Lecture 56

Okay, welcome back. So, where are we? We need to learn about this Rank Calculation Algorithm, okay. That's where we stopped in the last class. We will discuss that. That's only one part of the class and then I will teach you how these MIMO architectures are different for FR1 and FR2 bands, okay and another thing which we need to understand as a system designer, okay. So, what is like, what are the key differences between these? The way MIMO is designed, the idea of MIMO for these two different bands. Actually, if you look at FR2 band, MIMO serves entirely different purpose when compared with FR1 band, okay. So, it is important to understand that perspective also, okay. Before that, let's discuss this Rank Calculation Algorithm, okay. So, what happens, okay? So, our Rank Calculation Algorithm, what are we considering? We are considering our old system, 2 cross 2 system, okay, right. So, what will happen here is that in the, whatever the last discussion we had, okay, we implicitly assumed that the rank of the channel is 2, okay. If you remember what happened there, user assumed that rank is 2, it calculated the, it assumed the 2 cross 2, the precoder, right, or the code book, okay and then calculated the sum rate accordingly and then fed back that sum rate and the precoder matrix indication back to the base station, okay. But what we said was this channel could have rank 1 also, right, okay, fine. So, if that is the case, the user needs to find out the rank, okay. So, how is it doing? It will basically, even though the system is 2 cross 2, it will start with rank 1 code book, okay, right. It will assume that the channel rank is 1. It will begin with by assuming that channel rank is 1, not 2, okay. Then it will assume channel rank is 2 also later, okay. But how will it begin? Because it has to find out what is the rank. So, it first assumes that the rank is 1, okay. Then if the rank is 1, then what are we saying? User will start with begin with rank 1 code book and how many code book entries are there? 4 code book entries in that rank, in that code book, right. So, what is happening here? It starts with rank 1 code book VI for which the system model, what will be the system model? You look at it now. Channel is H only. Channel is 2 cross 2, right, okay. Channel has not changed. Channel is only 2 cross 2, okay. It will assume what is being sent. If it is a rank 1 system, how many symbols will be sent? Only 1 symbol will be sent, right, not 2. That is also, it is common sense. If the rank is 1, then only 1 symbol will be sent. So, how will the system model change in this case? It is not the scalar channel. It is the, it is not the vector channel. It is the matrix channel, right, because the system is 2 cross 2, correct. So, then what happens, okay? After this, it assumes the system is like this, okay, whatever we discussed earlier and it will be, pre-coded signal will in this case be one of those pre-coders into X, correct, okay. And if you multiply H into VI, what are you going to get? H is a 2 cross 2 channel. What is pre-coder 2 cross 1? You will get HI tilde into X, right, okay. Fine. So, what, we understand after this what happens. What will user do? It will calculate which pre-coder entry maximizes the SNR or the rate, right, okay. So, what happens? Now, this is HI tilde of X, okay, right. System has 2 receive antennas, not 1 receive antenna, correct, okay, right. The number of layer which is being transmitted is only 1, right. This is slightly different from when the user has only 1 antenna. Now, user has 2 antennas. So, it designs a receiver for that also because the 2 signal from 2 receive antennas need to be combined, correct, okay. So, let us say some receiver W. You understand why this W is coming now because user has 2 antennas, okay. So, it can design some receiver for that even though the number of layer is only 1. It combines these 2 signals, okay, and this is the combined, okay, right. So, this is what is happening, okay. What will happen? So, if you basically, if W is basically user knows this, okay, right, and if we have discussed this case earlier wherein what kind of system does it look to you? If this is happening, okay, you are transmitting 1 symbol but the receiver has 2 receive antennas. Does it look like 1 transmit and 2 receive antenna case? It looks like that, right, okay. If you look at this system, y is equal to hi tilde x plus n, right, okay, correct, 1 symbol but that is being received at 2 receive antennas, correct. That is how after pre-coding that is how the system has reduced to. Even though it is a 2 cross 2 system, okay, with pre-coding it has reduced to 2 cross 1 system and we know we calculated the SNR for this system. You remember we started by discussing this case when we started discussing MIMO, 1 transmit and 2 receive antenna case. If receiver does