Lecture 58

Okay, welcome to the class and we have been discussing this MIMO architecture for FR1 and FR2 band and whatever we have discussed primarily in context of MIMO is for FR1 band and we started discussing this MIMO architecture for FR2 band and the need for simplified architectures okay for FR2 bands. We discussed that in detail okay and the reason primary reason is that you need lot many more antennas for FR2 band because the channel is hostile and then you need them both at base station as well as at the UV side. So, we are considering a very simple example okay but typically till now FR2 is being used for this like single user kind of scenarios and then line of sight systems where frequency selectivity is not there. It is basically frequency flat channel okay. So we discussed one half of it and we will recap okay so this is the simplified transmitter architecture. So, this is the system framework we are considering single user and frequency flat channel and so what happens here is this is hiding I will just move it away okay so this is a pre-coded vector okay V which is constant across subcarriers okay because frequency the channel is flat across subcarrier and there is only a single user so the channel is not changing okay and then this pre-coding vector as we know there are lot of antennas and you need these pre-coding vector to basically let us say into maximum ratio transmission because it is single user what will you do what is the best thing to do the maximum ratio transmission okay right and for time being what we said there is only one RF chain and one antenna single antenna what happens to this V it becomes a scalar okay because now there is like only one RF chain and one antenna okay. So you take some x of k multiply it with some constant V which is constant across the subcarriers okay and to begin with and this is what we will consider so V we are writing as some constant phase pre-coder phase only pre-coder okay and this is the kind of system we considered for code book kind of beam forming wherein like you saw that you are feeding only the channel phase information not the amplitude information okay. So what happens this is what we discussed that if you then when you pre-code then what you do after that is basically take the IFFT and then do digital to analog conversion okay right. So we write that NFFT N point IFFT operation on these pre-coded signal just to understand something okay. So what happens so this is x tilde k is our pre-coded signal it is coming from here you are using N subcarriers okay and this is the N point IFFT of the pre-coded signal correct okay right and now we substitute x tilde of k from here J theta okay now J theta is not function of k because it is independent across subcarriers it is basically constant across subcarriers okay and we can move this out of the summation and now what is this? This is basically the IFFT of the un-pre-coded signal correct okay e raised to power J theta into what is this IFFT of the un-pre-coded signal right. So what have we done basically move this pre-coding from frequency domain to time domain right okay correct and so this is one achievement of whatever we have done till now okay. So this is x of n what we are saying this is the N point IFFT which is independent of the pre-coded when I say independent of the pre-coded this pre-coded is same for all n values okay right and because we treated that as a constant across time across frequency okay it turns out that it is becoming constant for time also okay right. So now what happens what is so what is the kind of system we are considering here we are considering a frequency flat you see the channel is not varying across any of these subcarriers because it is single user and line of sight system okay. So you take IFFT CP digital to analog converter right okay then I will show you that this operation can be implemented in analog domain okay right so and but here as of now it is only for one antenna we extend this exercise for multiple antenna and then see how easy it is to do this operation in analog domain okay. So what have we done while doing this exercise we have moved the phase only pre-coding from frequency to time domain okay right and what have we done what is the strongest assumption here is a frequency flat and we have allocated entire bandwidth to a single user correct okay with that we are able to basically and do this pre-coding in the time domain instead of doing it in the frequency domain okay correct. So that is the biggest difference what we are seeing till now okay so and I claim that phase shifting can equivalently be moved from baseband to RF also this I have shown that in the last slide that we have moved from baseband only baseband frequency domain to baseband time domain it can equivalently be done in the RF domain also okay. Now what are we saying okay so till here I showed you this exercise for a single RF chain and a single antenna system okay so what am I saying okay now instead of a single antenna I will consider two antenna system okay RF chain will I will show you will still need only one RF chain okay and that is what I am going to show you that is how the system will get simplified okay. So what I will be saying here that basically so you have this you have two antenna system okay right so from what will from two antenna system what are you going to transmit a pre-coded signal okay x1 tilde of k and x2 tilde of k earlier we had only x tilde of k which was e raised to power j theta into x of k right okay. Now what are we doing okay so this is basically x1 k is e raised to power j theta 1 into x of k and this is x2 tilde is e raised to power j theta 2 of x of k