0:00:13uh my is the weight down from a nation which in wireless didn't i one
0:00:16and this that's and it's to work with my
0:00:19uh the member
0:00:20when you one and uh my of my
0:00:23a original and G at an much more in
0:00:25and uh with
0:00:26it's so we can model and the province and and so and that's when is you most new home
0:00:33oh this work
0:00:34with that screen how see the uh
0:00:35then the model use of owning since the
0:00:38there's a just me to want to communicate with a set of
0:00:41single can use uses using chance may people
0:00:45do to maybe beamforming uh
0:00:46just meet that has to know the channel state information
0:00:49already used
0:00:50so you wisest as
0:00:52and i can T D system is then
0:00:55to never transmitted to obtain channel state information the user has to to uh bring the chain
0:01:00or you may have a dc since then users have to feed back their channel state information to adjust meat
0:01:05in our in
0:01:06i don't case
0:01:08no it doesn't
0:01:09like in
0:01:10you need is that the
0:01:11that channel estimation maybe be perfect or in F T D distance
0:01:15you to find a feedback the channel estimation may also be the train no information it just a meeting
0:01:20may also be of
0:01:21so the core over this work is try to decide a
0:01:24we mean vectors like best night okay and
0:01:27a low passed okay and thirty C as i
0:01:31so we you know a D S the number just me obtain a set just meet and
0:01:35case than um uh pay
0:01:37a the number of them go to not use a
0:01:40it you i is the i-th uses channel that to
0:01:42and uh you i
0:01:44involving that the used to chat me information a
0:01:47i you
0:01:49but a of or use i K is given by T equation here
0:01:53the you rate is the single in power and that this is called no interference
0:01:57and the signal my scores uh
0:01:59noise power
0:02:01if we assume that just meta has a
0:02:03perfect csi
0:02:04then a a you to uh
0:02:06it design for is given by is power minimization problem
0:02:10which i to minimize the which powers
0:02:12a such a that such a a a a subject to the constraint is
0:02:15that each are we use that can achieve
0:02:17that design snr requirement
0:02:19come i
0:02:21so this problem has been we'll start
0:02:23a a you can use like
0:02:24a the counting your eighteen you can use them at that do dictation all
0:02:29you can be formulated problem
0:02:30signal to calm program and it's be efficient
0:02:34so it's i say that all this work we can see that that that
0:02:37just need to either
0:02:38as the perfect i
0:02:40like we you not edge i S the a channel a able to is meet
0:02:45then this edge i've are what be if will found the true channel H I and that the difference
0:02:50yeah i is the csi M
0:02:53or this work we soon the
0:02:55i are are a and then in the following in the complex gaussian distribution with zero mean
0:03:00and variance
0:03:02combines matches the i
0:03:03which is a positive semidefinite
0:03:07so in the presence of a C is i ever as the receiver the user is going to
0:03:11are going to suffer from a a a it's an all T
0:03:17the core of the people mean he the people and idea to try to decide is W I i
0:03:21such a i'd the
0:03:23each of the receivers can achieve that is an hour requirement with a very high probability
0:03:29that's a common to say in i'd the we want each of a use can achieve a high it's than
0:03:33not if for collision probability so one this one
0:03:37this probably probability in because to one
0:03:40so that's but look at of what's going
0:03:43what's the to be call and you call set if occlusion probability of number of past design i
0:03:49this is a simulation example
0:03:51we can see the a and D a cape with a three and the noise covariance matches all one or
0:03:56which is uncorrelated and see my score is four point no one
0:04:01a a this is the result
0:04:02all of he spoke when of P and P recall and snr
0:04:05setting fiction probably
0:04:07is the full call mike a fine
0:04:09do you can eve only it's speaker for most of the cases
0:04:12no achieve a a a chip it's i not significant in probability is best ten
0:04:16or point fine which implies that more than fifteen percent that
0:04:20that users will suffer from a snr outage
0:04:23so if the what this to a should make it even was
0:04:26if we can see the if we're is use require required
0:04:29even higher is not required
0:04:31the goal here is try to design a beamformer
0:04:34to move these pointed to
0:04:36a a a like in as close to one
0:04:38like if want a a a each use that to what
0:04:41a a nineteen percent sinr i do not puppy eighteen
0:04:44then want to these points to move to a and sum up
0:04:50so uh
0:04:52that uh uh as you know that no i it's uh next mark of voice an outage probability for use
0:04:58then i'll can see that design formulation is
0:05:01we want to minimize just medium power and the subject to a constraint that
0:05:05each user will have a a a a as i not satisfaction probability of each user a
0:05:11is an or less than one minus low i
0:05:14but is problem is
0:05:15if typical
0:05:16because but so you can write to this problem is probably reading you court in a sort of a you
0:05:21and the U see died to the argument of these probability functions
0:05:24which is
0:05:25not convex
0:05:27with was that respect to that i
0:05:28this first
0:05:30second is so to the best of our knowledge we can uh find a a close form inspiration