MRC, this was the SNR, right. We calculated that hi tilde because what is there? Okay, then this is a system, okay. If W is designed such that if W is hi Hermitian, what will be the hi tilde Hermitian, right? What will be the SNR? We have calculated this here. I have showed it to you. I am not calculating it again, okay, right. So what user does now is for this 2 cross 2 system assuming that the pre-coder is VI, it calculates this SNR for each of the pre-coder VI, right and the pre-coder is rank 1 pre-coder, okay, right and what will happen? It will calculate the sum rate. It will calculate the rate, okay. What will it do? It will choose VI which maximizes the SNR and compute the maximum rate log 1 plus SNR of I. It keeps it, okay. At this stage, what has it figured out? It has figured out which rank 1 pre-coder is maximizing its rate, right, fine. This is step stage number 1 of this rank calculation algorithm, right. Is this clear what we have said here, okay? So what have we done here? If UE has calculated the pre-coder which will maximize the rate assuming that the rank is 1, done, okay, half of the process is done. What happens after that, okay? It denotes this pre-coder as VI tilde and calls this rate as rate for rank 1 maximum rate, rank 1 maximum rate, that is all, okay. It notes this pre-coder also, fine, okay. So for rank 1, this is the maximum rate and this is the pre-coder. Now what happens for rank 2 after that? Then it continues with rank 2 code books for which the system model we just discussed in the last class, right. It does exactly the same process whatever we discussed in the last class. What does it do? y is equal to hx tilde plus n. What happens here, right, VI of x, correct, okay. I can, in this case I will run from only 1 to 2, right, okay. I call this as hi tilde of x, okay, correct and then receiver, UE designs a receiver W, correct and then it assumes that 2 streams are being transmitted because the rank is 2, 2 layers are being transmitted, okay. So it designs zero forcing or MMSE receiver. Whatever we discussed in the last class, okay, does that same thing. I am not writing anything new here. These 2 bullets are exactly the same, right. Design the receiver, compute the SINR of 2 streams, exactly the same formula. I have copied that here, okay, right. SINR of pre-coder 1, layer 1, SINR of pre-coder 1, layer 2. Similarly, SINR of pre-coder 2, layer 1, pre-coder 2, layer 2, right, okay. Then what happens after that? It computes the sum rate, okay, sum rate using pre-coder 1 and pre-coder 2, fine, okay. So how many numbers? So this is fine. Then what it does? From this it will choose the pre-coder VI which maximizes the sum rate in this case, fine. This is also done, right, exactly the same as what we did for rank 2 pre-coding in the last class. There is this number and there is this number, fine, okay. What is this? Similar to this, this pre-coder, whichever pre-coder maximizing the sum rate, I call, I pick that pre-coder. I denote it as by V tilde, okay, V hat this is, okay, and VI, okay, and then sum rate as R2 max rate. What is this? It is maximum rate assuming rank is 2 and this is a pre-coder. Now very simple decision. How will we decide what is the rank? We will compare these two rates, right, correct, okay. What will it do? If R1 max rate is greater than R2 max rate, what does it tell? Rank is 1, right, okay. Rank indicator is 1 and the pre-coder matrix indicator which will be fed back is VI tilde. If it is other way round, is not this very intuitive because if the rank of the channel is 1, right, then when you transmit one stream, you will get a higher rate, okay, right. If the rank of channel is 2, then this rate will be higher than this rate, correct, okay, because if the rank is 1 and you transmit a second stream, the stream will never get transmitted, right, because the rank is 1. System cannot support the transmission of the second layer. This here I have mixed stream and layer, both of them are same, okay, right. If the rank is 2, if the rank is 1 and the system transmits two layers, second layer will get lost, correct. So, it is, so what will happen is R1 max rate is greater than R2 max rate. Essentially, UE declares that the rank is 1, feeds back this pre-coder and the MCS accordingly. So, what has it fed back? MI, RI and MCS in both the cases, whatever is the rank. We will do the same operation, right, for all other pre-coders, for all other configurations, right. If it is a rank 3, 4, 5, 6, 7, 8, up to 8, it can go, right. Who is going to tell that? UE is only going to tell that, right. So, what are we saying? Look at the complexity of doing it. UE has to do all that if base station does not have that channel information, right, okay. That is where, if now that you know both these systems TDD and FDD, that is why people want to implement TDD systems because