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