um so i just wanna apologise for a for Z O the um plane was getting in this morning and uh he has an right out yeah so i'm gonna give this talk for him uh this is work done between uh in and all our phones of for reno and the total of thought is exporting multipath for blind source separation with sensor okay so so here is the scenario um or face to the problem or we have a a a uh uh a multi channel receiver right and uh we receive a i yeah combination of a number of sources um possibly a source and each of the sources uh propagates it's signal to the receiver array be a uh a a potentially multipath channel and who and and addition to each of the um the multipath signals could be a made up of uh mike a multi um um so also one of and one example of this is the uh H and signal environment where you can have a a a a uh a source signal that propagates be the ionosphere and can propagate via two distinct i sphere mode which are well separated in angle and time delay um and and then addition to the the modes or were the propagation layers can be disturbed and uh they can exhibit it this micro a multipath phenomena so of the problem will be to um given all of this this this different kind of propagation environment try and recover and estimate of the different uh sec okay so here is the data model uh you have a a a we have our array snapshots better modelled as a combination of the different sources and also a combination of the did uh different distinct multipath modes and um on each of those multi that modes the uh the source waveforms um can be modelled as having a a a a um a time delay um as well as a a a uh doppler uh a doppler shift if uh that actually the uh one of the uh propagation modes is uh movie um in addition to that with within each of the uh distinct no it uh we can the uh the the wavefront vectors can be modelled as basically crank only uh also quickly wave fronts where the creek are caused by um mike from mel T my think that the occurs within the the uh distinct propagation um and he's michael or mapping that can be modelled as a a uh a mixture of unique directions of arrivals um which um are or not resolve or by the aperture that is used to uh at that the signal but they can still calls distortion on the way from um so somebody at the assumptions here uh so basically uh we assume that uh this is this is like a a and i R my mouse is um so we have uh each each uh a channel is model as an F I R channel and because there are multiple uh source signals and multiple receive sensors it's considered a multiple input multiple out a and so that us system model or the the data model for the uh the array snapshot vectors can be written um in this sort of uh um when you're model here on the right um so as we said there are uh there's and there's soon to be multipath present um and else uh there is a a a uh one of the assumption as in to make this algorithm work is a uh small assumption on the complexity of the source waveforms that are being estimated so it's assume that the source waveforms um can be is described by a a moderate degree uh uh when your calm complexity and uh so that um requirement of stated here on the right otherwise it uh the uh source waveforms are assumed to be are to um it's also assume that there are sufficient degrees of freedom in the uh receiver racist system uh such that um but total the total a number of multipath channels is less than the total number of receive set okay so um basically the problem is um uh uh to go beyond um estimating the source waveforms by only spatial at that processing um a a and uh will to do this you need to uh rope you you requires a uh so separation and multipath cancellation uh um and the traditional method for uh doing the waveform estimation would be uh for i mean this this uh this particular um spatial filter um essentially a space spatial folder optimises is the sinr output and stay years no holes in the direction of uh be the signals that you're not trying to S um but it can suffer for when um um when you uh it britain T or all in the direction of the that the signal you're trying to test um so and then so some of the challenges he list here or one on that the parametric models on available for the signal spectrum um and we don't know where so mean that we don't know anything about the source um so in total though the blind processing need to rely on relatively mild assumption so this is the summary of the existing approaches for uh blind deconvolution and blind source separation um and he's broken them down in in this this high R here where um they're blind source or source separation techniques that are based on a meetings source props some source properties yeah um or a blind source separation techniques that are based on assuming some channel characteristic prop um and this method for as to this assumption this this part of a tree about as to mean some mild conditions about the channel characteristics and about the the multipath and by in particular it's going to uh and describe the uh channel in terms of time delays and and doppler shift um so uh uh that of a breeze your calls out for than that the gems algorithm and uh i believe that stands for generalized estimation of multipath signals and so the idea is to construct this uh this cost function where um the uh the variables over which the cost function varies R uh delay and and doppler so the cost function is constructed by take uh oh can take this matrix a which consists of uh K a a snapshot um um and then in addition and auxiliary matrix is formed uh you which consist of uh or a snapshots that are the and doppler shift uh and a the uh the cost is parameterized by these two sets of weights what he calls a reference weights and on weight and each of these weights is actually private eyes by i um delay and doppler shifts so this this total squared error cost function is parameterized by uh uh delay and uh doppler shift um and doing to map you can re formulate the problem uh and it and this matter um and number to here and you can and uh come up with a a uh close form solution uh W that uh describes the uh uh the the solution to this problem um so algorithm the the we're team works by take you or snapshot vectors um uh the and doppler shift in them to give you an auxiliary vector you uh that goes into this this jen they they go to this uh jan gems