right okay because what are we doing we are taking x of this is happening in the frequency domain right okay so what are we taking one symbol we are pre-coding it from we are pre-coding it for two antennas correct okay. So what will happen e raised to power j theta 1 into xk e raised to power j theta 2 into xk this is for first antenna this is for second antenna okay right so now what after what happened after taking IFFT of this system okay so what will you do so what is this you have to convert this signal x1 tilde of k okay to the time domain okay and what is this you take n point IFFT of that I am calling this as x1 tilde of n okay right so what is this e raised to power j theta 1 x of k right into this IFFT operation earlier we were considering only for single antenna we had theta that is the only difference I have done okay this e raised to power j theta 1 and this e raised to power j theta 1 is basically constant across subcarrier you can move it out okay fine what happens after that e raised to power what is this there is a time domain signal x of n into e raised to power j theta 1 okay. So what again the precoding for first antenna we are able to move out of the frequency domain to the time domain correct same thing we can do for the second antenna also x2 tilde of n nothing changes okay correct because what is x2 tilde of k it is e raised to power j theta 2 into x of k what is happening I am this same symbol is after precoding is getting multiplied from the second antenna right okay because that is what we are doing okay we are taking the same symbol precoding it and transmitting. So what happens here x2 tilde of n with x2 tilde of k e raised to power this is the IFFT operation x2 tilde of k this moves parallel to this you will have e raised to power j theta 2 correct inside of e raised to power j theta 1 will have e raised to power j theta 2 into x of k okay fine then e raised to power j theta 2 comes out and then you have this what happens e raised to power j theta 2 into x of n. So similarly for second antenna this is the precoding is being done in the time domain nothing changes I move from one antenna to two antenna system with the same assumptions that then precoded is constant across the subcarriers okay right. So what are we saying here okay so this is x1 tilde of n x2 tilde of n are n point FFT of precoded data symbol for two antennas they are precoded data symbols okay in principle like we should do this precoding as in the frequency domain that is what we have been doing okay. Now if this is a special kind of precoder where it is constant across subcarriers I can do this operation equivalently in time domain okay right x of n x of n but e raised to power j theta 1 and e raised to power j theta 2 what is it telling us that you take this all these symbols OFDM symbol take all these subcarriers okay take IFFT then do the precoding okay right. So what is happening here now you have two antenna system what are we doing okay and you remember we had 64 antenna system how many point FFT you had to do 64 different IFFT because you are creating 64 different resource grids right okay what are you doing here you are creating only one resource grid right okay and digital to analog conversion up conversion and then do this phase shifting in the RF domain okay. So what is happening you have only one RF chain and how many antennas as many antennas as you can want to have it there is no restriction on the number of antennas because number of antennas when compared with RF transceiver okay is a very small piece of hardware okay right here you know you know for each chain you require two digital to analog converter one up converter one bar amplifier right okay. So this is this is how we are reducing it so you look at this this is architecture where I was alluding to okay right how many there is only one pair of DAC one up converter what are these what have we done okay right you take that get the IFFT of one corresponding to X of n okay do the up conversion what is this e raise to power j theta 1 e raise to power j theta 2 e raise to power goes on e raise to power j theta whatever antennas you want to have what have we done by assuming making some certain assumptions on the system okay we have been able to move this precoding from the frequency domain to the time domain and how is it helping it is helping us in reducing the hardware immensely okay equivalent there is you are able to equivalently do it in the time domain with only phase shifters antenna and phase shifters okay. So this is basically called the analog transmitter architecture okay whatever we studied earlier was completely digital okay and this part of the precoding was done completely before this right okay and what did you need to enable that you need as many RF chains as the number of antennas okay right. So this is simple analog transmitter architecture with one RF chain and multiple antennas and you will get all the precoding in because as we remember like when for the code book based beamforming what was happening we were basically doing this phase only feedback and I claim that we will be getting most of the gain right okay that is what is happening okay. So this is the transmitter architecture used in 5G NR for FR2 this is one kind of architecture do not generalize it but typically this is most commonly used okay right and then what are we saying be careful about where this architecture is applicable is applicable for single user flat fading channels basically line of sight right okay you have to ensure that channel does not change across subcarriers okay and you have to satisfy these two conditions okay. Now what happens this is the receiver