uh my is the weight down from a nation which in wireless didn't i one

and this that's and it's to work with my

uh the member

when you one and uh my of my

a original and G at an much more in

and uh with

it's so we can model and the province and and so and that's when is you most new home

oh this work

with that screen how see the uh

then the model use of owning since the

there's a just me to want to communicate with a set of

single can use uses using chance may people

do to maybe beamforming uh

just meet that has to know the channel state information

already used

so you wisest as

and i can T D system is then

to never transmitted to obtain channel state information the user has to to uh bring the chain

or you may have a dc since then users have to feed back their channel state information to adjust meat

in our in

i don't case

no it doesn't

like in

you need is that the

that channel estimation maybe be perfect or in F T D distance

you to find a feedback the channel estimation may also be the train no information it just a meeting

may also be of

so the core over this work is try to decide a

we mean vectors like best night okay and

a low passed okay and thirty C as i

so we you know a D S the number just me obtain a set just meet and

case than um uh pay

a the number of them go to not use a

it you i is the i-th uses channel that to

and uh you i

involving that the used to chat me information a

i you

so

but a of or use i K is given by T equation here

the you rate is the single in power and that this is called no interference

and the signal my scores uh

noise power

oh

if we assume that just meta has a

perfect csi

then a a you to uh

it design for is given by is power minimization problem

which i to minimize the which powers

a such a that such a a a a subject to the constraint is

that each are we use that can achieve

that design snr requirement

come i

so this problem has been we'll start

a a you can use like

a the counting your eighteen you can use them at that do dictation all

you can be formulated problem

signal to calm program and it's be efficient

so it's i say that all this work we can see that that that

just need to either

as the perfect i

so

like we you not edge i S the a channel a able to is meet

then this edge i've are what be if will found the true channel H I and that the difference

yeah i is the csi M

or this work we soon the

i are are a and then in the following in the complex gaussian distribution with zero mean

and variance

combines matches the i

which is a positive semidefinite

so in the presence of a C is i ever as the receiver the user is going to

are going to suffer from a a a it's an all T

so

the core of the people mean he the people and idea to try to decide is W I i

such a i'd the

each of the receivers can achieve that is an hour requirement with a very high probability

so

that's a common to say in i'd the we want each of a use can achieve a high it's than

not if for collision probability so one this one

this

this probably probability in because to one

so that's but look at of what's going

what's the to be call and you call set if occlusion probability of number of past design i

this is a simulation example

we can see the a and D a cape with a three and the noise covariance matches all one or

two

which is uncorrelated and see my score is four point no one

then

a a this is the result

all of he spoke when of P and P recall and snr

setting fiction probably

is the full call mike a fine

do you can eve only it's speaker for most of the cases

no achieve a a a chip it's i not significant in probability is best ten

or point fine which implies that more than fifteen percent that

that users will suffer from a snr outage

so if the what this to a should make it even was

if we can see the if we're is use require required

even higher is not required

the goal here is try to design a beamformer

to move these pointed to

a a a like in as close to one

like if want a a a each use that to what

a a nineteen percent sinr i do not puppy eighteen

then want to these points to move to a and sum up

so uh

that uh uh as you know that no i it's uh next mark of voice an outage probability for use

uh

then i'll can see that design formulation is

yeah

we want to minimize just medium power and the subject to a constraint that

each user will have a a a a as i not satisfaction probability of each user a

is an or less than one minus low i

but is problem is

if typical

because but so you can write to this problem is probably reading you court in a sort of a you

and the U see died to the argument of these probability functions

which is

not convex

with was that respect to that i

this first

point

second is so to the best of our knowledge we can uh find a a close form inspiration

for is probability

oh also but existing works

they focus on of a uh

two

uh folks on

some approximation that's S

like

the one by my question or the even is be in two thousand a

they use the probabilistic a it's are not constrained as all she problem

as a approximation

our previous work we use a was case robust be from design as an approximation

is to methods up score coding brown to a

a console if that's S which means the up ten approximate solutions

okay in to be feasible

the original design problem is would in price these probably be it's i'm not sitting fixation probably

is getting to be set you five

or these work are we are going to present a a a a a a new mass says that we

be shown to perform better than

no previous work

so the first stage that we use "'em" at that in addition

we try to remove it this non-convex in arguments of these probably in found

in that used as the a will be price each of the rank one mention is W i that information

by a cost use them at that frame match kept a copy i we sought out any

true

so we end up with this

probably a bit in culture

so a rate at in your life in these

oh argument that does not help too much because

is a probability of changed the old

a has not from

it's

oh next they or try to approximate

you can see that these E I S complex comes so these probably in

a training can be a

uh a an S it is up to form that

is the court form

of complex comes the the both

is the pop been you quality of called ready for complex culture of in the right

the want to find approximation to this

yeah quote

uh

all that's that's based on these they

we

is the name of a died uh if we we have a

how but cost to the better

back to and uh we have Q are it's up to but

therefore for any you know which you

braun to one to going to one

and

for these these right is

the probability of these quite return grading equal to T

is given by Q

is

oh is no less than one may scroll so these is going to host to it's it's that in this

