0:00:13 | uh my is the weight down from a nation which in wireless didn't i one |
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0:00:16 | and this that's and it's to work with my |

0:00:19 | uh the member |

0:00:20 | when you one and uh my of my |

0:00:23 | a original and G at an much more in |

0:00:25 | and uh with |

0:00:26 | it's so we can model and the province and and so and that's when is you most new home |

0:00:33 | oh this work |

0:00:34 | with that screen how see the uh |

0:00:35 | then the model use of owning since the |

0:00:38 | there's a just me to want to communicate with a set of |

0:00:41 | single can use uses using chance may people |

0:00:45 | do to maybe beamforming uh |

0:00:46 | just meet that has to know the channel state information |

0:00:49 | already used |

0:00:50 | so you wisest as |

0:00:52 | and i can T D system is then |

0:00:55 | to never transmitted to obtain channel state information the user has to to uh bring the chain |

0:01:00 | or you may have a dc since then users have to feed back their channel state information to adjust meat |

0:01:05 | in our in |

0:01:06 | i don't case |

0:01:08 | no it doesn't |

0:01:09 | like in |

0:01:10 | you need is that the |

0:01:11 | that channel estimation maybe be perfect or in F T D distance |

0:01:15 | you to find a feedback the channel estimation may also be the train no information it just a meeting |

0:01:20 | may also be of |

0:01:21 | so the core over this work is try to decide a |

0:01:24 | we mean vectors like best night okay and |

0:01:27 | a low passed okay and thirty C as i |

0:01:31 | so we you know a D S the number just me obtain a set just meet and |

0:01:35 | case than um uh pay |

0:01:37 | a the number of them go to not use a |

0:01:40 | it you i is the i-th uses channel that to |

0:01:42 | and uh you i |

0:01:44 | involving that the used to chat me information a |

0:01:47 | i you |

0:01:48 | so |

0:01:49 | but a of or use i K is given by T equation here |

0:01:53 | the you rate is the single in power and that this is called no interference |

0:01:57 | and the signal my scores uh |

0:01:59 | noise power |

0:02:00 | oh |

0:02:01 | if we assume that just meta has a |

0:02:03 | perfect csi |

0:02:04 | then a a you to uh |

0:02:06 | it design for is given by is power minimization problem |

0:02:10 | which i to minimize the which powers |

0:02:12 | a such a that such a a a a subject to the constraint is |

0:02:15 | that each are we use that can achieve |

0:02:17 | that design snr requirement |

0:02:19 | come i |

0:02:21 | so this problem has been we'll start |

0:02:23 | a a you can use like |

0:02:24 | a the counting your eighteen you can use them at that do dictation all |

0:02:29 | you can be formulated problem |

0:02:30 | signal to calm program and it's be efficient |

0:02:34 | so it's i say that all this work we can see that that that |

0:02:37 | just need to either |

0:02:38 | as the perfect i |

0:02:39 | so |

0:02:40 | like we you not edge i S the a channel a able to is meet |

0:02:45 | then this edge i've are what be if will found the true channel H I and that the difference |

0:02:50 | yeah i is the csi M |

0:02:53 | or this work we soon the |

0:02:55 | i are are a and then in the following in the complex gaussian distribution with zero mean |

0:03:00 | and variance |

0:03:02 | combines matches the i |

0:03:03 | which is a positive semidefinite |

0:03:07 | so in the presence of a C is i ever as the receiver the user is going to |

0:03:11 | are going to suffer from a a a it's an all T |

0:03:15 | so |

0:03:17 | the core of the people mean he the people and idea to try to decide is W I i |

0:03:21 | such a i'd the |

0:03:23 | each of the receivers can achieve that is an hour requirement with a very high probability |

0:03:28 | so |

0:03:29 | that's a common to say in i'd the we want each of a use can achieve a high it's than |

0:03:33 | not if for collision probability so one this one |

0:03:36 | this |

0:03:37 | this probably probability in because to one |

0:03:40 | so that's but look at of what's going |

0:03:43 | what's the to be call and you call set if occlusion probability of number of past design i |

0:03:49 | this is a simulation example |

0:03:51 | we can see the a and D a cape with a three and the noise covariance matches all one or |

0:03:55 | two |

0:03:56 | which is uncorrelated and see my score is four point no one |

0:04:00 | then |

0:04:01 | a a this is the result |

0:04:02 | all of he spoke when of P and P recall and snr |

0:04:05 | setting fiction probably |

0:04:07 | is the full call mike a fine |

0:04:09 | do you can eve only it's speaker for most of the cases |

0:04:12 | no achieve a a a chip it's i not significant in probability is best ten |