architecture do the same thing and the receiver also you have the receiver has multiple antennas as I told you in the beginning of this class that receiver also needs to have not 2, 4 multiple antennas so that it can combat the hostile channel FR2 hostile channel okay. So this fellow will also do the receiver will same operation will happen okay right because receive combining can also happen in a similar way whatever way we did the transmit combining receiver combining will also happen in a similar way how will it happen you will have these multiple antennas bandpass filters then you will have phase shifters combine all of them then do the down conversion ADC get a single basically single symbol X of n right okay all that pre-coding has already been done in the analog domain correct okay so it does not matter right what are we achieving with that by doing this that you want to pre-code correct and but you want simpler architectures you are able to do that this pre-coding is what are these very simple phase shifters okay now right so one RF chain and multiple antennas whatever pre-coding gain you are getting in the transmitter side the similar pre-coding gain you will get at the receiver side as well. So now what happens so this is one okay correct what is happening so you what are we moving from MIMO transmitter architecture in 5GNR for with 2 RF chains okay so whatever I showed you earlier was completely analog okay now what are we saying here this something typically known as hybrid okay what are we doing here this is happening for one let us say user right okay correct so this is we discussed what happens here now you consider one user is located here okay correct then you consider another user which is located in this direction okay now so there is one user there is another user here right okay correct some of course had multiple antennas now what are what was the limitation earlier okay that we could serve only one user in entire 400 megahertz band right okay so if I do this kind of architecture I serve one user with the pencil beam here right another user with the pencil beam here correct what are we doing basically serving more than one user on the same 400 megahertz band right okay but for each one of them I am generating the signal such that they do not interfere with each other right okay what is this these are considered you are transmitting two layers what will happen at the what will MAC layer do it MAC layer will give one transport block for one layer for one user another transport block for another user okay for each one of them you are doing this analog beam forming okay but you are doing them simultaneously on the same 400 megahertz grid right so this is an example of extending that single user architecture analog architecture to multi-user analog architecture okay right this again there is one flavor of it right okay so there are multiple architectures so you can call this loosely as a hybrid architecture okay wherein you are able to basically multiplex more than one user you have another system like this you put one another system like this okay there is another user basically which is located far away from these two users then multiplex that user also okay what are we doing we are saying we are figuring out those users which have kind of like well separated channels okay right their channels if you see the kind of orthogonal to each other okay right so they do not interfere with each other I can serve both of them simultaneously on 400 megahertz band also okay by using this kind of architecture okay so the base station will have multiple such RF chains 1, 2, 3, 4 maximum that is all each one of them will have 64 to 128 antennas okay this is not so what is this this is not digital architecture for each one of them we are doing analog beam forming this is for user 1 this is for user 2 okay right so simple analog transmitter architecture with two RF chain and multiple antenna okay correct and then what happens this is receiver architecture counterpart of that okay wherein like this is one user this is another user okay correct or you would have on the same user also if you can they are well separated like one you can basically you have a laptop kind of a system right wherein one patch antenna you put on one side other patch antenna you put on other side not in a typical normal mobile system but if the like the this your device has a like large dimension okay then you could do this also okay right so that is how we are basically extending this simple analog architecture to something on hybrid architecture okay fine with two RF chains and multiple antenna okay so now this is one way of serving multiple users okay right now let us say you do not consider this you come back to our like one RF chain and multiple antenna okay how do you serve multiple users there because each user you are allocating the complete 100 400 megahertz bandwidth okay right so I will show you it is inherently there in the slot structure itself okay you will see that like immediately kind of the subcarrier separation we use in millimeter wave FR2 systems you will be able to serve multiple users much better multiple users also like in an architecture like this okay let us see that okay so what happens so how do you serve okay that one way which I showed you will have to keep extending the number of RF chains right what is the other way so if you go back to the slot structure what happens remember this right okay what is this one frame 10 millisecond okay right then what happens if the subcarrier spacing which is typical FR1 spacing this is 30 kilohertz slot duration is 0.5 millisecond this one slot okay you can basically what happens you