sure so my name is same and are this is the joint work with uh most of these is due to me and my supervisor pure just an i'm K H or is to to technology in stockholm i'm here to talk about channel one station the sign not to use my i'm system and we will look at this problem both a simple to go em with um practical to go or or it's immolation so as an direction we will look at multiuser user mimo a one recent working can with multi as my ways is that you can get the good the multiplexing gain but we also look at what happened with the multiplexing gain if we have uh on channels sir can do what is the impact and talking about the channels this kind of channel information we can divide into different categories we can look at the directional information which we have the improve relation C the i and the quality information which could be the the warm some of to measure of the cold channel and we will roll right this C Q and that there's a basic a trade off between the directional and the quality information since the if we estimate the channel them to feedback we have a limited number of feedback bits a question is how should we divide is between direction and the quality and is there an impact of having spatial correlation just system or having many users well of the pen this this is things to be are trying to look at use some asymptotic analysis and we try to confirm them using simulations on the what we can practical condition so we look at the downlink transmission system we have a base station here with and then us we have many users here with one antenna each and there are more it user stunned yeah and ten equal and there is some kind of constraint on two how and we serve them use space division multiple access as to make so we select someone the users and we transmit and at the same time and why do we look at as T make well we if we look at the asymptotic but on this kind of system there's something called the multiplexing gain which says that the sum rate the sum of the rates the different do uses would get at high snr will look like a are which is a multiplexing gain times a log of the snr a seconds which basically means that if a look at the slow in the curve here with a not in the B and the sum rate over we here then having a slow problem means that at high as will go like this line and not ties now we would go it this line if we also still and as they may improve the multiplacing gain sense uh the base again is more or less the number of interference free streams that because that so we just a the may we can in principle get the number of transmit ten it's and if we as the one used would one on ten not that we can all and one screen to the use but this analysis here is and that when we have perfect channel state information so but in practice we will have to estimate the channel have to compress it and feed back to do base station using you and i and limited number of bits what least we need to do this in and if you D C's them in a T D system uh at some estimation error uh but this is more like an F system so in practical system will have some kind of channel a certain a S maybe requires very actual channel state information in a to control the co used interference that will have a didn't kind of system to jen was shown in two does a six use in there a got some rate that the model in game with the bound the by one on the contest as C is i if we haven't limited number of bits we can't increase and i look and this curve are this will be an S to make a with ten last here were single user case once slow for slope and what have as if we introduce some kind of channel uncertainty here well the single user a case here is quite robust we can't in really see the difference here between the black and a blue curve and we will use slit the bits since we don't know or channel perfectly but it's quite robust to have a channels are wow as they may is very sensitive since we need is information to be able to separate use do if we just proceed with transmitting for screens then we will come interference limited in yet and of course we can switch off use few of yours streams and and just one screen one one user and for a single speaker so what do some i mode contest feedback if we have just B bits per user the not low large there is no point of using as team may since uh the low while the sex will only depend look like X so it's no point to make in yeah how in ministry and at high snr as may will come interference limit so sort is basically an interval here a medium snrs where it's reasonable to work with estimate and if we increase the number of bits that we having the system them we can perhaps increase this interval but in the end we will always have an bomb where there's no point of using as they in more since we don't have and feed sir and before we and a i things here and the question is how do we evaluate before and in kind of systems and one way would be the actual some rates this is a sum rate that we yeah it she would our precoders are so if we would know exactly what what the channels but the problem is we don't know the channel so there's no point of a can this one since we can't really select the right rate and transmit with them another approach would be to use the goal dig summary a that would mean that we it use a some that will uh be the the meeting over all channel real sections but the problem is that we were like to have a short delay student transmission will like to select the uses all the time so we can't really do this with short terms to get schedule still these are the performance measure the people are using a literature pretty can just but two but i claim here is that this is infeasible that we have the what more lot look like this that first we estimate the channel then we quantized it's and feed it back and then we just use a selection transmission for a while until list information is up eight uh we do over again but we need to use in this can system is quite to explore its the of information to select uh a some kind of of rate that support that with high probability and the way that we're doing this is use F some out that's right cool call it are K out and this is the rate that is always larger than the actual rate with a probability that's a a a and we won't types of useful and our proposed performance measure here's then if so to some way we some up this out the rates for for use and in order to analyse this we need to have some assumptions we assume that we have B bits for feedback