0:00:17so my name is same and are this is the joint work with
0:00:21most of these is due to me and my supervisor pure just an
0:00:25i'm K H or is to to technology in stockholm
0:00:29i'm here to talk about channel one station the sign
0:00:31not to use my i'm system
0:00:33and we will look at this problem both a simple to go em with um
0:00:37practical to go or or it's immolation
0:00:42so as an direction
0:00:44we will look at multiuser user mimo
0:00:46a one recent
0:00:48working can with multi as my ways is that you can get the good
0:00:50the multiplexing gain
0:00:52but we also look at what happened with the multiplexing gain if we have
0:00:56uh on channels sir can do what is the impact
0:01:00and talking about the channels this kind of channel information we can divide into different categories
0:01:05we can look at the directional information which we
0:01:08have the improve relation C the i
0:01:11and the quality information which could be the the warm some of to measure of the cold channel
0:01:15and we will roll right this
0:01:17C Q
0:01:19and that there's a basic a trade off between the directional and the quality information
0:01:23since the
0:01:25if we estimate the channel them to feedback
0:01:28we have a limited number of feedback bits
0:01:30a question is how should we divide is between direction and the quality
0:01:34and is there an impact of having spatial correlation just system or having many users
0:01:40well of the pen this
0:01:42this is things to be are trying to look at
0:01:45use some asymptotic analysis
0:01:47and we try to confirm them using simulations on the what we can
0:01:51practical condition
0:01:54so we look at the downlink transmission system
0:01:56we have a base station here with and then us
0:01:59we have many users here with one antenna each
0:02:02and there are more
0:02:03it user stunned
0:02:05yeah and ten
0:02:08and there is some kind of constraint on two
0:02:13and we serve them use space division multiple access as to make so we select someone the users and we
0:02:18transmit and at the same time
0:02:22and why do we look at as T make
0:02:24well we if we look at the asymptotic but on this kind of system there's something called the multiplexing gain
0:02:29which says that the sum rate
0:02:30the sum of the rates the different do uses would get at high snr will look like a are which
0:02:35is a multiplexing gain times a log of the snr
0:02:38a seconds
0:02:40which basically means that if a look at the slow in the curve here with a not in the B
0:02:45and the sum rate over we here
0:02:46then having a slow problem means that at high as will go like this line and not ties now we
0:02:52would go
0:02:53it this line if we also still
0:02:56and as they may improve the multiplacing gain sense
0:02:59uh the base again is more or less the number of interference free streams that because that so we just
0:03:04the may we can in principle get the number of transmit ten
0:03:08and if we as the one used would one on ten not that we can all and one screen to
0:03:12the use
0:03:15but this analysis here is
0:03:17and that when we have perfect channel state information
0:03:20so but in practice we will have to estimate the channel
0:03:23have to compress it and feed back to do
0:03:25base station using you
0:03:28i and limited number of bits
0:03:30what least we need to do this
0:03:31in and
0:03:32if you D C's them in a T D system uh at some estimation error
0:03:37but this
0:03:38is more like an F system
0:03:40so in practical system will have some kind of channel a certain
0:03:45a S maybe requires very actual channel state information
0:03:48in a to control the co used interference that will have a didn't kind of system
0:03:52to jen was shown in two does a six use in there a got some rate
0:03:56that the model in game with the bound the by one on the contest
0:03:59as C is i if we haven't limited number of bits we can't increase
0:04:08look and this curve are this will be an S to make a with ten last here were single user
0:04:11case once slow for slope
0:04:15and what have as if we introduce some kind of channel uncertainty here
0:04:19well the single user a case here is quite robust we can't in really see the difference here between the
0:04:23black and a blue curve
0:04:25and we will use slit the bits since we don't know or channel perfectly but it's quite robust to have
0:04:29a channels are