0:04:16 | or point fine which implies that more than fifteen percent that |

0:04:20 | that users will suffer from a snr outage |

0:04:23 | so if the what this to a should make it even was |

0:04:26 | if we can see the if we're is use require required |

0:04:29 | even higher is not required |

0:04:31 | the goal here is try to design a beamformer |

0:04:34 | to move these pointed to |

0:04:36 | a a a like in as close to one |

0:04:38 | like if want a a a each use that to what |

0:04:41 | a a nineteen percent sinr i do not puppy eighteen |

0:04:44 | then want to these points to move to a and sum up |

0:04:50 | so uh |

0:04:52 | that uh uh as you know that no i it's uh next mark of voice an outage probability for use |

0:04:57 | uh |

0:04:58 | then i'll can see that design formulation is |

0:05:01 | yeah |

0:05:01 | we want to minimize just medium power and the subject to a constraint that |

0:05:05 | each user will have a a a a as i not satisfaction probability of each user a |

0:05:11 | is an or less than one minus low i |

0:05:14 | but is problem is |

0:05:15 | if typical |

0:05:16 | because but so you can write to this problem is probably reading you court in a sort of a you |

0:05:21 | and the U see died to the argument of these probability functions |

0:05:24 | which is |

0:05:25 | not convex |

0:05:27 | with was that respect to that i |

0:05:28 | this first |

0:05:29 | point |

0:05:30 | second is so to the best of our knowledge we can uh find a a close form inspiration |

0:05:34 | for is probability |

0:05:37 | oh also but existing works |

0:05:39 | they focus on of a uh |

0:05:41 | two |

0:05:42 | uh folks on |

0:05:43 | some approximation that's S |

0:05:45 | like |

0:05:46 | the one by my question or the even is be in two thousand a |

0:05:49 | they use the probabilistic a it's are not constrained as all she problem |

0:05:53 | as a approximation |

0:05:55 | our previous work we use a was case robust be from design as an approximation |

0:06:00 | is to methods up score coding brown to a |

0:06:03 | a console if that's S which means the up ten approximate solutions |

0:06:07 | okay in to be feasible |

0:06:09 | the original design problem is would in price these probably be it's i'm not sitting fixation probably |

0:06:15 | is getting to be set you five |

0:06:18 | or these work are we are going to present a a a a a a new mass says that we |

0:06:22 | be shown to perform better than |

0:06:23 | no previous work |

0:06:26 | so the first stage that we use "'em" at that in addition |

0:06:29 | we try to remove it this non-convex in arguments of these probably in found |

0:06:34 | in that used as the a will be price each of the rank one mention is W i that information |

0:06:39 | by a cost use them at that frame match kept a copy i we sought out any |

0:06:43 | true |

0:06:43 | so we end up with this |

0:06:45 | probably a bit in culture |

0:06:47 | so a rate at in your life in these |

0:06:50 | oh argument that does not help too much because |

0:06:52 | is a probability of changed the old |

0:06:54 | a has not from |

0:06:55 | it's |

0:06:57 | oh next they or try to approximate |

0:07:00 | you can see that these E I S complex comes so these probably in |

0:07:05 | a training can be a |

0:07:07 | uh a an S it is up to form that |

0:07:09 | is the court form |

0:07:11 | of complex comes the the both |

0:07:13 | is the pop been you quality of called ready for complex culture of in the right |

0:07:18 | the want to find approximation to this |

0:07:20 | yeah quote |

0:07:21 | uh |

0:07:23 | all that's that's based on these they |

0:07:25 | we |

0:07:25 | is the name of a died uh if we we have a |

0:07:28 | how but cost to the better |

0:07:30 | back to and uh we have Q are it's up to but |

0:07:33 | therefore for any you know which you |

0:07:34 | braun to one to going to one |

0:07:36 | and |

0:07:37 | for these these right is |

0:07:39 | the probability of these quite return grading equal to T |

0:07:42 | is given by Q |

0:07:43 | is |

0:07:44 | oh is no less than one may scroll so these is going to host to it's it's that in this |

0:07:48 | T |

0:07:48 | is a |

0:07:49 | it is a |

0:07:51 | that you right |

0:07:52 | at that thing are functions of these low R S is given parameter is and the this low |

0:07:56 | is |

0:07:57 | a Q R S P given problem in in this |

0:07:59 | all uh two probability |

0:08:02 | a the problem you quality in these the post and type in you quality so but this person typing court |

0:08:08 | uh that's |

0:08:09 | you do will refer to at least you in up was time watching |

0:08:13 | means that they are you qualities not problems that to probability team |