optimization techniques and uh you the outputs uh get the some here and you looking at all squared error and uh you but just you just this this this uh routine for different delay and doppler shifts than that adjust your troll squared error matt error metric and you look for a minimum of this and that gives you um in in L and V to use uh in this side of the chain and to produce an estimate of the uh that's the signal snapshot um um so basically the main points are summarise the bottom it so there's a close form solution for this technique can much is combined with a grid search procedure over delay and doppler which produces to different weight vectors um and uh and you can actually start this procedure by um can mean it from a and order ambiguity so you can you the delay and doppler search in this manner so this is this is now now now has some examples of this data being drawn on uh i to each a data collected with they yeah and experimental or a um in in northern australia um a rated to collected this data way is a a two dimensional L shape to write it's is in a protocol model poles and is a did the receiver per element uh there sixteen um model elements and uh the B and with collected was uh sticks six Q point five dollar um so uh the picture on the lab shows be uh a um it's actually a um at them C W waveform form um and the uh the data was collected such that there was only one signal being uh one signal present um and and in the second example but he shows a are there's going to be two signals there is and F M C W signal overlapping with a a a and brought guess uh so the idea is we run the out where them and we're gonna extra uh the different way four so here's an example of um the uh the the first case which is actually a F I R C mo case because there's a single input waveform a single um F M C W away for and this is an ink this is the uh and example the channel scattering function for that case so we have the delay on the right a a the delay on the lab and doppler shift on the right on the on the bottom mean uh and what you can see is that uh there are multiple model as and within this um source to receiver channel and you can see that but had there's a several different peaks and delay doppler space so basically there's these uh different um multi modes and they all exhibit different uh delay and doppler ships um and the rows and because of that uh you get distortions of the wavefront with with respect to the normal plane wave propagation so on the on this graphic here on the right each showing uh the the amplitude distortion of cross the receiver index um um for the blue is mode one and the the red is mode to and this is plot with respect to uh the uh what would be expected for a plane um similarly on the right you showing uh the doppler spectrum for these two different mode and um on the right on here on the bottom he showing the uh a distortion for these two different modes uh so a basically this is this is same the channel composed of uh multipath and actually some mike or multipath the the distortion here is caused by a or multi but within each of these uh delay doppler channel so uh to compare this could to compare the a signal estimation technique um what he's done is uh compared uh looked at the uh the waveform output um in comparison to the that to when known the known reference signal so in this case you know what the the rubber single was it's a of of them C W waveform so compare uh uh uh estimate um so yes okay so this would be as a standard technique uh just trying to do uh uh trying to steer beam towards the direction of the known reference signal and um see that the uh the reference way we form a a should have a a uh a a a uh signal that looks like the black a black line um and uh when you that we trying to steer beam towards the uh the no signal direction you get a a a uh you get an estimate of the wave form but highly distort now if you quite is this gems technique um if we work at that the bottom right picture you get a much better estimate of the uh of the signal waveform so again in black show on the reference signal and green actually show the estimate of the uh of the source a and and what he showing here on the top of the of the page is the uh the gems cost function and delay doppler space um and just for comparison he showing the uh auto and but you would you function um so he's also done some complexity analysis uh to determine how costly it is to run the routine um not gonna go through all of this um joe will be here later so when he shows up you can ask a question um but last example he has is for uh the multiple signal in case so is the F I R my um um and a basically if you look at the uh so it's old but on the right is the a uh music expect and one is showing is the elevation as it uh directional spectrum for this the uh the source waveforms that are and you know near right in what you can see is that they're two sources the F M C W source and the a and modulation sure source coming from um different spatial location um and at the bottom the uh showing estimates uh uh the signal estimates four uh in red is a single receiver um bloom of the blue was a single receiver well go so uh if you run the gems his is uh so uh estimation uh method that on this these two overlapping signals um you get a a um a cost function that looks like like this with two different minimum in it and uh one of the minimum corresponds to one of the source signals and the one of the other minimums corresponds to the second source signal uh and he shown here on the bottom be estimated uh and them C W source signal um again in black is the true source signal um in blue is is uh jen's estimation technique and uh the uh the the red is a uh a traditional spatial only estimate oh of the source signal um and then on the right is uh in estimate of the and broadcast signal um and you can see that the the gems technique gives you fairly actually rather good estimate of the this a and broadcast know in the F M C W signal on multi um so in conclusion um this uh gender technique can with separate multiple sources and multicast components by spatial processing um in incorporates multipath structure and way for wavefront front calls into the um that the channel model um it the uh the form lady here enables a relevant practise problem to you dressed in a novel way um other lines