0:04:30wow as they may is very sensitive since we need is information to be able to separate use
0:04:36do if we just proceed with transmitting for screens
0:04:39then we will come interference limited in yet
0:04:41and of course we can switch off use few of yours streams and and just one screen
0:04:46one one user
0:04:47and for a single speaker
0:04:51so what do some i mode contest feedback if we have just
0:04:54B bits per user the not low large there is no point of using as team may since
0:05:00the low while the sex will only depend
0:05:02look like X so it's
0:05:04point to make in yeah how in ministry
0:05:07and at high snr as may will come interference limit
0:05:11so sort is basically an interval here a medium snrs where it's reasonable to work with estimate
0:05:16and if we increase the number of bits that we having the system them we can perhaps increase this interval
0:05:21in the end we will always
0:05:22have an bomb where there's no point of
0:05:24using as they in more since we don't have and
0:05:32and before we and a i things here
0:05:34and the question is how do we evaluate before and in kind of systems
0:05:38and one way would be the actual some rates this is a sum rate that we
0:05:42yeah it she would our precoders are so if we would know exactly what what the channels
0:05:47but the problem is we don't know the channel so there's no point of a can this one since we
0:05:51can't really select the right rate
0:05:53and transmit with them
0:05:55another approach would be to use the goal dig summary
0:05:59that would mean that we it use a some that will uh
0:06:02be the
0:06:03the meeting over all channel real sections
0:06:05but the problem is that we were like to have a short delay student transmission will like to select the
0:06:10uses all the time so we can't really do this with short terms to get schedule
0:06:14still these are the performance measure the people are using a literature pretty can just
0:06:19but two
0:06:20but i claim here is that this is infeasible that we have
0:06:23the what more lot look like this that first we
0:06:26estimate the channel then we quantized it's
0:06:28and feed it back and then we just use a selection transmission for a while
0:06:31until list
0:06:32information is up eight uh we do over again
0:06:36but we need to use in this can system is quite to explore its the of information to select
0:06:42a some kind of of rate that support that with high probability
0:06:47and the way that we're doing this is
0:06:48use F some out that's right
0:06:50cool call it are K out
0:06:52and this is the rate
0:06:54is always larger than the actual rate
0:06:56with a probability that's a
0:06:59a a and we won't types of useful
0:07:01and our proposed performance measure here's then
0:07:04if so to some way we some up this out the rates for for use
0:07:10and in order to analyse this we need to have some assumptions
0:07:13we assume that we have B bits for feedback for user
0:07:16i want to use them efficiently
0:07:18well to maximise that's non out it's
0:07:20some right
0:07:21we assume rayleigh fading channels
0:07:23so there
0:07:24channel vector which
0:07:25zero mean and some alone
0:07:27covariance matrix E which in general will not be an
0:07:30i don't
0:07:32and is two categories some channels that information
0:07:34i can get to rate
0:07:35right it's like this the direction of one more less be that
0:07:38normalize vector
0:07:40and we want to use it to select users that are in different directions
0:07:44i well to use to just transmit in those direction would be four
0:07:47and the quality information want to use them to select you just a strong channel four moments are we
0:07:53a good channel properties
0:07:54and then select maps and a discrete
0:07:56and with
0:07:57that is high
0:07:59there's basically in trade of them
0:08:01yeah how i certainly do we want to be about the direction and about the quality
0:08:06which is often disregarded in different papers just assume that one of these ones are perfectly known and the other
0:08:11one is
0:08:13but the
0:08:14the question we trying to answer is how do we divide B bits per user
0:08:18between direction for information
0:08:21and purse will do this using some asymptotic an L
0:08:25and the first of the asymptotic observation we have space the following
0:08:29it should be absent here was something wrong there's a bullet inside of it
0:08:33but it is up so i'll sum rate it behaves