T

is a

it is a

that you right

at that thing are functions of these low R S is given parameter is and the this low

is

a Q R S P given problem in in this

all uh two probability

a the problem you quality in these the post and type in you quality so but this person typing court

uh that's

you do will refer to at least you in up was time watching

means that they are you qualities not problems that to probability team

of of sound of random variables be eighteen functions mean like

the

mark of in you quarantine

could be shipping quarter know that one of buttons and train the open to leave

but typing court

so actually is can help us a lot

using the above a i can show like that these conditions is going to be a sufficient condition for achieving

these probability quality

so the the same for in you court

these can you question here is that

this is deterministic and no

probability in this in which

so we can use this equation in you

equation as an approximation

to these probability in you quality

so

so the think was is not as if we you you can see I D in quality may a are

quite about the which is not convex

but that a crucial observation so actually

and and use uses some slack variables

you can

before my

these can you quality S is well come S and constraints

which in price we can use these for a convex constraints that's a approximation

to these probability inequality

so we can right this idea to each of the

uh i an a certification probably give users then we

are up with these

how mix problem

so it you can check each the file of D function all constraints all

so we can stop with a very efficient

uh because we use S T are so one probably is that the up that we should may not be

rank one

and in that case we have to use some additional as was an approximation procedures like

comes in the might agents

to obtain a rank one approximate solution

but a quite surprisingly all some racial results if fall the knight's very where

it does it six have look solutions is very rare

to obtain a hiring solution

so like the preset

some to measure results we consider a a a a simple case of speech as me a you know as

we use as

but

a channel estimate that just is uh

a complex gaussian distribution

the

all to probability

or point one and a noise variance of point one

the csi comments metrics is or one two which is as window the errors that are uncorrelated this

especially

so we first look go drink once that which

you we say a a a a few ice rank one face

the ratio of the largest eigenvalue of of be one

to a ways to is it's great and you go to

or point nine nine so which you

in bright light that uh

that may have mike can batteries are around a to times larger than T a race of a very

a and we say i the the problem will people link one some J for W I they all say

to find his condition

so these this that's to the first lois estimation results

for low like what to a point one which missed nineteen percent out

is a not to defect region probably it

and the teacher or to here that you know had to

means that non ball

uh be

feed the about channel is we test it and that the you might take here use a

the number or channel or i'd H for which are bank once so which is up to a

so you can see from here to for or phone got mike to one two

the fifteen

fifteen

that

that's a one two percent that

we all of ten one solution

but if if we

that no i point open or one which implies that more demanding the phones requirement

then we encode the case

a a column i with see

three db and is one problem channel died vision that the so which change not bring one

but if we do in

for the you'll find a i'd uh for this particular case

the the these ratio show a lot or point a or a two to or series of which that's is

also quite close to a link so which is so if you use

got the minimization best going you obtain quite

quite good performance

the

so that they can we want to check if the proposed approximation formulation can

so you find a it's an set if probably due not

yeah we also compare with the mess by my question or time the in them is an it is what

you

and this is our previous work

is is the proposed to that's in this

in this work

the we can see that

or or next we S can see defined a desired like ninety percent

certificates fiction would be at but you can see that

a this one seems to kinds about if

because we only one ninety percent

it gives you want to per

is once is and this white

the proposed a given

is given beta

so

that's so we want to compare a transmission power

and here the recognise uh

one by mac channel that that this one is by

a previous work in this one is the proposed will

the problem lies uh

just mission power not low design so which can

so as a benchmark for

these robots robust

again we can see these figures i full

from got got model in to find one to nineteen is that's going in the

propose a have its most power you fish

you want to compare the computational complexity in the stream S

yeah we can pick uh will compute the

that i

the time of C V X

solving the form a nation is of each for the mess on the test

then you can see that a a going to of proposed method more

a computationally efficient then that one

proposed

by i'm sure that and but it's

more computational

expensive it in our previous work

so this is a a a cup and the performance trade

but to in uh

the work proposed in this

the the the mess the proposed in his work and our previous work

so in summary uh we have a pretty sent uh

new approximation for a probably probably if the

it's i not constrained

robust beamforming problem

and that the to all mess up a some to in great the to in gradient

the first it's segment that and relaxation

that's second is a

but and typing you according which you so so

convex

comes of better approximation to a probability you cost straight

then estimation result have shown that the proposed method based quite

a of X six in message

thank

i we asked or sometimes all questions uh and questions from the audience

oh in a single question because i one of the corpus

you have to ask

with the money

microphone for simple

okay so i was here just out of it to i apologise to that

um but it is your you approximation a conservative one or or is that the

you can so what he is it is

okay

that's what i would of to the beginning thanks

think

but actual one have a few words so is

restriction and and them relaxation

relaxation this semi-definite relaxation and restriction is with the pop up this the constraint

yeah

so that run realisation when you get to to rank to solution

can be sure that to

wasn't and rank one solutions to

sorry

a a in this scenario when you a the uh will find a rank two solution

it could to be rank one solution will so

to me

mean and you to the X the france one or of the this the set of solution perhaps

could to be used at

some under solution that's rank one

i i i not sure if i'll

correct

you mean when you to

so you me vibe obtain a drink two solution

then

that even if you obtain the rank

two solution the might excess

my one solution that you

C doesn't happen to find

uh i

uh

this is the response is one strange

oh is this

so yeah that you calm down brand

when one that were then when one solution

in in nineteen nine nine nine nine percent of cases is just run what

well do what would you mind can scroll back to

a the situation now or or or do the the back here yeah at the situation where we see round

one

well here we you very strange shape see a one room a situation

but this right and you can use some other tricks to get around the

i don't questions

okay can you just a normal one that's past the speaker