base station can do all that. Base station can infer the downlink channel information from the uplink channel information, okay. Then look at it, UE implementation will be simple because UE will not have to do any of these things. Base station will not have to transmit CSIRS, that large port CSIRS, right. If it had 32 antennas, okay, it will have to transmit 32 port CSIRS, correct, okay. And it is a system design, right. If I am, it is our system, okay, whatever we have designed. If I do not do TDD calibration, if I do not know how to do it, my system is designed poorly, correct, okay. So, it is either you learn to do the TDD calibration or you will, then if you do not do that, you will have to do it, right, okay. So, and it is entirely commerce at the end of the day. If I am a system vendor, there is another system vendor, somebody knows how to do this TDD calibration, they will be able to provide better rate because base station knows everything and then it will not have to send back CSIRS, that uncoded CSIRS and pre-coded CSIRS, data rates will be higher, right, okay. That is how it is done, fine. So, this is pretty much whatever we wanted to learn about the intricacies of the MIMO, the algorithms part, how it is done in the standard, okay. So, that stops here, okay. In the rest of the class, what we are going, I am going to tell you is basically as I said in the beginning of the class that how is this MIMO different across these two bands, okay, FR1 band and FR2 band, okay. There are subtle differences in the architectures, the way the system is architected across these two bands, okay, right and one thing you have to remember that if when you talk about FR1 band, bandwidth is, maximum bandwidth an operator can get is 100 megahertz, okay and the FR2 band because the bandwidth is available, the minimum bandwidth one can get is, operator can get is 400 megahertz, okay, right and that is why we are moving to higher bands because at the lower band, the availability of bandwidth is scarce, okay, right. So, if larger amount of bandwidth is available at FR2, okay, the idea of MIMO implementation becomes slightly different there. Bandwidth, the large amount of bandwidth is available but the channel become hostile. As you move towards FR2, right, okay, the, your signal travels a lesser distance because the attenuations are higher, just we understand it to capture the idea, right. So, the distance travels smaller, travelled by the signal is very small when compared with FR1, okay, right. So, I will show you MIMO in FR2 is primarily meant for combating that hostile channel in FR2, okay. You do not even talk about transmitting multiple layers there because why are you transmitting multiple layers? Because you want to increase the data rate, because the bandwidth is limited, right. Already the bandwidth is 4 times there, correct, right. So, why would you want to transmit 4 layers? Anyway, you have a larger amount of bandwidth there, right, okay. So, the primary concern there in FR2 is basically the channel is hostile. Use this larger number of antennas to combat that channel, okay, when compared with FR1 wherein channel is like more benign or more harmless when compared to FR2, okay. But the bandwidth is limited. So, you do this multi-layer transmission, so that you can increase the data rate. One difference you are immediately able to see and that is what will change the architectures also, okay. So, MIMO architecture for FR1 and FR2 bands will consider multiple users. We are trying to make it as generic as possible, okay, right. So, that is what we will discuss now and in order to understand this FR2, we will have to again like revise some of these FR1 architectures which we have just discussed, okay, so that this FR2 discussion fits in nicely, okay, correct. So, let us do that. So, I am beginning with the SISO system, okay, because I have to build on this MIMO, how this was conceived for FR1 and how it becomes different for FR2. You should not get surprised why I am coming back to SISO system, okay, because it is good to start from fundamentals and then understand why the architecture of FR2 system is slightly different, okay, right. So, that is what it is. We understand this change, modulation, right. I have not added rest of the MIMO paraphernalia here because we are talking about single antenna system, okay, right. Then what happens is it is mapped on to the two-dimensional grid, take IFFT, time domain, add CP, give it to the DAC and then upconvert, correct, okay, and then what is happening here? There are two users sitting in the system. This is one PRB. This is second PRB. You can do it for other PRBs as well, right, okay, fine. So, this is the SISO system, single antenna system. Just to keep things simple, we will quickly come to MIMO also, okay, right. We consider a single antenna base station and single