0:08:36like and T time slot obvious nor seconds like meaning that is
0:08:39we assume the full multiplexing gain of and T
0:08:43when snr goes to infinity for is all
0:08:45if we know that directional information
0:08:48the normalized vector for users
0:08:53and the proof i is quite similar to what in do use when you work with their go like
0:08:57yeah some some rate
0:08:59we can do is force beamforming since
0:09:01zero for means we want to know
0:09:03the of total space of the channel
0:09:05and no in the direction and or knowing you
0:09:08along that
0:09:09that the channel or it doesn't matter we have the same in space
0:09:13and then we can select and nap some out a rate based on statistics that we know channel and cheap
0:09:18source a
0:09:20the indication of this results look like that the the most important thing here is that we have a direction
0:09:27but we don't know really at what this say for practical snrs this is all the when a snore scroll
0:09:35but this this they the true
0:09:37there is another kind of observation what we can make
0:09:39saying that the abs out to sum rate will assume this multiplexing gain of T
0:09:43when the snug as affinity for an well
0:09:46if we know that
0:09:47quality of them information of the channel
0:09:50perfectly for users and this is not exactly normal vector this is metric and indicate that we have in the
0:09:55paper which is
0:09:57a a little bit base some directions to
0:10:00this happens if the number of users is large so should increase with as an R such that it's not
0:10:06a by log K
0:10:08uh them or you just an goes to a that comes
0:10:12and the proof idea here is that
0:10:14we select strong users based on these
0:10:19if we have a non id channel we need to have a low
0:10:22we can't have an I D but if we have a what just a little
0:10:25with the
0:10:26correlation here's a one on that
0:10:28directions it is these different beams there indicate the a strong different eigen directions
0:10:33if just one of them is large another one and we that the strong
0:10:36select the use a strong then with high probability it would be the strong as eigen direction that we can
0:10:42yeah power channel
0:10:47so the indication of this kind of result
0:10:50uh with it proof use some uh
0:10:52a large number
0:10:54uh results uh
0:10:56is that it seems like we only need quality information insist
0:10:59as one where many users so the quest is how many use do we need to practise the C kind
0:11:04with it
0:11:05a also another objection might be that's
0:11:08it the rayleigh fading channel isn't
0:11:10perfect does a model
0:11:12uh there is a small small probability
0:11:14that the channel will become infinitely strong
0:11:17but if we have many used in sect strong one we might
0:11:20uh and up
0:11:21operating in those take which is
0:11:23and modeling or to factor or the fading distribution
0:11:28and a weight this is
0:11:29one of the a simple to so we can G
0:11:32third a simple to get result say the following that we can is you
0:11:36the so some rate will achieve the full multiplexing gain pen
0:11:39a not goes to infinity and that's a
0:11:41if we have a large
0:11:43spatial correlation
0:11:44and we can't to grow right this
0:11:46characterised this using the two largest eigenvalues of the covariance matrix
0:11:51take a large one divided by that
0:11:53second are just
0:11:54and we want this
0:11:55uh uh
0:11:57become large such size this an are divided by a goes to to con
0:12:02and a proof D is that we have a
0:12:04high spatial correlation that means that the strong as eigen direction will contain more more uh a percentage of that
0:12:11top power and then with the channel direction is known to line almost of direction
0:12:16so an indication of this a simple to results that's set
0:12:18we need really need no feedback make a as long as we have a local spatial correlation just
0:12:24what was the summer here
0:12:26well the conclusion for a a simple can analysis is that
0:12:29we can very diverse observations
0:12:31one says that only directional information is sufficient
0:12:35uh one says that only quality information sufficient as long as we have many users
0:12:39a was says the we don't thing in the V back at all as long as we make sure that
0:12:43we have a
0:12:44high spatial correlation channel
0:12:46but which one or
0:12:48or multiple of these ones that actually applying a practical scenarios
