S S are french i'll and uh am working with professor say right i still uh the topic i going to tell us the about the performance limits of the lms based adaptive that works so in this work uh we compared the performance of that if you're and algorithms bit adder or them for example the uh centralized a block a or mess and uh uh a distributed incremental a mess and the we conclude that if we can optimize the come combination weights it coefficients for if you're in tree rhythms then we can show that that if you're in algorithms well be other algorithms alright so that start so that but that team that it works were talking about uh there consists of uh inter active inter connected to no and there are uh interesting a common objective for example for this graph a we have bus eight nodes and their inter that's assume that you know model here so every node the can get it access to some uh or men that they to uh do use book hey a i i uh and the use of K i and all the nodes are interesting you to estimate the top you not and uh besides the data the every P can crack the from the local environment they can also exchange some information through with the a links between them and to help each other to improve the uh estimate and the diffusion and strategy can provide a powerful me can is em's two uh uh the adaptation over networks here i wa i would like to number size the networks uh can be also uh you can be a static and that worse and it can also be a mobile on that the bricks here um we're more uh for the mobile L not uh a more well that works uh every node in the network and moving so the um the topology of the network it's changing although a is change always and so here yeah so that will yeah uh introduce some very challenging uh things to the are written so the first the solution is a centralized solution and here are you need a a a a powerful a fusion center sitting on top of the network and it a can uh a connected to every node in the network of work and eight uh i could the data from every node and the put the all the data together to perform the adaptation and we note there uh for this kind of a solution it's suffer from several or uh drawbacks the first thing is that you have a power centre which is the super node in a work so it's a suffer from uh um faders for example if you if the power centre uh used the a fusion center is down the everything's go alright and another drawback is that it's separates from the random being figures so if and one of the link it drops you you do some node and you lose some data this is not a good a um so we may think about that distribute but the solution i one possible way is the using the uh incremental solution uh the increment of solution eight to uh update to estimate you a sequential manner here for example look at this speaker um let's state the no the one will start uh estimate uh uh a a will start uh update so it first uh it will use its previous estimate top you i as one and the use its own data to update at this uh estimate two i so but uh five but one common i and the forward at this intermediate that estimated to know the two and then the no to to will but joss to this uh estimated according to his own data and so a and a well pass the estimate to the next to no and so after node eight the last the node node the it uh improve the um intermediate media according to his own data it will pass past the uh the resulting uh estimated to the know the one and which you which we will become the new estimate of W i alright for this kind of a solution it also so that the good point is that it does need a power a powerful to rinse under this is good but it also suffer from or drawbacks one drawback since the um it also so for from the the milling feet for example if you uh it's this link is that a maybe you can find another way or wrong but if this link is the then you cannot do it another drawback is if the network is moving that topologies changing then do in the adaptation you need to repeatedly calculate or a a cycle through the network on the fly this is the not trivial you know that before it is it's uh and P hard problem you need to do it and usually it's some very very hard alright right so we may think about a outer solutions one possible solution is the diffusion strategies here a a lucky likes shown in this figure every node will perform two things one thing is that adaptation according to its own data and the thing is that exchanging changing the uh inter mediate estimate with its neighbours two uh further improve his own estimate a every communication is the down in the local area a so uh it doesn't consume a lot of energy and uh usually just all with them is a robust to to the run them three adding feel we be queries if anyone of the link it's down you can always and you you you don't lose any noting thing the now work or and so there are two different kinds of algorithms one is the called at that then combine at C is strategy it's first the perform the adaptation then do the combination uh another a one is the uh combine then that that C T a strategy uh just for first the perform the uh a combination stuff and then do that adaptation i here we and the size that win uh used in a complex combine a combination coefficients uh to guarantee the compared right so before we compare different algorithms rhythms we need to be will a weird of a two important factors uh of the performance of the uh a if order one is the convergence rate and a an otherwise the state a i mean squared error that's how look at the speaker so this is that you learning curve of uh and the long