can let us say you give one symbol to each user right because what is the constraint in this FR2 architecture we are considering you have to give entire 400 megahertz band to each user in each symbol right but in the next symbol I can basically serve another user right because the next symbol is another resource in a slot okay so first symbol is allocated to first symbol because then the recorder will remain constant across all the subcarrier second symbol I give it to another user right okay fine so if you look at a slot basically how many users can I serve with the architecture I have one RF chain and multiple antenna I can serve 14 users in a slot right okay fine and that 14 users in a slot basically over a duration of 0.5 millisecond if it is a 30 mega 30 kilohertz system but that is not the case okay what happens if it is a millimeter wave system okay FR2 system then I said typically the subcarrier spacing is 120 kilohertz okay what is happening this the kind of like the relationship between the subcarrier spacing and the slot duration okay then again help you in serving multiple users in very small duration of time how because if you look at from 30 kilohertz to 120 kilohertz okay the slot duration is 0.5 millisecond here slot duration will become one-fourth of that right okay so 0.125 millisecond okay again 14 symbols correct okay so in each of the symbol basically serve one user right okay the slot duration has come down considerably and so that will allow you to multiplex user faster by giving each user complete 400 megahertz right and by doing phase only pre-coding in analog domain there is only one RF for each user you will need to have one RF chain and as many antennas as you want okay plus the delay of serving each user comes down considerably because the slot duration is smaller for the subcarrier spacing has increased that reduces the slot duration and then in turn help you in serving the users fast correct okay. So this is what I am said here slot duration for FR1 system the 30 kilohertz subcarrier spacing is 0.5 millisecond okay right slot duration with 120 kilohertz is 0.125 millisecond multiple users are served using shorter slots or shorter symbols okay right in the same duration if I am and just for example allocate a complete slot to a user also okay and compared with this system I will be able to serve in the same duration I will be able to serve 4 times the number of users if I am right okay correct so this is because this duration has come down okay right so this is basically FR2 system okay a simplified architecture and I have to like alert you also the kind of architecture we have considered I have given you a very simple example okay right people have much more sophisticated systems also just to give you example let us go back now that we have understood this okay this has 1 RF chain let us say 64 antennas okay right so 1 RF chain is connected to 64 antennas why not connect this RF chain to these antennas also right okay why not connect this RF chain to these antennas also why do we have this kind of block structure this is simple to implement and simple to like basically draw design to extend it from 1 RF chain to 2 RF chain okay but then if you look at a millimeter wave literature you will find all sorts of transceiver architectures okay this is one of that and what people do is connect this RF chain to these antennas also these phase shifters also okay right so that you could do because you will now you have look at this when you connect these antennas this RF chain is connected to these antenna this RF chain is connected to these antenna you can do something called digital pre-coding along with this what you call as analog pre-coding okay right so that there are okay so just do not get carried away by this fact that there is only this architecture for FR2 system which exists in the literature no this is one there is this one connecting RF chain to all that and that also exists that has a gives you better performance than this because again you are complicating okay right so the pre-coded design will be slightly different okay so now this actually brings us to a closure of this MIMO architecture understanding MIMO architecture for FR1 and FR2 okay our primary requirement was for FR2 system that it should be much more simpler because now what is happening there like you do not have to really transmit multiple layers in parallel okay wherein there are entirely like 400 megahertz huge bandwidth okay you can serve the data rate of each user without doing this fancy multiple layer transmission okay then in the beginning the kind of systems millimeter wave system they are like designed for line of sight okay so these two requirements have helped us in simplifying the transceiver architecture plus this also helps in the fact that for a millimeter wave system user also needs to have multiple antennas okay and as we discussed last time that for a millimeter wave system the antenna spaces reduces okay you cannot in the you can have 256 antenna in a patch of this side but you cannot have 256 RF chains okay it is not only about the space constraint plus the power consumed by each of the RF chain is humongous your battery will run out in no time okay this kind of architecture very simple one RF chain right and all these are like very simple consume minimal power phase shifters and these antennas they consume minimal power that is key point behind implementation of these MIMO architecture at least on the user side okay so I will stop here then the last two classes I will basically talk about the initial access which we have not spoken I will briefly be able to tell you for the time we have thank you.