0:05:34for is probability
0:05:37oh also but existing works
0:05:39they focus on of a uh
0:05:42uh folks on
0:05:43some approximation that's S
0:05:46the one by my question or the even is be in two thousand a
0:05:49they use the probabilistic a it's are not constrained as all she problem
0:05:53as a approximation
0:05:55our previous work we use a was case robust be from design as an approximation
0:06:00is to methods up score coding brown to a
0:06:03a console if that's S which means the up ten approximate solutions
0:06:07okay in to be feasible
0:06:09the original design problem is would in price these probably be it's i'm not sitting fixation probably
0:06:15is getting to be set you five
0:06:18or these work are we are going to present a a a a a a new mass says that we
0:06:22be shown to perform better than
0:06:23no previous work
0:06:26so the first stage that we use "'em" at that in addition
0:06:29we try to remove it this non-convex in arguments of these probably in found
0:06:34in that used as the a will be price each of the rank one mention is W i that information
0:06:39by a cost use them at that frame match kept a copy i we sought out any
0:06:43so we end up with this
0:06:45probably a bit in culture
0:06:47so a rate at in your life in these
0:06:50oh argument that does not help too much because
0:06:52is a probability of changed the old
0:06:54a has not from
0:06:57oh next they or try to approximate
0:07:00you can see that these E I S complex comes so these probably in
0:07:05a training can be a
0:07:07uh a an S it is up to form that
0:07:09is the court form
0:07:11of complex comes the the both
0:07:13is the pop been you quality of called ready for complex culture of in the right
0:07:18the want to find approximation to this
0:07:20yeah quote
0:07:23all that's that's based on these they
0:07:25is the name of a died uh if we we have a
0:07:28how but cost to the better
0:07:30back to and uh we have Q are it's up to but
0:07:33therefore for any you know which you
0:07:34braun to one to going to one
0:07:37for these these right is
0:07:39the probability of these quite return grading equal to T
0:07:42is given by Q
0:07:44oh is no less than one may scroll so these is going to host to it's it's that in this
0:07:48is a
0:07:49it is a
0:07:51that you right
0:07:52at that thing are functions of these low R S is given parameter is and the this low
0:07:57a Q R S P given problem in in this
0:07:59all uh two probability
0:08:02a the problem you quality in these the post and type in you quality so but this person typing court
0:08:08uh that's
0:08:09you do will refer to at least you in up was time watching
0:08:13means that they are you qualities not problems that to probability team
0:08:17of of sound of random variables be eighteen functions mean like
0:08:22mark of in you quarantine
0:08:23could be shipping quarter know that one of buttons and train the open to leave
0:08:28but typing court
0:08:30so actually is can help us a lot
0:08:33using the above a i can show like that these conditions is going to be a sufficient condition for achieving
0:08:38these probability quality
0:08:40so the the same for in you court
0:08:42these can you question here is that
0:08:45this is deterministic and no
0:08:47probability in this in which
0:08:51so we can use this equation in you
0:08:53equation as an approximation
0:08:55to these probability in you quality
0:08:59so the think was is not as if we you you can see I D in quality may a are
0:09:03quite about the which is not convex
0:09:06but that a crucial observation so actually
0:09:09and and use uses some slack variables
0:09:11you can
0:09:12before my
0:09:13these can you quality S is well come S and constraints
0:09:17which in price we can use these for a convex constraints that's a approximation
0:09:21to these probability inequality
0:09:23so we can right this idea to each of the
0:09:26uh i an a certification probably give users then we
0:09:30are up with these
0:09:31how mix problem
0:09:32so it you can check each the file of D function all constraints all
0:09:36so we can stop with a very efficient
0:09:40uh because we use S T are so one probably is that the up that we should may not be
0:09:44rank one
0:09:46and in that case we have to use some additional as was an approximation procedures like
0:09:50comes in the might agents
0:09:52to obtain a rank one approximate solution
0:09:54but a quite surprisingly all some racial results if fall the knight's very where
0:09:58it does it six have look solutions is very rare
0:10:01to obtain a hiring solution
0:10:05so like the preset
0:10:06some to measure results we consider a a a a simple case of speech as me a you know as
0:10:10we use as
0:10:12a channel estimate that just is uh
0:10:14a complex gaussian distribution
0:10:17all to probability
0:10:18or point one and a noise variance of point one
0:10:22the csi comments metrics is or one two which is as window the errors that are uncorrelated this
0:10:30so we first look go drink once that which
0:10:33you we say a a a a few ice rank one face
0:10:36the ratio of the largest eigenvalue of of be one
0:10:39to a ways to is it's great and you go to
0:10:42or point nine nine so which you
0:10:44in bright light that uh
0:10:45that may have mike can batteries are around a to times larger than T a race of a very
0:10:51a and we say i the the problem will people link one some J for W I they all say
0:10:56to find his condition