0:08:17 | of of sound of random variables be eighteen functions mean like |

0:08:21 | the |

0:08:22 | mark of in you quarantine |

0:08:23 | could be shipping quarter know that one of buttons and train the open to leave |

0:08:28 | but typing court |

0:08:30 | so actually is can help us a lot |

0:08:33 | using the above a i can show like that these conditions is going to be a sufficient condition for achieving |

0:08:38 | these probability quality |

0:08:40 | so the the same for in you court |

0:08:42 | these can you question here is that |

0:08:45 | this is deterministic and no |

0:08:47 | probability in this in which |

0:08:51 | so we can use this equation in you |

0:08:53 | equation as an approximation |

0:08:55 | to these probability in you quality |

0:08:58 | so |

0:08:59 | so the think was is not as if we you you can see I D in quality may a are |

0:09:03 | quite about the which is not convex |

0:09:06 | but that a crucial observation so actually |

0:09:09 | and and use uses some slack variables |

0:09:11 | you can |

0:09:12 | before my |

0:09:13 | these can you quality S is well come S and constraints |

0:09:17 | which in price we can use these for a convex constraints that's a approximation |

0:09:21 | to these probability inequality |

0:09:23 | so we can right this idea to each of the |

0:09:26 | uh i an a certification probably give users then we |

0:09:30 | are up with these |

0:09:31 | how mix problem |

0:09:32 | so it you can check each the file of D function all constraints all |

0:09:36 | so we can stop with a very efficient |

0:09:40 | uh because we use S T are so one probably is that the up that we should may not be |

0:09:44 | rank one |

0:09:46 | and in that case we have to use some additional as was an approximation procedures like |

0:09:50 | comes in the might agents |

0:09:52 | to obtain a rank one approximate solution |

0:09:54 | but a quite surprisingly all some racial results if fall the knight's very where |

0:09:58 | it does it six have look solutions is very rare |

0:10:01 | to obtain a hiring solution |

0:10:05 | so like the preset |

0:10:06 | some to measure results we consider a a a a simple case of speech as me a you know as |

0:10:10 | we use as |

0:10:11 | but |

0:10:12 | a channel estimate that just is uh |

0:10:14 | a complex gaussian distribution |

0:10:16 | the |

0:10:17 | all to probability |

0:10:18 | or point one and a noise variance of point one |

0:10:22 | the csi comments metrics is or one two which is as window the errors that are uncorrelated this |

0:10:28 | especially |

0:10:30 | so we first look go drink once that which |

0:10:33 | you we say a a a a few ice rank one face |

0:10:36 | the ratio of the largest eigenvalue of of be one |

0:10:39 | to a ways to is it's great and you go to |

0:10:42 | or point nine nine so which you |

0:10:44 | in bright light that uh |

0:10:45 | that may have mike can batteries are around a to times larger than T a race of a very |

0:10:51 | a and we say i the the problem will people link one some J for W I they all say |

0:10:56 | to find his condition |

0:10:58 | so these this that's to the first lois estimation results |

0:11:01 | for low like what to a point one which missed nineteen percent out |

0:11:05 | is a not to defect region probably it |

0:11:07 | and the teacher or to here that you know had to |

0:11:09 | means that non ball |

0:11:11 | uh be |

0:11:12 | feed the about channel is we test it and that the you might take here use a |

0:11:17 | the number or channel or i'd H for which are bank once so which is up to a |

0:11:21 | so you can see from here to for or phone got mike to one two |

0:11:25 | the fifteen |

0:11:26 | fifteen |

0:11:27 | that |

0:11:27 | that's a one two percent that |

0:11:29 | we all of ten one solution |

0:11:31 | but if if we |

0:11:33 | that no i point open or one which implies that more demanding the phones requirement |

0:11:38 | then we encode the case |

0:11:41 | a a column i with see |

0:11:42 | three db and is one problem channel died vision that the so which change not bring one |

0:11:47 | but if we do in |

0:11:49 | for the you'll find a i'd uh for this particular case |

0:11:52 | the the these ratio show a lot or point a or a two to or series of which that's is |

0:11:58 | also quite close to a link so which is so if you use |

0:12:01 | got the minimization best going you obtain quite |

0:12:04 | quite good performance |

0:12:06 | the |

0:12:07 | so that they can we want to check if the proposed approximation formulation can |

0:12:13 | so you find a it's an set if probably due not |

0:12:16 | yeah we also compare with the mess by my question or time the in them is an it is what |