antenna users, multiple users, okay. So, data for multiple users has mapped across different resource blocks, fine, okay. One resource block over 14 symbol, another one over 14 symbol. We have seen all that. Just revise it. So, what are we saying? Users are multiplexed in frequency domain. You can only differentiate these users in frequency domain, correct, okay. That is where like in the frequency domain even at the receiver you know this is my data, user will know, user will, another user will know this is its own data, but only in the frequency domain. No notion of orthogonality in time domain after taking IFFT. Here you cannot figure out what are different users, correct. Once you have taken this IFFT, all this gets like moved to a time domain. They are not orthogonal, right, okay, fine. It is orthogonality only in the frequency domain. And what happens? These IFFT symbols after RF upconversion are transmitted by the base station. Here to the upconverter transmit, correct. In the time domain, there is no notion of orthogonality. You cannot differentiate, user 1 cannot be differentiated from user 2, fine. All the users will receive the time domain symbols, okay, correct, multi-user we are talking about. What happens? I am not showing the RF chain, but it will be downconverted, fed back to ADCs, right, get the digital signal, remove CP, time domain signal, take IFFT, bring it, create this grid, user 1 knows it is, its data, user 2 know it is, this is his data, do the rest of the processing, correct, okay, right. So, each user will perform the above received processing. There are two users. Both these users will separately process. That is how data is transmitted, okay, right. Now, what happens for FR1 MIMO? Okay, correct. This is whatever architecture we have discussed. That is what I am calling it FR1 MIMO. Modulation, no need to repeat this. We have discussed this in all the details. Mapping, layer mapping, right, pre-coding, do it, all this for, do it for each of the antennas, 64 antennas, do this processing for 64 antennas, okay. We consider anti-antenna base station and multi-antenna users, okay. We are, correct, what are we saying from SISO? Where are we moving now? Base station and multiple antennas and each user has multiple antennas and there are multiple such users, correct, okay, right. So, users are multiplexed again in the frequency domain, right, okay. Pre-coded multi-layer data for multiple users is mapped to different resource blocks, okay, right. So, no notion of orthogonality in time domain after taking IFFT, right. The pre-coded vector is generated for each subcarrier. We learned that, okay. Then what happens after that? This is, look at this. That is where you have to focus on, okay. Vk into Xk, what is this contained in the pre-coder, okay, right. So, if it is a TDD system, pre-coder amplitude and phase, both of them change, correct, okay. If it is a FDD system, only pre-coder amplitudes are going to change. We saw that, okay, but what I am making it a generic case that both amplitude and pre-coder phase can change, okay, right and how do they change? That is what you have to see. This pre-coder is different for each of the subcarrier. It can be different for each of the subcarrier also, right. Typically, it is not, at least it is constant over each PRD, correct, but what are we saying that this pre-coder, if you look at here, it is changing for each of the subcarrier. Please remember this when we are talking about this architecture. How are we doing this process? That is what I bring to your, want to bring it to your notice. What are we doing? We are doing this operation for each of the subcarrier, right. So, this architecture gives me a flexibility of changing the pre-coder across each subcarrier, right, because what are we doing? We are basically doing all this operation in a digital domain, right. After that we do digital to analog conversion. Where is this happening? It is happening in one of these devices, which do all these operations, FPGAs or DSPs, right. You do all this, you can do it because you have control over the entire resource grid, correct. You are doing this operation. That is how we have done. You look at each of the subcarrier, do this operation. I am stressing upon this because the architecture which I am going to discuss, this will not be possible and that is where it will be used in FR2. That is why I am spending time over here, okay, right. But this pre-coder is designed, can be designed in principle separately for each of the subcarrier, right, okay. So, when will this be designed separately for each of the subcarrier? Channel is basically, if the channel is changing across subcarrier, each subcarrier will have a different pre-coder according to its channel, right, okay. So, but this architecture is allowing us to do that, fine. And what is happening