Přepis řeči - ON OPTIMAL CHANNEL TRAINING FOR UPLINK NETWORK MIMO SYSTEMS

0:00:13	okay
0:00:13	every but i'm quite happy that i is that if
0:00:16	face
0:00:17	and and means the last they at its many people for already let so it's would to see that some
0:00:21	people and first
0:00:22	topic
0:00:23	a i don't then some work on optimal channel training a think that of mine was system
0:00:29	i'm sure most of you know this famous paper by a back of C B and bound to why on
0:00:33	how much training
0:00:35	is needed in
0:00:36	wireless fading links
0:00:38	you kind of
0:00:38	same work but in a network my setting with if you needing ingredients
0:00:43	um that get started directly
0:00:45	what we consider
0:00:46	as in some sense the distribute and ten system
0:00:49	so you have and a station to just give you didn't or
0:00:53	each base station is equipped with an intel
0:00:56	and this study a much a lexus channel from K single antenna user to i mean a
0:01:01	transmit to Z
0:01:02	E base stations
0:01:04	and see the stations do not to that its since for thing what's if receive
0:01:08	to a central process a which would do
0:01:10	all the joint decoding
0:01:12	the central
0:01:13	or
0:01:14	so is you is that the past
0:01:16	see
0:01:17	of of back calling link from one based they
0:01:19	and for station is see bits but channel use
0:01:22	i three you one may if you and quite schemes so this means we have and a have all frequency
0:01:27	sub-bands
0:01:28	but all use that time of you
0:01:30	the transmit on all of this up and
0:01:33	the same
0:01:34	um as i set
0:01:36	um Z base stations are of they can't to code then you of the user score work
0:01:41	and you also as you that need does use the time and it's not as the base station at any
0:01:45	channel state information
0:01:47	so the station it's the end
0:01:49	what estimate the channel
0:01:51	but then use this channel estimate to decode messages we see from more
0:01:57	the the motivation would be what is the optimal fraction of a coherent time of the korean style of the
0:02:03	channel we should use and this setting
0:02:05	for sending uplink pilot tones
0:02:07	for actually transmitting data
0:02:10	and since we have a limited back haul capacity we can also study what to see in impact of this
0:02:15	capacity on the optimal change set training time
0:02:19	um yeah i was system on is quite simple so on a
0:02:23	uh
0:02:24	yeah sub and a sub a and so we have at sub carriers
0:02:28	we have received signal back the of size be times and because we E base station each equipped with an
0:02:34	a
0:02:35	at the receive back the X K is and complex question where we assume that each user split it's of
0:02:41	i'll
0:02:41	available power key uniformly over all subcarriers
0:02:45	i
0:02:46	since a reasonable assumption because
0:02:48	use use time and have no channel information at all channels uh
0:02:52	the channel statistics on each subcarrier sir
0:02:54	same the splitting the power you you form me over the subcarriers carriers a
0:02:59	but we have some simple and noise
0:03:01	so far a specified how be one of the channel i would come to this something the
0:03:07	um um was base stations so the base station this that it back the right
0:03:13	i was what sea base station C
0:03:15	now
0:03:15	the base station a quantized observation and four but the quantized yep channel observation to the central station as a
0:03:22	central station would joint you all messages
0:03:25	um we are no
0:03:27	she yeah i have facing a distributed compression problem
0:03:31	so
0:03:31	quite
0:03:32	quite complex
0:03:33	solar
0:03:34	and especially
0:03:35	it's the base station
0:03:36	do not know what to the actual channel state you can't do any channel deep and compression scheme
0:03:42	yeah so you could too much but if you know
0:03:44	what is the extra standard state
0:03:46	you could do not and some since you're your quantization resolution
0:03:50	do actions channel state but since the base station do not have this information they can't do it
0:03:55	we can say a a sub you know
0:03:57	compression scheme
0:03:59	a which can be seen as simply adding a complex course noise to the observation
0:04:04	and of course the "'em" quantisation is
0:04:07	depends on the capacity of your channel
0:04:10	and i was on rate distortion theory
0:04:12	you can actually come
0:04:14	pressure for the um
0:04:15	for the quantisation noise variance
0:04:17	pa
0:04:18	um
0:04:19	uh uh uh uh uh but for channel
0:04:22	and this is nothing that's in something
0:04:23	as to of that you don't we made to the receive noise
0:04:26	how
0:04:27	or not to with the noise power plus the received signal power from or use of time in
0:04:32	and actually if you increase the capacity infinity at this balance with when image if it goes to zero rule