0:12:51this is something that we tried to
0:12:53illustrate i've simulation
0:12:58and we you just look at the simple as they make a C with one i feedback
0:13:01we use a D bits for direction and we use a meaning code book that's been at that
0:13:06uh in a simple way for correlation
0:13:09and we have a cube bits
0:13:10for dixie C Q i and we use and be maximizing code
0:13:14and of course we can have better co which we can you
0:13:16used a log codebook the optimization here but we want something that's simple
0:13:21and we can these or or or or separate
0:13:23that's as still
0:13:24as soon as we
0:13:26have some kind of correlation
0:13:29we actually want to have a a combined book
0:13:32for every direction we have
0:13:34the distribution of the game will be look but different
0:13:37but we have separate here
0:13:40i we have fixed number bits B
0:13:43it to the of Q
0:13:45and we assume perfect csi at receiver it's only the conversation that's great
0:13:51average as our location we have four and as
0:13:54and the transmitter
0:13:56i look we have a a are used as randomly look at on the circles that have the same
0:14:00oh close just make things very simple
0:14:03and uh we select a this this getting alley were done that i board from
0:14:06a paper from
0:14:07a lot the
0:14:08no seven
0:14:09just to
0:14:11that's the most simple greedy i wouldn't you can
0:14:14but he works well
0:14:17we calculate an approximate lower bound on a sign are using these
0:14:21feedback like information
0:14:22it's more or less
0:14:26the error
0:14:27uh a one station
0:14:30and to since this estimate isn't perfect and we want to
0:14:33uh achieve a certain the
0:14:35if some out just
0:14:36performance formants we have to have a fate
0:14:40so we multiply out uh
0:14:43that's sign are we have a cheap
0:14:45and we select and i'll but such that
0:14:47probability that
0:14:48this estimate the sign are it's larger than actual snr is small
0:14:52five percent
0:14:57and the first simulation results here is for uncorrelated channel I D
0:15:02on the y-axis we have that some out it's some rate
0:15:05here we have a
0:15:06that's an art up to varying and we have twenty users
0:15:09on the right care
0:15:10here we have
0:15:11varying the number of users and we have fixed an are ten db
0:15:16here we have a talk a twelve bits
0:15:18well bits
0:15:19and the lower to ones are eight bits and total make bits in total and of course
0:15:24represent different locations
0:15:26and what we can see here is that the top most curves here are when we take to
0:15:31a bits per use or for the information and the remaining one directional information
0:15:36and we can see here that these two curves here they are going little bit together someone we increase number
0:15:41of users it seems like having a hold information
0:15:44becomes slightly more important
0:15:46but uh still
0:15:47this always
0:15:49in these simulations best to
0:15:55this increase quite well with the first a simple to summation at we have that
0:15:58or to it that directional information is the most important thing
0:16:03but what happens when we
0:16:04yeah introduced some spatial correlation
0:16:07well we use is simple model here
0:16:10where the angle spread represents a spatial correlation so angle spread is the
0:16:14uh average direction and
0:16:17angle angle direction where
0:16:18it should transmit an or for
0:16:20it to C
0:16:21but the user
0:16:24so having a small angle spread means that have high correlation and
0:16:28a week increase we the correlation and we we increase it we decrease the like so it's not direction
0:16:34and we have a tend to be that's an hour and twenty years
0:16:38and it's very hard to read anything at all here about the sure of the
0:16:42so that we can gain a little bit here when we have a very high correlation
0:16:46and by
0:16:47allocating locating that bit more bits for cold information
0:16:50but the difference where small and that's in as we increase and
0:16:53to an angle spread of ten to fifty
0:16:55reese for example
0:16:56and once again see that which should allocate the but to to free bits
0:17:00for for the information the rest of for direction
0:17:05so this also reach quite well with the
0:17:07with asymptotic observation while that if you bits
0:17:10for called information and the rest of direction
0:17:14as a summer here