in this architecture? There are 64 antennas, okay. There are 64 into 2 ADC DACs over here, right, correct. That is how you do this processing digitally, then convert into analog domain. And then IFFT, after IFFT there is no notion of different users, right, no different subcarriers, correct, because the signal is in time domain. So, you can do this processing for different subcarriers, you can do this processing for different users, right. When you have this kind of architecture, whatever we have considered till now, okay. So, what happens? That is what it is. So, once that is done, okay, you feed these signals to digital to analog converters. If there are 64 chains, there will be 64 such chains at the transmitter, right. We know that, okay. So, each transmit chain will require 2 DACs, 1 upconverter, 1 power amplifier, right. So, how many such DACs at that transmitter? 128 DACs if it is 64, 64 upconverters, 64 power amplifiers, okay. And at the receiver, what happens? If the receiver has multiple chains, okay, what will happen there? If it has let us say 4 receive chains, okay, what will happen? Each receiver chain will require 2 ADCs, 1 downconverter. Base station normally has 64 antennas and mobile have 2 to 4 antennas, receive antennas, okay, right. So, users, so what is happening here? This architecture will come again later, wherein you can do this processing like this, wherein each antenna is connected to each of its RF chain with ADC on receiver side and DAC on transmitter side. It is called a fully digital architecture. Why it is called a fully digital architecture? Because you are digitizing signal from each of the antenna. Whether it is receive antenna, you are digitizing the complete receive signal from each of the antenna, right, okay, fine. You could do that at the receiver, you could do that at the transmitter because at the transmitter also, what are we doing? Let us go back, right. You are getting the signal, digital signal from each or for each of this antenna separately, right. Do the digital domain processing exactly, okay. In the frequency domain, take IFFT, then add CP and then feed it back to the, feed it to the DAC, right. So, the complete digital processing for each chain is being done at the transmitter as well as the receiver. That is why I am calling this as fully digital architecture, okay, right. So, now what is happening here? So, as I said user will have 64 antennas, base station will have 64 antennas and user will have 224 antennas, right, okay. Now, why users typically have multiple antennas? So, that you can do multiple layer transmission, correct. Otherwise, what is the need? And you can, user can have only one receive antenna, it will do and it will be happy with nl is equal to 1 layer. You are putting 2 antennas so that multiple layers could be transmitted and the data rate could be increased, correct. And as I said, this is typically a requirement for FR1 systems wherein the bandwidth is small when compared with FR2 systems, okay, right. So, keeping this in mind, is not it, does not it look fine that if the user has multiple antenna at the FR2, okay, it will not use those multiple antennas for the, for transmitting the multiple layers, right, because there is no need to do that at FR2 because the bandwidth is huge, correct, okay, right. So, and what will happen there is that the channel is hostile, user will, or the base, even the base station will use these antennas to basically combat the channel, correct, okay. So, look at the decisions now that here for FR1, multiple antennas typically at high SNR will be used to increase the capacity or the rate of the user by transmitting multiple layers in parallel, okay. So, this is one aspect to remember and you should also remember this, you have to distinguish between RF transmitter receiver chain and antenna, okay. When I say, what did I say? I said complete digital architecture. This kind of architecture is completely digital wherein each RF, each antenna is connected to a separate RF chain, right. So, that is what I am saying. So, we have to start distinguishing between antenna and the RF chain, okay, because when I start talking about FR2, you will see that multiple antennas have a common RF chain, okay, right. So, if in that case, if I say multiple antennas, do not assume that each antenna will have its own RF chain, because that will, whatever we will not, will be discussing over there will not be completely digital architecture. This is something called analog architecture or hybrid architecture, okay, right. So, fine, this is, right. So, you have to distinguish. I am alerting you to all this. You have seen all this. I am alerting you to these key aspects which will become different for FR2, okay, fine. So, right. So, this is the receiver part, okay. What happens after that? From four antennas, it will, it is a