Přepis řeči - CHANNEL QUANTIZATION DESIGN IN MULTIUSER MIMO SYSTEMS: ASYMPTOTIC VERSUS PRACTICAL CONCLUSIONS

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

CHANNEL QUANTIZATION DESIGN IN MULTIUSER MIMO SYSTEMS: ASYMPTOTIC VERSUS PRACTICAL CONCLUSIONS

Multiuser and Network MIMO

Přednášející: Emil Björnson, Autoři: Emil Björnson, Konstantinos Ntontin, Björn Ottersten, KTH - Royal Institute of Technology, Sweden