0:10:58so these this that's to the first lois estimation results
0:11:01for low like what to a point one which missed nineteen percent out
0:11:05is a not to defect region probably it
0:11:07and the teacher or to here that you know had to
0:11:09means that non ball
0:11:11uh be
0:11:12feed the about channel is we test it and that the you might take here use a
0:11:17the number or channel or i'd H for which are bank once so which is up to a
0:11:21so you can see from here to for or phone got mike to one two
0:11:25the fifteen
0:11:27that's a one two percent that
0:11:29we all of ten one solution
0:11:31but if if we
0:11:33that no i point open or one which implies that more demanding the phones requirement
0:11:38then we encode the case
0:11:41a a column i with see
0:11:42three db and is one problem channel died vision that the so which change not bring one
0:11:47but if we do in
0:11:49for the you'll find a i'd uh for this particular case
0:11:52the the these ratio show a lot or point a or a two to or series of which that's is
0:11:58also quite close to a link so which is so if you use
0:12:01got the minimization best going you obtain quite
0:12:04quite good performance
0:12:07so that they can we want to check if the proposed approximation formulation can
0:12:13so you find a it's an set if probably due not
0:12:16yeah we also compare with the mess by my question or time the in them is an it is what
0:12:21and this is our previous work
0:12:23is is the proposed to that's in this
0:12:26in this work
0:12:27the we can see that
0:12:28or or next we S can see defined a desired like ninety percent
0:12:33certificates fiction would be at but you can see that
0:12:36a this one seems to kinds about if
0:12:38because we only one ninety percent
0:12:40it gives you want to per
0:12:42is once is and this white
0:12:44the proposed a given
0:12:45is given beta
0:12:49that's so we want to compare a transmission power
0:12:52and here the recognise uh
0:12:54one by mac channel that that this one is by
0:12:57a previous work in this one is the proposed will
0:12:59the problem lies uh
0:13:01just mission power not low design so which can
0:13:04so as a benchmark for
0:13:06these robots robust
0:13:07again we can see these figures i full
0:13:10from got got model in to find one to nineteen is that's going in the
0:13:14propose a have its most power you fish
0:13:18you want to compare the computational complexity in the stream S
0:13:22yeah we can pick uh will compute the
0:13:25that i
0:13:26the time of C V X
0:13:27solving the form a nation is of each for the mess on the test
0:13:31then you can see that a a going to of proposed method more
0:13:35a computationally efficient then that one
0:13:39by i'm sure that and but it's
0:13:42more computational
0:13:43expensive it in our previous work
0:13:45so this is a a a cup and the performance trade
0:13:48but to in uh
0:13:50the work proposed in this
0:13:51the the the mess the proposed in his work and our previous work
0:13:56so in summary uh we have a pretty sent uh
0:14:00new approximation for a probably probably if the
0:14:03it's i not constrained
0:14:05robust beamforming problem
0:14:06and that the to all mess up a some to in great the to in gradient
0:14:11the first it's segment that and relaxation
0:14:13that's second is a
0:14:14but and typing you according which you so so
0:14:18comes of better approximation to a probability you cost straight
0:14:23then estimation result have shown that the proposed method based quite
0:14:26a of X six in message
0:14:36i we asked or sometimes all questions uh and questions from the audience
0:14:40oh in a single question because i one of the corpus
0:14:56you have to ask
0:14:57with the money
0:14:58microphone for simple
0:15:02okay so i was here just out of it to i apologise to that
0:15:05um but it is your you approximation a conservative one or or is that the
0:15:11you can so what he is it is
0:15:14that's what i would of to the beginning thanks
0:15:17but actual one have a few words so is
0:15:20restriction and and them relaxation
0:15:23relaxation this semi-definite relaxation and restriction is with the pop up this the constraint
0:15:35so that run realisation when you get to to rank to solution
0:15:39can be sure that to
0:15:40wasn't and rank one solutions to
0:15:44a a in this scenario when you a the uh will find a rank two solution
0:15:49it could to be rank one solution will so
0:15:53to me
0:15:54mean and you to the X the france one or of the this the set of solution perhaps
0:15:59could to be used at
0:16:00some under solution that's rank one
0:16:03i i i not sure if i'll
0:16:06you mean when you to
0:16:08so you me vibe obtain a drink two solution
0:16:12that even if you obtain the rank
0:16:14two solution the might excess
0:16:16my one solution that you
0:16:17C doesn't happen to find
0:16:19uh i
0:16:23this is the response is one strange
0:16:26oh is this
0:16:28so yeah that you calm down brand
0:16:31when one that were then when one solution
0:16:33in in nineteen nine nine nine nine percent of cases is just run what
0:16:37well do what would you mind can scroll back to
0:16:40a the situation now or or or do the the back here yeah at the situation where we see round
0:16:46well here we you very strange shape see a one room a situation
0:16:51but this right and you can use some other tricks to get around the
0:16:58i don't questions
0:17:02okay can you just a normal one that's past the speaker