completely digital architecture, it gets the digital signal for each of the antenna, does this processing, right, okay, correct, CP deletion, IFFT, it can do, it can do resource log demapping, then channel estimation for each of the antenna, right, okay, MIMO receiver, it can do all that. And why is it possible? As I said, I have stressed on it multiple times. It is a completely digital architecture, okay. Receive signal after FFT, you get this, right. Each user will perform the above receiver processing, okay, right. So, fine, okay. Now, what are the key aspects? I think we are running short of time, but I will just summarize this here, okay. So, what is this MIMO use case in 5G NR for FR1, okay. We are looking at multi-user MIMO. This 100 megahertz bandwidth is shared across multiple users, okay. How are you able to share it across multiple users when you are using MIMO? Because you are doing completely digital processing, right. You can do this pre-coded design separately for each of the PRB, right, okay. And what is allowing us to do that? Where are we getting this flexibility? Because of the completely digital architecture, you can do this processing, then convert it to analog domain at the transmitter. Similarly, at the receiver, get this signal, do the entire processing in the digital domain, okay, right. So, if it is a single user MIMO, right, then you can transmit from rank 1 to multiple rank, okay, correct. We have seen that. If it is a multi-user MIMO, then again you can transmit these multiple layers to one layer to each of the users. What are we saying? That you can increase the data rate like that. System gives you an immense flexibility because it is a completely digital system, okay, right. So, what happens? So, what is this? Transmitter architecture for multi-user MIMO, okay. If it is just to put everything together, if it is a multi-user MIMO, what will happen? You will get one transfer block for one user, another transfer block for another user, right. You can do that. It is a digital architecture, right. Do this processing, do this processing for another user, do the layer mapping. Now, this I did not discuss last time, okay. What are we saying here? These two transfer blocks correspond to different users, right, okay. That can also be done because it is all digital architecture, right. Over the same TRP, you can have transfer block of one user, transfer block of another user because you are doing multi-user MIMO, okay, right. And then do this. Once you have this, done the pre-coding, you do the 64 antenna and then do digital to analog conversion, okay. So, what will happen at the receiver? User 1 knows where its channel is, where its data is coming. It will get signal from how many, what are we assuming? We are assuming that there are multiple users with 4 antenna each, okay. Get the signal from 4 antennas, does this processing. It knows where its data is, okay, designs the receiver, MIMO receiver, layer demapping and feed it back. It gets it, validates its CRC, user 1, user 2, right, okay. Each one of them is able to do this because each one of them has access to all the digital signals from all the antennas, right, okay. And that is how this FR1 MIMO systems are typically implemented, right, okay. Because why are they implemented like this? There is a bandwidth constraint of 100 megahertz, okay. Now you want to share this bandwidth across multiple users and how will you be able to share this bandwidth across multiple users? But you need to do completely digital processing, right, okay. And how is that possible? You design this MIMO system with completely digital architecture, wherein you design the pre-coder separately for each user, you design the pre-coder for different PRBs, okay. You can do that because there is a flexibility of doing it, right. And you are forced to do that because you have to provide higher data rate for all the users, correct, because the bandwidth is limited. Now you move to FR2, you do not have some of these constraints are not there because the bandwidth is large. But there are other constraints wherein the user, wherein the channel is hostile, right, okay. So you will see that in the next class when I discuss this, okay, that immediately I will show that the multiple antennas in FR2 are basically used to combat the hostile channel. We are not even bothered about transmitting these multiple layers, okay. I will take an example and then I will show it to you, okay. What is in FR1, MIMO is used to increase the spectral efficiency or the rate, okay, and serve multiple number of users, right, in the 100 megahertz spectrum, fine, okay. You see that because there is at FR2 already the bandwidth is high, do not really have to worry about transmitting multiple layers, okay. So I will stop here. I will continue discussing this in the next class, okay. Thank you.