0:17:15we look that multi use a mimo which and show excellent performance if we have perfect channel
0:17:20they'd information
0:17:22but in practice limit by have a feedback station
0:17:25and we
0:17:26this guest how to compress the channel
0:17:28and there's a tradeoff between the cold information and the direction information
0:17:32and we'll try to or was the relative importance between a
0:17:36and when we look at some topic
0:17:38they were
0:17:39very different thing we can show we can show and
0:17:41and anything
0:17:42do we did have them the asymptotic to what we K
0:17:45but B look
0:17:46that's simulations with saw but to to free bits for user should use but quality and the remaining money direction
0:17:51is is very important
0:17:53to have
0:17:53a good
0:17:55control of interfere
0:17:57and if you compare is with L D's done as for example where we have a codebook of four bits
0:18:01per user for old information
0:18:03we see here that
0:18:05we can decrease at a the bit but a since we know channel statistics
0:18:09to we all the use of portion of which for example
0:18:12we not
0:18:12strong channel
0:18:14i have a
0:18:16and in fact of spatial correlation and the number of uses is quite small
0:18:22our simulations agrees with one of a simple cells which
0:18:25probably the most recent
0:18:28so we like to thank you for listening
0:18:30my paper some presentation available on
0:18:33and i will let also question
0:18:47yes so have a a question or
0:18:49or maybe some or multiple questions depending oh what other people wanna ask um
0:18:53so yeah i i mean i like the comparison and the
0:18:56the asymptotic messages is kind of interesting um
0:18:59so i guess i wanna push back a little bit on your epsilon
0:19:03my understanding is that
0:19:05normally the rate
0:19:07the the issue is uncertainty about the rate you don't know what log of one plus S and Rs which
0:19:11you quantized the thing and S and R yeah but my understanding is normally that's this is what the use
0:19:15this fast hybrid really or Q for
0:19:17to kind of fix that
0:19:20that's what every time i talk to someone an industry were some three D B P that's all so i
0:19:23guess i'm wondering like
0:19:25do you have any results that show that doing the apps line gives you something
0:19:30in that's not captured by
0:19:32just using the log one process and are "'cause" i didn't
0:19:35and see that can person
0:19:37is it is central to we to what you did
0:19:40well at the same time this say when the in the standard that they should
0:19:43a a the having a maps so that about ten percent
0:19:47but uh
0:19:49we are not really taking care of the the errors that that we gets a with five percent
0:19:53these are run reasonable
0:19:55numbers that we add up
0:19:56to it but um
0:20:01it's hard to i
0:20:03yeah i guess you yeah need to run simulations to see how large absolute you can accept in or to
0:20:07take care of the rest of their or student using have but i yeah Q but i'm quite sure that
0:20:12you can't take care of everything you
0:20:16yeah you
0:20:16yeah mean there's always some more errors i guess i'm wondering go
0:20:19some of these results depend on that
0:20:22measure of performance as opposed to
0:20:25yeah i that that's basically what model but i guess of that's the case then you would not have the
0:20:31Q i would probably not place what role
0:20:33i think if we won't do anything able
0:20:36here for example uh that we will have a fifty percent
0:20:40probability of the uh
0:20:42a getting now each and taken care to this with
0:20:45a a a a to is not really what was meant for for the beginning again
0:20:50i mean a hybrid are who you're gonna get sums of these things you're going to get
0:20:54i mean
0:20:55it does appear a little bit of the way a kind of
0:20:58goes away
0:21:01yeah or are alright
0:21:39so basically we made the
0:21:41those assumptions stuff was the
0:21:44need in nor to
0:21:45if fixed do proofs of this free a simple tick things in the and i guess paper but the i
0:21:50think we we can
0:21:52expand things there are quite a lot uh minute of these of may should could be proved
0:21:57uh asymptotic asymptotically an
0:21:59different user
0:22:06but but but not not only set we need it is not a very hard to prove that you see
0:22:11don't to most basic in the constant to come very large should use
0:22:14is proofs are more based on of this quite easy to prove