0:12:21 | you |

0:12:21 | and this is our previous work |

0:12:23 | is is the proposed to that's in this |

0:12:26 | in this work |

0:12:27 | the we can see that |

0:12:28 | or or next we S can see defined a desired like ninety percent |

0:12:33 | certificates fiction would be at but you can see that |

0:12:36 | a this one seems to kinds about if |

0:12:38 | because we only one ninety percent |

0:12:40 | it gives you want to per |

0:12:42 | is once is and this white |

0:12:44 | the proposed a given |

0:12:45 | is given beta |

0:12:48 | so |

0:12:49 | that's so we want to compare a transmission power |

0:12:52 | and here the recognise uh |

0:12:54 | one by mac channel that that this one is by |

0:12:57 | a previous work in this one is the proposed will |

0:12:59 | the problem lies uh |

0:13:01 | just mission power not low design so which can |

0:13:04 | so as a benchmark for |

0:13:06 | these robots robust |

0:13:07 | again we can see these figures i full |

0:13:10 | from got got model in to find one to nineteen is that's going in the |

0:13:14 | propose a have its most power you fish |

0:13:18 | you want to compare the computational complexity in the stream S |

0:13:22 | yeah we can pick uh will compute the |

0:13:25 | that i |

0:13:26 | the time of C V X |

0:13:27 | solving the form a nation is of each for the mess on the test |

0:13:31 | then you can see that a a going to of proposed method more |

0:13:35 | a computationally efficient then that one |

0:13:38 | proposed |

0:13:39 | by i'm sure that and but it's |

0:13:42 | more computational |

0:13:43 | expensive it in our previous work |

0:13:45 | so this is a a a cup and the performance trade |

0:13:48 | but to in uh |

0:13:50 | the work proposed in this |

0:13:51 | the the the mess the proposed in his work and our previous work |

0:13:56 | so in summary uh we have a pretty sent uh |

0:14:00 | new approximation for a probably probably if the |

0:14:03 | it's i not constrained |

0:14:05 | robust beamforming problem |

0:14:06 | and that the to all mess up a some to in great the to in gradient |

0:14:11 | the first it's segment that and relaxation |

0:14:13 | that's second is a |

0:14:14 | but and typing you according which you so so |

0:14:17 | convex |

0:14:18 | comes of better approximation to a probability you cost straight |

0:14:23 | then estimation result have shown that the proposed method based quite |

0:14:26 | a of X six in message |

0:14:28 | thank |

0:14:36 | i we asked or sometimes all questions uh and questions from the audience |

0:14:40 | oh in a single question because i one of the corpus |

0:14:56 | you have to ask |

0:14:57 | with the money |

0:14:58 | microphone for simple |

0:15:02 | okay so i was here just out of it to i apologise to that |

0:15:05 | um but it is your you approximation a conservative one or or is that the |

0:15:11 | you can so what he is it is |

0:15:13 | okay |

0:15:14 | that's what i would of to the beginning thanks |

0:15:16 | think |

0:15:17 | but actual one have a few words so is |

0:15:20 | restriction and and them relaxation |

0:15:23 | relaxation this semi-definite relaxation and restriction is with the pop up this the constraint |

0:15:32 | yeah |

0:15:35 | so that run realisation when you get to to rank to solution |

0:15:39 | can be sure that to |

0:15:40 | wasn't and rank one solutions to |

0:15:43 | sorry |

0:15:44 | a a in this scenario when you a the uh will find a rank two solution |

0:15:49 | it could to be rank one solution will so |

0:15:53 | to me |

0:15:54 | mean and you to the X the france one or of the this the set of solution perhaps |

0:15:59 | could to be used at |

0:16:00 | some under solution that's rank one |

0:16:03 | i i i not sure if i'll |

0:16:05 | correct |

0:16:06 | you mean when you to |

0:16:08 | so you me vibe obtain a drink two solution |

0:16:11 | then |

0:16:12 | that even if you obtain the rank |

0:16:14 | two solution the might excess |

0:16:16 | my one solution that you |

0:16:17 | C doesn't happen to find |

0:16:19 | uh i |

0:16:22 | uh |

0:16:23 | this is the response is one strange |

0:16:26 | oh is this |

0:16:28 | so yeah that you calm down brand |

0:16:31 | when one that were then when one solution |

0:16:33 | in in nineteen nine nine nine nine percent of cases is just run what |

0:16:37 | well do what would you mind can scroll back to |

0:16:40 | a the situation now or or or do the the back here yeah at the situation where we see round |

0:16:46 | one |

0:16:46 | well here we you very strange shape see a one room a situation |

0:16:51 | but this right and you can use some other tricks to get around the |

0:16:58 | i don't questions |

0:17:02 | okay can you just a normal one that's past the speaker |