0:04:38	the quantization was are simply goes to
0:04:44	no how to be model of the channel or so we you want a rayleigh fading channel
0:04:49	a rayleigh block fading channel so we draw a random
0:04:52	realisation
0:04:53	based fixed for T channel uses that it changes independently from one block to the other
0:04:59	well a and of this big channel matrix of this the channel from all use that and all and at
0:05:04	all base station
0:05:06	actually have a different variances
0:05:08	yeah i J
0:05:09	and this variance
0:05:11	and on the past loss
0:05:13	from a a base station and tell a to user to i mean
0:05:17	since true that's a past most from a user turn the
0:05:20	to a and tell us of one base station is the same because the quite close together
0:05:24	it it a part was fact that at K and be multiplied by a and dimensional vectors so the actually
0:05:30	gets this balance profile of a watch and make sure
0:05:33	yeah so H is nothing it's in it
0:05:35	complex caution matrix which each
0:05:37	and a has a different variants yeah i
0:05:41	oh the channel estimation procedure quite standard
0:05:44	so we split the coherence time in tile
0:05:47	so that's for yeah for training and the rest is used for data transmission
0:05:52	or if you use the sort of the training so it's actually the base station these central station would estimate
0:05:57	a particular channel coefficients H I J
0:05:59	what this observation
0:06:01	you feel a training snr but depends of course of the length of your you're on training sequences you have
0:06:07	mouse
0:06:07	but use your have so that give quantization error
0:06:10	so the estimate the channel estimate would be an that
0:06:13	but the back wall
0:06:15	a few takes the ever the estimate of this channel you can decompose it in they estimate and in independent
0:06:20	noise term you computes the variances of C received signal back of the use for signal on a
0:06:26	channel energy and the energy of C estimation error
0:06:30	i see that the seems to see yeah quantisation of no uh variance of P
0:06:36	now if you consider that
0:06:38	received vector
0:06:40	and it's the same station
0:06:42	a connection prior to it
0:06:44	as the estimate channel H that might apply but a signal week which was sent
0:06:48	and
0:06:49	to which
0:06:50	which contains the contribution from some noise quantisation errors and channel estimation
0:06:57	of course
0:06:58	in the set to this isn't a few months to um this not depend of the signal you sent
0:07:03	so actually capacity of this channel is not known
0:07:05	are we use the them
0:07:07	yeah the same um rather have and on the true information as and the paper by have C
0:07:12	that's use you humour
0:07:14	that's the noise would be gosh an independent of few transmitted signal or with the covariance matrix K easy
0:07:22	i map and i is it by a number of a station and the number of antennas so the
0:07:26	a man about the true information per a given time
0:07:30	and this doesn't take into account the that we actually spent
0:07:34	for channel training data transmission so what we want to do is work to maximizing that about the achievable rate
0:07:40	was a simply please just about a good you but R T
0:07:43	apply by a discount factor
0:07:45	and would like to maximise this expression of was the conditions that can lead to have at least
0:07:49	can
0:07:50	a training symbols because you have use that time but but we can train or something could you
0:07:56	now if you think about it the quite tough problem
0:07:58	"'cause" you have in fact the expectation
0:08:01	i have a a a a a a complex course matrix of each and and
0:08:05	has a different variants so this a very um which was of to profile
0:08:09	and this is not known in closed-form
0:08:12	those was where you can calculate cd eigenvalue distribution of this matrix in closed form
0:08:16	what we do have a it is we use so to an approximation based to from the matrix re
0:08:22	so we assume your yeah was that we would have a many user turn it's
0:08:26	it and the about
0:08:27	of the number of base station and it's number of a tell us per base station it's some since the
0:08:32	total number of antennas goes to infinity
0:08:35	and as this
0:08:36	assumption
0:08:38	hmmm two information will converge to a deterministic quantity or we can find a deterministic approximations of the about but
0:08:44	which information
0:08:46	such that what the system was infinitely large
0:08:48	the difference between the approximation and exact result close to zero
0:08:54	this is actually results so the result for a channel a random matrix either the entries were but each with
0:09:01	a different variants was that a lapel of by by by tasha
0:09:04	two thousand seven
0:09:05	or simply applied to to i was set to is just one greedy and um
0:09:10	well it you