for user i want to use them efficiently well to maximise that's non out it's some right we assume rayleigh fading channels so there channel vector which zero mean and some alone covariance matrix E which in general will not be an i don't and is two categories some channels that information i can get to rate right it's like this the direction of one more less be that normalize vector and we want to use it to select users that are in different directions i well to use to just transmit in those direction would be four and the quality information want to use them to select you just a strong channel four moments are we a good channel properties and then select maps and a discrete and with that is high there's basically in trade of them yeah how i certainly do we want to be about the direction and about the quality which is often disregarded in different papers just assume that one of these ones are perfectly known and the other one is but the the question we trying to answer is how do we divide B bits per user between direction for information and purse will do this using some asymptotic an L and the first of the asymptotic observation we have space the following it should be absent here was something wrong there's a bullet inside of it but it is up so i'll sum rate it behaves like and T time slot obvious nor seconds like meaning that is we assume the full multiplexing gain of and T when snr goes to infinity for is all if we know that directional information the normalized vector for users perfect and the proof i is quite similar to what in do use when you work with their go like yeah some some rate we can do is force beamforming since zero for means we want to know the of total space of the channel and no in the direction and or knowing you along that that the channel or it doesn't matter we have the same in space and then we can select and nap some out a rate based on statistics that we know channel and cheap source a the indication of this results look like that the the most important thing here is that we have a direction information and but we don't know really at what this say for practical snrs this is all the when a snore scroll up but this this they the true well there is another kind of observation what we can make saying that the abs out to sum rate will assume this multiplexing gain of T when the snug as affinity for an well if we know that quality of them information of the channel perfectly for users and this is not exactly normal vector this is metric and indicate that we have in the paper which is a a little bit base some directions to and this happens if the number of users is large so should increase with as an R such that it's not a by log K uh them or you just an goes to a that comes and the proof idea here is that we select strong users based on these holding information and if we have a non id channel we need to have a low we can't have an I D but if we have a what just a little with the correlation here's a one on that directions it is these different beams there indicate the a strong different eigen directions if just one of them is large another one and we that the strong select the use a strong then with high probability it would be the strong as eigen direction that we can take yeah power channel so the indication of this kind of result uh with it proof use some uh a large number uh results uh is that it seems like we only need quality information insist as one where many users so the quest is how many use do we need to practise the C kind with it a also another objection might be that's well it the rayleigh fading channel isn't perfect does a model uh there is a small small probability that the channel will become infinitely strong but if we have many used in sect strong one we might uh and up operating in those take which is and modeling or to factor or the fading distribution and a weight this is one of the a simple to so we can G third a simple to get result say the following that we can is you the so some rate will achieve the full multiplexing gain pen a not goes to infinity and that's a if we have a large spatial correlation and we can't to grow right this you characterised this using the two largest eigenvalues of the covariance matrix take a large one divided by that second are just and we want this uh uh become large such size this an are divided by a goes to to con and a proof D is that we have a high spatial correlation that means that the strong as eigen direction will contain more more uh a percentage of that top power and then with the channel direction is known to line almost of direction so an indication of this a simple to results that's set we need really need no feedback make a as long as we have a local spatial correlation just what was the summer here well the conclusion for a a simple can analysis is that we can very diverse observations one says that only directional information is sufficient uh one says that only quality information sufficient as long as we have many users a was says the we don't thing in the V back at all as long as we make sure that we have a high spatial correlation channel but which one or or multiple of these ones that actually applying a practical scenarios this is something that we tried to illustrate i've simulation and we you just look at the simple as they make a C with one i feedback we use a D bits for direction and we use a meaning code book that's been at that uh in a simple way for correlation and we have a cube bits for dixie C Q i and we use and be maximizing code and of course we can have better co which we can you used a log codebook the optimization here but we want something that's simple and we can these or or or or separate that's as still as soon as we have some kind of correlation a we actually want to have a a combined book since for every direction we have the distribution of the game will be look but different but we have separate here simple i we have fixed number bits B it to the of Q and we assume perfect csi at receiver it's only the conversation that's great error average as our location we have four and as and the transmitter we i look we have a a are used as randomly look at on the circles that have the same oh close just make things very simple and uh we select a this this getting alley were done that i board from a paper from a lot the no seven just to i that's the most simple greedy i wouldn't you can imagine but he works well and we calculate an approximate lower bound on a sign are using these feedback