And the different antennas will have different behaviors-- or, different frequencies-- and the accumulation, as well, of the non-linearity will impact your transmitter differently. And here, also, you verify the actual effective isotropic radiated power.
From undesired emissions on the transmitter, let's move to the reciprocal problem and estimate the impact of interfering signals on wideband receivers. This is the fourth class of impairments that we will see today that affects millimeter wave systems.
Interfering signals are particularly dangerous for wideband receivers because they might cause saturation and desensitization. In particular, they might raise the noise floor and reduce the signal to noise ratio to the point that your receiver will not be able to recover the desired information.
Interfering signals sometimes can be removed, either by filtering in the frequency domain, if they are out-of-band, or maybe by null steering. This is one degree of freedom that is added by using arrays of antennas-- phased array systems-- where essentially, we can steer a null towards the direction of arrival of an interfering signal, and essentially, reduce its impact.
So let's consider an example where we have a 400 MHz, 3 GPP FR2 test model 3.1 signal coming in at 27 GHz, and a 60 degrees, with an input power of -70 dBm, as an input to our receiver. And we also consider an additional interfering signal that is a modulated waveform with 100 MHz of bandwidth-- so a different characteristic-- coming in at 19 GHz and at 40 degrees for the array, with the same input power-- -70 dBm.
Here, we chose both the frequency and the angle to represent a worst case scenario. Because we steer the beam at 60 degrees, in this case, due to the dispersion or to the dispersive effect in the receiver, when we look at the beam at 19 GHz, it actually gets steered toward 40 degrees. So we have maximum directivity in this direction, which is very undesired. It's sort of a worst case analysis.
Similarly, 19 GHz is the image frequency for our demodulator. So when 19 GHz mixes with the local oscillator of 23 GHz, it also downconverts to 4 GHz that is our intermediate frequency. In other words, the interference signal gets downconverted straight on top of our desired signal.
Of course, the demodulator has an image rejection filter, but because the receiver is wideband, the rejection of the filter is finite, which means that part of the interfering signal will still map onto the desired bandwidth. The result is, unfortunately, that the resulting EVM is degraded from 3.6% to 4.2% in presence of the interferer, and when we look at the EDM per subcarrier, we can really see the folding of the 100 MHz OFDM signal straight in the middle of our receiver bandwidth.
So we go back to another MATLAB Test Bench, where essentially we again have global variables where we load our design of the antenna as well as the splitter. We also generate our 3 GPPP waveform just like we did before, and scale the input power-- this is our desired signal-- and feed it through another system-- an RF system-- that in this case, is called RF RX.
So here is our RF system where we see on the top branch, the 3 GPPP waveform coming in to our antenna array, and on the bottom side, the OFDM signal coming in. The antenna array has two input frequency and two direction of arrival-- the one for the desired signal and one for the interfering signal.
If we look at our demodulator, we can see that we insert an image rejection filter. Is a simple Butterworth filter of third order with very large bandwidth, so its rejection on 19 GHz will be limited. This is just an example. On the left-hand side, we see the spectrum of the interfering signal, and on the right-hand side, we see the spectrum of the received signal-- the combination of the desired plus interfering signal.
And because the interfering signal is essentially slower in power than the desired signal, we can't really see much from the spectrum. We completed a simulation. Fast forward, we look again at the-- we measured the output power. We can look at the spectrum.
But it's more interesting to look at the EVM measured using the standard compliant functions that allows us to visualize how the EVM for those subcarriers, that are right in the middle, is actually degraded. And this is really the effect of the interfering signal that folds in the middle of our received bandwidth.
Let's now cover the fifth and last class of impairments for today and talk about RF propagation. In particular, we will discuss how to use ray tracing to model a channel and stitch together a transmitter and a receiver.
Ray tracing is a very interesting technique, because it allows us to model multiple paths in between the different antennas on the transmitter on the receiver side. This can be particularly important at millimeter wave, where line of sight is essential for communication, and when you have, for example, complex scenarios, such as in urban configuration, where you have multiple buildings with lots of surfaces and lots of bouncing rays.