uh adaptive few adaptive filter so basically it you can't do by the the curve into two parts and uh one part is the trend in the face and the other part is that steady state uh in the trends in the face were interest in the uh how fast the uh this curve for drop down and in the type state or interesting to how much errors to remains in the steady state so when you compare different rhythms you need to um be fair uh for example here in this work because course are more interested in the steady-state state for formants so we fix the uh convergence rate of four every read them so that means are pretty algorithm we have the same convergence rate in this that in the trends and fate and the way we compared to uh steady-state mean-square error and to a a simplified duration and to and high light a uh i'd so we use the to note networks it's simple called but it it the the uh considering the um uh uh the and uh uh and the oh of course that the to note that the that that that an a work has to knows already use it a lot of a reach and in interesting dynamic and it's easy to uh analyse right so let's have a a can't the uh algorithms for to note networks so this one is for a at C and this one for C T um the of uh is the combination coefficient of four at a four inter mediate to estimate from the one self a it's here and the to is the combination weight coefficient of for inter mediate as to a from to two alright right um so after some a a considerable how our job or a you are uh we can get this too close to form yeah mse i expression um this is the a network average yeah see you we should define in this way and we can find out that this the mse is a function of the combination coefficient alpha and the beta so we can do some optimization over this two arguments to minimize this to you messy and the result is shown in this uh slide here we show that a after some comes out larger bra which is nontrivial trivial um we can show that this combination weight i'll for you close to this and the bit i close i one is done optimal one and this combination rule is a a co uses coincides with the um i i'm true uh in the digital communication area which is a for the uh the rake receiver for this we me system and the in this uh two optimize the the uh combination coefficients backing to a you sees expression you are get the uh minimize that you man C for a key C rhythm and the minimize the mse for C or with them here the role the uh role is the uh uh i mean and the commerce convergence mode the for the diffuse are out with them and a calm eyes the uh re sure that the noise of variance the for the two nope and for D block are a mess the first thing we need to do is to normalize the starts size the for this are rhythm bic queries uh in a texas i so we can show that if the step size it's very small or they you block our mass can be uh approximate as uh incremental a mass so for incremental or mass we have two consecutive tape adaptation steps in one i i iteration so to current the same convergence rate we need to normalized the step size in this way and the yeah the E M S this are with them in in here and the role prime is the common in the convergence small the for this all words them and we can have a look at the if the step size the me is very small this term is dominant the by one minus two meals segment new square and in the previous vice we can see the the dominant calm uh that mean and a part of for this convergence jensen mode it's a also one minus two new segment use square so they're almost the same this is the uh a yeah messy you for incremental or immense um similarly we need to normalize the step and here we gave the revelation to show that if this stepsize it's small enough the incremental our mass and the block are our mess there are almost the same just plug in the equation here and that you can or the high order more terms here you and up with this expression and this is the mse expression for the incremental algorithm um here we also propose a we also uh put that the standalone there are mess here and so there there's no cooperation between the two nodes then we were compared to the yeah mse performance uh with with this over algorithm also so this is the uh uh results of the come and so have a look at this highlights part so the the optimized you say it C are with them can is a slight will slightly better than the optimized the C T A a and is better than the outer three algorithms um just as shown by D uh theoretical results and also fish thought uh demonstrated in the simulation okay guess so this is a for the network every G M S C a here we we can see a team optimize at scenes the best a one and another interesting comparison is we compared the individual yeah ms uh yes the mse of these stand the long filters with the uh a diffusion uh as algorithms and the result shows that for optimize the if you C oh of also of the two nodes kind reach a uh yeah messy you which is less than either either one of the individual uh future oh this is some very interesting course this means even that would not with the lower noise level can benefit somehow from the information sharing them is the bad and now this a um this interesting interesting be course um we can imagine that every node if if the node a selfish it eight only want to a a when it can uh core parade with the each other or with other note it want get something from it if it can a in a from the corporation it well not do it here we show that if you can but optimize the combination weight then every note about if a the from the corporation that means for example we we use these