0:09:11	that's the using split so power of it a fink at men subcarriers
0:09:16	so reason for this is quite simple
0:09:18	if you system was infinitely large need to make sure that the energy in the system states finite
0:09:23	if you start spreading
0:09:25	just signal of an infinitely many sub carriers the energy per subcarrier goes to zero
0:09:29	but still the energy in the entire system states fixed
0:09:34	yeah and actually can computed for each
0:09:37	there are
0:09:37	can ever ever
0:09:39	a deterministic quantity
0:09:41	such as just different converters to zero i don't provide a on you because it doesn't provide a lot
0:09:47	oh have of the only thing we to compute since quality
0:09:50	is seen covariance matrix of single and of so interference in rows
0:09:55	and the variance profile of the estimated channel
0:09:59	and actually to see that's is makes L
0:10:01	i i i mean we consider an infinite large systems so what we actually looking at would be three base
0:10:06	station was we use that term that's in each base station is to tell us
0:10:11	and
0:10:11	that's what we consider him a smell medical example
0:10:15	so i have
0:10:16	like a screen
0:10:17	three corpora to base station seven three is a sum three different set
0:10:21	i drop some randomly
0:10:24	you you can that lot just but past was model and obvious we every every or over channel a realisation
0:10:30	actually is C
0:10:32	we this plot the
0:10:34	i got rate of
0:10:36	well as a cs so a
0:10:38	for a a system
0:10:39	what each base station has
0:10:41	two ten as
0:10:42	you have only one subcarrier
0:10:44	with have coherence time of a sound channel uses and B was optimize in was saying
0:10:49	we have a a training time of to
0:10:52	a lot for me that based on the asymptotic approximation
0:10:57	the um the not "'cause" of what got by simulations
0:11:00	and i mean for me is this look
0:11:02	as good as if you had C perfect um
0:11:05	that is and some since the asymptotic
0:11:07	approximation works better very well even for channel of size a six times three
0:11:13	no i i since for three different back haul capacities so the black the black light was corresponds to what
0:11:19	you would get was a back work that's your one
0:11:21	um
0:11:22	a channel was and you start increasing in of course you get
0:11:26	well i what we do see approach so
0:11:28	optimize of the train time is instead of optimising the the a got a rate but we can't which we
0:11:35	can't country treat a or
0:11:38	we try to optimize our
0:11:40	deterministic approximation
0:11:42	so we want to optimize a deterministic approximation of the mutual of the about get you the rate
0:11:47	for this still need to compute the first derivative
0:11:50	you need to show that it's called okay for once you have done this
0:11:53	a a simple line search what but you wish
0:11:56	and finds the optimal train at time
0:11:58	then
0:11:59	we show that
0:12:02	up to a lower value of have on
0:12:04	um asymptotic approximation converges to the optimal
0:12:08	so we real up to a result you would get
0:12:11	and if you can also concluded C optimal training time to you compute
0:12:15	converges to the optimal time
0:12:19	and lastly it is it remains to do was to better five as some of that are a some type
0:12:23	to optimal to try to to trust a is very close to the
0:12:28	to to what you would get if you could optimize to problems and some since we simply do mount to
0:12:32	colour based optimization we one many
0:12:35	many you see which training time maximise the or right
0:12:39	um
0:12:40	first of just to show that section a concave function
0:12:43	you see the uh got a get you rate as a function of the training length
0:12:47	would then first different back haul capacity is
0:12:49	so that and that i so i computed of the two most approximation it's to marcus simulation
0:12:56	and and makes sense if you that the so close together
0:12:58	but is you to look at a maximum point some but here it won't make a big difference whether to
0:13:03	optimize
0:13:04	like our approximation or not
0:13:06	and
0:13:08	when i had to all that is for a given
0:13:10	S and a a a a a of a coherence it's time of T one hundred
0:13:14	i so that this optimization problem this is a black man
0:13:18	that's a function of C "'em" S N
0:13:21	but that leads to to an exhaustive search opposed to meant to colour up to a um
0:13:25	yeah simulations and you see that the difference between these two values is actually legible
0:13:30	especially
0:13:31	well that exhaustive search i and to do some kind of a to just search because i current so for
0:13:36	vol
0:13:37	yeah a kind of an infant find groups of values
0:13:40	and that have a
0:13:41	you current to try to twenty point twenty five point three symbols you need to round at some point