So ray tracing allows us to model multiple radiated and incident direction, different path loss, as well as phase rotation that occurs at all these levels. When we combine ray tracing together with an accurate electromagnetic model of the antenna arrays, then we can also take into account antenna coupling and frequency dependency.
So when we use a channel together with our transceiver, we can really perform an end-to-end simulation, spanning multiple domains, from the signal flow to circuit envelope multicarrier simulation for the RF front end, to EM analysis for the antenna arrays, to ray tracing for the channel itself.
So let's see an example in practice. So in this case, I'm going to start from the MATLAB documentation. So I'm going to search here for channel. And the first hit is going to lead me to the channel block in the circuit envelope library. Fairly straightforward.
I open up the documentation of the channel block, and I see, immediately, a script that, essentially, I use to model a scenario. Central frequency in 27 GHz. Base station position and UE position are given in latitude and longitude, and you can see them here, that they are inserted in a scenario with buildings. They're actually located in Hong Kong.
For the transmitter and receiver, we just use a simple dipole, in this case, and a propagation model that uses ray tracing with two bounces. This is the model. It's fairly straightforward. You see that it uses a certain location for the transmitter and for the receiver-- what we just defined in terms of latitude and longitude-- and now, we can also visualize them with all the rays in between them.
And we can see, actually, estimate the distance as well as the path loss, as well as the direction of arrival and departure, both from the transmitter and the receiver, which is very interesting. So in this case, we are good, because there is direct line of sight.
We can now perform the simulation and look at the budget. But let's look at the slightly more interesting scenario, where instead of using a single antenna, we actually use our antenna array-- eight circular patches. So I'm going to use this array, both on the transmitter on the receiver side.
Additionally, I'm going to move the UE-- so I'm going to move the receiver side-- in such a way that we will not have any more direct line of sight. We keep a proclamation model with two reflections, and we now open our RF model that has eight branches-- so we have, again, the transmit and the receive with the channel that connects them.
We see that we receive a -69 dBm of power, and we can actually verify the link on the scenario situation. So in this case, like anticipated, we don't have line of sight, and it's interesting, because if we select one of the rays, we can see what is the angle of departure and the angle of arrival. Again, for the transmit and the receive.
Well, let's stop the simulation for a second, and let's now beamform at the transmit and the receive side, in such a way that we steer the beam towards the desired direction, and we can actually increase the received power. This is a simple example that allows you to connect a ray-tracing channel to a complex transmitter and a complex receiver, and eventually, also perform end-to-end simulation.
Before I wrap up with the conclusion, I would also like to point out that ray tracing is not the only way to model a channel, and that in MATLAB, you find many other channels-- statistical and standard compliant-- if you would like to use a different representation for the propagation effects.
Summarizing, today we have seen a lot. We started with antenna arrays and saw the impact of coupling on beamforming algorithms. We have seen the impact of dispersion and frequency dependency over and over again, over wideband modulated signals.
We talked about amplifiers non-linearity, and saw how digital pre-distortion can help in mitigating it. Then we jumped into receivers and saw the impact of interfering signals, and how they can degrade the quality of the received signal. And last, we saw the how to model RF propagation effect using ray tracing.
The bottom line is that designing 5G millimeter wave systems is complex. The physics are just complex. But using modeling and simulation can make it significantly easier, because with models, you can anticipate and understand what really matters.
Is it antenna coupling? Is it dispersion? Is it non-linearity? What is the impact on my end-to-end link?
With models and simulation, you can scale up the system beyond simple calculation and beyond CW measurement. We've used modulated waveforms over large bandwidth that give a much higher degree of accuracy in your system model. And you can validate results at every step. You can isolate impairments one by one, and with this, you can really gain true insights into your system architecture and your algorithms, before and during building complex lab prototypes.
I thank you very much for your attention. I hope that this was useful for you. Please follow up with MathWorks, and look at all the resources that we have online. Thank you.