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