like information it's more or less averaging uh the error uh a one station and to since this estimate isn't perfect and we want to uh achieve a certain the if some out just performance formants we have to have a fate margin out so we multiply out uh with that's sign are we have a cheap and we select and i'll but such that probability that this estimate the sign are it's larger than actual snr is small five percent and the first simulation results here is for uncorrelated channel I D on the y-axis we have that some out it's some rate here we have a that's an art up to varying and we have twenty users on the right care here we have varying the number of users and we have fixed an are ten db and here we have a talk a twelve bits well bits and the lower to ones are eight bits and total make bits in total and of course these represent different locations and what we can see here is that the top most curves here are when we take to a bits per use or for the information and the remaining one directional information and we can see here that these two curves here they are going little bit together someone we increase number of users it seems like having a hold information becomes slightly more important but uh still this always in these simulations best to is it's information this increase quite well with the first a simple to summation at we have that or to it that directional information is the most important thing but what happens when we yeah introduced some spatial correlation well we use is simple model here where the angle spread represents a spatial correlation so angle spread is the uh average direction and angle angle direction where it should transmit an or for it to C but the user so having a small angle spread means that have high correlation and a week increase we the correlation and we we increase it we decrease the like so it's not direction and we have a tend to be that's an hour and twenty years and it's very hard to read anything at all here about the sure of the so that we can gain a little bit here when we have a very high correlation and by allocating locating that bit more bits for cold information but the difference where small and that's in as we increase and to an angle spread of ten to fifty reese for example and once again see that which should allocate the but to to free bits for for the information the rest of for direction so this also reach quite well with the with asymptotic observation while that if you bits for called information and the rest of direction as a summer here we look that multi use a mimo which and show excellent performance if we have perfect channel they'd information but in practice limit by have a feedback station and we this guest how to compress the channel and there's a tradeoff between the cold information and the direction information and we'll try to or was the relative importance between a and when we look at some topic they were very different thing we can show we can show and and anything do we did have them the asymptotic to what we K but but B look that's simulations with saw but to to free bits for user should use but quality and the remaining money direction is is very important to have a good yeah control of interfere and if you compare is with L D's done as for example where we have a codebook of four bits per user for old information we see here that we can decrease at a the bit but a since we know channel statistics to we all the use of portion of which for example we not strong channel i have a and in fact of spatial correlation and the number of uses is quite small and our simulations agrees with one of a simple cells which probably the most recent well so we like to thank you for listening my paper some presentation available on and i will let also question i yes so have a a question or or maybe some or multiple questions depending oh what other people wanna ask um so yeah i i mean i like the comparison and the the asymptotic messages is kind of interesting um so i guess i wanna push back a little bit on your epsilon because my understanding is that normally the rate the the issue is uncertainty about the rate you don't know what log of one plus S and Rs which you quantized the thing and S and R yeah but my understanding is normally that's this is what the use this fast hybrid really or Q for to kind of fix that so that's what every time i talk to someone an industry were some three D B P that's all so i guess i'm wondering like do you have any results that show that doing the apps line gives you something in that's not captured by just using the log one process and are "'cause" i didn't and see that can person is it is central to we to what you did well at the same time this say when the in the standard that they should a a the having a maps so that about ten percent uh but uh we are not really taking care of the the errors that that we gets a with five percent these are run reasonable numbers that we add up to it but um and it's hard to i yeah i guess you yeah need to run simulations to see how large absolute you can accept in or to take care of the rest of their or student using have but i yeah Q but i'm quite sure that you you can't take care of everything you yeah you yeah mean there's always some more errors i guess i'm wondering go some of these results depend on that measure of performance as opposed to yeah i that that's basically what model but i guess of that's the case then you would not have the quality Q i would probably not place what role i think if we won't do anything able here for example uh that we will have a fifty percent probability of the uh a getting now each and taken care to this with a a a a to is not really what was meant for for the beginning again i mean a hybrid are who you're gonna get sums of these things you're going to get i mean it does appear a little bit of the way a kind of goes away or yeah or are alright as i but uh so the i oh oh oh no oh i oh oh i i so basically we made the those assumptions stuff was the uh need in nor to if fixed do proofs of this free a simple tick things in the and i guess paper but the i think we we can yeah expand things there are quite a lot uh minute of these of may should could be proved uh asymptotic asymptotically an for different user fusion that but but but not not only set we need it is not a very hard to prove that you see that yeah don't to most basic in the constant to come very large should use is proofs are more based on of this quite easy to prove okay um okay okay