are with them to model the animal behavior i think it's uh this is a kind of a a reasonable a to do it for at a uh them you need a sum a condition to to show that the you could note also a a if benefit the from the corporation this is the is simulation results so first let's have a look at the uh trends in the face so all the are with them have the thing uh convergence rate here and uh the optimized the at C and a C T A you can reach the lowest yeah mse and uh is used is a slightly better than it uh it is a it's that slightly better than C T A here and uh it also shows that a a block error mess and uh uh incremental error T have almost the same uh status stay the performance here and uh the worst the one is not corporation as expected the simulation per foul he shown here so we use the uh a few order of the lance ten the step size is uh a point zero or five and uh the a noise the and have for no the winds point five the variance for no to is a three and uh we also assume the whites uh regressor requires or to not there uh the power of the regressor is one and with similarly to two thousand uh iterations and over a uh and average the curves over one thousand file a here are some references as we can see that um by using that to field and algorithm we can model manning animal a here it behaviours in the nature for them up back to maria D honey bee and the uh lies and uh feast screws and also we can use the are with them for they uh uh a me radio radio alright right so i'm gonna down here i guess for the gaussian case that you use and use simulations to mikes sense that this maximum margin come component thing and this is optimal um oh one if you could make any comments or you done the thing with um uh uh be tiled distribution so that was to uh whose what we have done in i would scale in that you always get something from taking into account camp the bad stuff but in some more gas in problems uh you the rules to yeah what this war filling stuff for a right we've know i i is i i deletion i D the message of okay and the idea here you have to notes one has good noise the other that has bad not at each one of them is to estimate some channel some unknown parameter if they do it independently of course T was uh and all we get it was estimate right now if a a of them to a but it let's see using diffusion we expect big the bad not to do back to the "'cause" he's getting access also the information from the good no one can close it from ellis is is that the good little also do but even though he's getting bad the information from the but not of "'cause" so that's one conclusion not to do i have this expression there was no assumption about a gaussian at of these simulations actually good is also cost and but the mse expressions that C live do not the singles and to so this was not cope was a but the other one close which is very interesting from the table you go to the table is what if you take these these two not state the they and send it diffusion sent i a sense that can do block lms that only complaining lms processing so if you just sent that can do block lms well it do that the then the this T do to the and the and the and the not to that they okay and the on set is is actually diffusion will all the for even and diffusion solution but this is counted that into it right and then you might say well it's to just send that can do anything light doesn't it just implemented efficient algorithm a diffusion sent suppose to can do that but then what's the point the diffusion algorithm can be implemented in it see that it man okay so that you know that it still call this this call he it is a is a of just a all that was diffusion you can help the form the block lms solution that implement in a fusion center of P but the expressions that he did i they do not assume cost it to but i think in the simulations are showing assume probably and yeah thank you oh you want to you or a region you want a lie for the a be the coefficient efficient you do rhymes are using the study the uh result could that the uh N E a better way to derive a adaptive all on the fly coefficients sure thank you a a good question like i watch is doing is the i in the optimal weights for optimized the steady-state performance we have another it but actually a the published it was presented then i cast us to use that and on they paper that B it would yeah i i i i have that on the fly and the nation we find what the optimal weights i and at that it on the fly yeah we have we have done yeah i yes you you know to like this yeah i i can see we will expressions but do these optimal combine yours require a local information only your you're required a it's a statistical profile of an able to find them uh yeah have here the optimal a a cool combination coefficients need need to know uh noise per for L per file course the network and uh we uh we are uh here here were trying to find out some more with that you can estimate or somehow to know a noise profile cross the network then you can come up with this oh that's a good question this expression as you can see that the optimal coefficients depend on the noise profile in the network okay so this is it performance to it's that it's that time to tell you what's the best you can hope for if you knew this information in the article i first to before the one would you at that is coefficients on the fly that is done based on a thing as they that that you have that the a lot of there's everything is estimated on the fly yeah i think we should move along a get to be fair to the law at to add to the last is the last speaker here