0:13:48	okay uh just class to to look at C and of the back haul capacity on the optimal training length
0:13:54	you see that the optimal true as is actually of tobacco capacity
0:13:59	this is so cute
0:14:00	a each affect
0:14:01	but you compress it is no
0:14:03	man says of
0:14:04	the from was used C is actually due to quantisation rose
0:14:08	next right of a quantisation quantization have from a a a try to now
0:14:12	once or capacity bounds are back or lectures and infinite capacity
0:14:16	a train or depends and and so on
0:14:19	yeah on the on this is and nice you have an edge
0:14:24	a of course them just to point out the um
0:14:27	how bad actually are a sub optimal quantisation scheme was so so that's a lot to a
0:14:32	um can see the back haul capacity on the X
0:14:36	well as as the um
0:14:37	and and the go to go we're rate
0:14:40	and for
0:14:42	if you look at is value two point five
0:14:44	this was "'cause" is a um
0:14:46	relative power base station time teller
0:14:49	so if would multiplied by a two because we've to tell us
0:14:52	you would see to a Q chief as like
0:14:54	as a spectral efficiency of five bits per second per channel use
0:14:59	you that to have
0:15:00	twenty bits per second pitch and use of back or pass
0:15:06	yeah to conclude what um
0:15:07	we have used them
0:15:09	results from lot from the matrix you read to tech a you a and optimization problem in context
0:15:15	and have treated to channel is the variance profile of just you like a distributed and in a system was
0:15:19	um with the back haul capacity
0:15:22	uh yeah but we have to on the parents it's is asymptotic approximation but extremely rather for channel it's of
0:15:28	size three times we even to by two works quite well
0:15:31	a it's that it's a pack of back or limitation on the optimal training length
0:15:37	that's well that we can have the cross it's that's you and we work on distributed compression was in perfect
0:15:43	csi
0:15:44	so actually how do you compress when we don't know the channel
0:15:47	so i i i'm not aware of any paper which which problem so someone has some put that would what
0:15:51	have happy to get it
0:15:53	i
0:15:54	last as a question of how to decide whether but require parade or not
0:15:58	and some some that's the back back capacity we go to zero
0:16:01	i ever go to zero as well doesn't make sense because it's space station could at least decode individually
0:16:07	and then be treated like a set of B base station which live in the isolated you are so this
0:16:12	low in to the it's we haven't done it
0:16:16	um
0:16:16	i'd down so the extension a very straight but because when you do to take well some to come pilot
0:16:21	contamination
0:16:22	which happens
0:16:23	because can you to read like your sample training
0:16:27	um
0:16:28	last a just a few references so
0:16:30	we've of can subtract version of for our paper but just
0:16:32	going to be published in june
0:16:34	the transaction on signal processing
0:16:37	um like since
0:16:38	can is that for uh
0:16:40	right the as was about as but from bonnie touch and
0:16:44	of can see a classic paper or for for do that just just a good point a if you don't
0:16:48	know so much about that of my nose is over you paper by provide just back
0:16:53	and
0:16:54	yeah that that that you
0:17:21	yeah
0:17:28	okay
0:17:28	so we could have assumed from the beginning
0:17:31	that's a variance of the channel it's as one of a and
0:17:35	uh so as a classical assumption and people start it could be don't of
0:17:39	i i and on channel but each element like has the energy
0:17:43	you know just so from the big have an energy was i a channel was the a finite energy the
0:17:48	fresh start a is that it can't gain one more G you U and the back up some more energy
0:17:54	then work was actually sent right
0:17:56	so
0:17:57	we kind of either start to directly but making this assumption
0:18:00	a a some scale as a parallel
0:18:03	by a some so which goes to infinity that's the power up uh frequency band goes to zero
0:18:09	and the and it doesn't make a diff
0:18:13	yeah
0:18:17	yes you but infinite double T and it's a good i mean it's some point if you have but a
0:18:22	station it's a very far where you can let's this diversity
0:18:25	so that's is a reasonable assumption and for the scale in the N is C have used
0:18:30	we subcarrier
0:18:32	so in some since you didn't scale at all
0:18:35	and
0:18:35	so
0:18:36	much much Q do but to that mathematically correct you something new to
0:18:41	to this kind of scale the energy per uh
0:18:44	for channel and she was go to zero otherwise this doesn't work

ON OPTIMAL CHANNEL TRAINING FOR UPLINK NETWORK MIMO SYSTEMS

Multiuser and Network MIMO

Přednášející: Jakob Hoydis, Autoři: Jakob Hoydis, Mari Kobayashi, Mérouane Debbah, Supélec, France