spatial processing techniques not is on the same so so it's it basically designed under different channel assumptions um and he's saying that uh it provides a in the van capability for this F I R uh my no problem um and i think that he can uh is looking to continue look you know the points out or them to um different datasets not limited just to the H okay okay K it there any questions thank you not sense um the yeah that quickly did you do the uh X number i no estimation and the doppler and delay estimation separately because you show this the music spectrum first and then later on the uh as to um the doppler um and apple delay plane yes what i believe what we did in that is sort of two just to illustrate that the two sources and that the coming from different directions just produce the traditional music okay but can't to incorporate an it i and then to have a like a dimension estimation and that would have a high resolution probably right if you um an estimate the nation and doppler shift and delay jointly yes uh i i think i believe varied in the routine he's somehow doing a joint um but this is a different technique as music right this is nice i and so that a showing in the the space role spectrum okay um to uh the recover the waveforms these uh instructing in this this cost function that is parameterized by delay and doppler but within that delay doppler space there it's it's also estimate in the uh source direction okay because because you point than out there and yeah the model and you that's what is doing and it does you only allow for integer delay an integer future uh a doppler shift in and the and your with data model um i believe so i think he's is so mean that the uh uh the sources is oversampled hmmm yeah that's you can approximate of by integer delay okay more yes place you take a mic thanks i i see from the uh six a bit the sources is a vector shot so E i E i to some stranger to so i have a now to the but i we we have a this it in the sprite that is a a a a a is a you so oh i i i i have some problem uh a complete your you but for me the were your uh a a fine so you're of the correlation so that we could expect spectrum well uh yeah it was it seems that well uh you know i i i is it we have been so i'm are even in the team uh in some level even a a a a really low bit the are have so a little bit are we have so E E a single was uh right just like a reference it can be done a seven or a a of me check at the base of um the algorithms in the a the estimate estimator uh i a billy that the a is a the problem of the also be uh for the but i i E um the much it should the processing yeah why the these uh a uh uh a a little shopping to two that have uh and uh uh a a and i of a and in the say a a combine the sum of of the up with some clever she is the um do this discrete in science i'm i'm or this is a is possible in the existing so that techniques of of some memories you you need to to a a sort the tool blind separation um well i'll try is answer can can is that there is it is a problem i i i i a from mister still i a i whatever or a i E we can can so we can see some some things the the the the sprite exist time right is that i scale some of the from the some the action yes yeah so walks i well to use the fact that a peaks a shot again well that there i okay that's i but the six Q you can be seen five that the okay are you sort of a yeah i the directions a right not with the have no need to should original use fine i'm yeah should i mean you also him uh you the in this manner a a in assume that the the is that the steering vector a is a like one okay is was like to wind the for example the but the but the prince you public gimmick has have set in parts a distribution since a a a a a a lack uh function a a a a we win the word so that they have a set of of them up it was uh a to me yeah my strike and the last is the can "'kay" thank you common um maybe the best thing is when when doctor for busy gets you discuss a okay we sure i i can say is that you know think the idea is to describe the uh uh eight distinct multipath mode by a so like a quickly wavefront because within that single to the rain mode um there's your resolve able um um plane wave from but the did you rate that you're trying to sample the but not to the the with from but you you you are you you have mixing it to have moments right the source scroll relation this was of addition and and the the initial was uh out of time have a clue to the to this mode sort of plan at this is that possible position on or my plane waves shall speech use scriptures as so the problem is and have it signal and the all not the sprite and that's right yes but was what but the sprite that i for the by different the your might trying to combine as um but or oh or back up with the scene you have a that publish you to come to be the exactly you know now or but the but the should not but the the and those provide that for an G for what a metric care meet me minimum minima sure meant them uh image and of the source can be and said that but i the by should the kings which you need so that even in this case should but like two that's some shown might yeah but are a block or race in coming to from are i one that's a set thing the uh the action right last a of the components you could do that you can model below that i was uh ba by a robust to beamformer sense yeah think it's not it's not a but music yeah is use a is a robust is based on a robust to beamforming your is story got show this okay goes this performs what so but but also been farmers should perform well okay yeah so so the the the the techniques are not mutually exclusive the mean in some sense it's sort of like an approximation to a match field technique i i can i think that that is but there's some relation there the second thing is that it this is not just about there as as the in direction of arrival it's about estimating the source wave for so it's not enough to just get a gross estimate of where the signals the coming from you have to have a good idea of what that mike or multi that is like so that you can uh accurately as an eight oh what is supposed to be a plane white okay okay but to can discuss discussed this with the a think that's a for four a to come coming to the to thank you marry much for your a questions and and not this be a um for all the speakers thank