0:00:15so i just wanna apologise for a for Z O the um
0:00:19plane was getting in this morning and uh he has an right out yeah
0:00:23so i'm gonna give this talk for him
0:00:25uh this is work done between uh in and all our phones of for reno
0:00:29and the total of thought is exporting multipath for blind source separation with sensor
0:00:38so so here is the scenario
0:00:41or face to the problem or we have a a a uh uh
0:00:43a multi channel receiver right
0:00:46and uh we receive a
0:00:48i yeah combination of a number of sources
0:00:51possibly a source
0:00:53and each of the sources
0:00:55uh propagates it's signal to the receiver array
0:00:58be a uh a a potentially multipath channel
0:01:03and and addition to
0:01:05each of the um
0:01:07the multipath signals could be a made up of uh mike a multi
0:01:12um um
0:01:13so also one of and one example of this is the uh H and
0:01:17signal environment
0:01:19you can have a a a a uh
0:01:21a source signal
0:01:22that propagates be the ionosphere
0:01:25and can propagate via two distinct i sphere
0:01:30which are well separated in angle and time delay
0:01:34and and then addition to the the modes
0:01:37or were the propagation layers can be disturbed
0:01:39and uh they can exhibit it
0:01:42this micro a multipath phenomena
0:01:46so of the problem will be to um
0:01:49given all of this this
0:01:51this different kind of propagation environment
0:01:53try and recover
0:01:54and estimate of the different uh
0:02:01so here is the data model
0:02:03uh you have a a a we have our array snapshots better modelled as a combination of the different sources
0:02:10and also a combination of the did uh different distinct
0:02:14multipath modes
0:02:16and um on each of
0:02:17those multi that modes the uh the source waveforms
0:02:21um can be modelled as
0:02:23having a a a a um a time delay
0:02:26um as well as a a a uh
0:02:30uh a doppler shift
0:02:32if uh that actually
0:02:33the uh one of the uh propagation modes is
0:02:36uh movie
0:02:39in addition to that with within each of the uh distinct
0:02:43no it
0:02:44uh we can
0:02:46the uh the the wavefront vectors
0:02:48can be modelled as
0:02:50crank only uh also
0:02:53quickly wave fronts
0:02:54where the creek are caused by um mike from mel T my think that the occurs within the
0:03:00the uh
0:03:01distinct propagation
0:03:03um and he's michael or mapping that can be modelled as a a uh
0:03:07a mixture of unique
0:03:09directions of arrivals
0:03:15or not resolve or by the aperture that is used to uh at that the signal
0:03:20but they can still calls distortion on the way from
0:03:28so somebody at the assumptions here
0:03:31uh so basically uh we assume that uh this is this is like a a and i R
0:03:36my mouse is
0:03:38um so we have uh each each uh a channel
0:03:42is model as an F I R channel
0:03:44and because there are multiple
0:03:47uh source signals and multiple receive sensors
0:03:51it's considered a multiple input multiple out
0:03:54a and so that us system model or the the data model for the uh the array snapshot vectors can
0:04:00be written
0:04:01um in this sort of uh
0:04:04um when you're model here on the right
0:04:07so as we said there are uh there's and there's soon to be multipath present
0:04:17uh there is a a a uh one of the assumption as in to make this algorithm work is a
0:04:22uh small assumption on the complexity of the source waveforms that are being estimated
0:04:28so it's assume that the source waveforms um can be is described by a a moderate degree uh
0:04:33uh when your calm complexity
0:04:36and uh so that um requirement of stated here on the right
0:04:41it uh
0:04:42the uh source waveforms are assumed to be are to
0:04:46um it's also assume that there are sufficient degrees of freedom in the uh receiver racist system
0:04:53uh such that um but total
0:04:56the total a number of multipath
0:04:59channels is less than the total number of receive set
0:05:10um basically the problem is um
0:05:14uh uh to go beyond um estimating the source waveforms by only spatial
0:05:20at that processing
0:05:25a a and uh will
0:05:27to do this you need to uh rope you you requires a uh
0:05:31so separation and multipath cancellation
0:05:36and the traditional method for uh doing the waveform estimation
0:05:41would be uh
0:05:43for i mean this this uh this particular um
0:05:46spatial filter
0:05:49essentially a space spatial folder optimises is the sinr output and stay years
0:05:55no holes in the direction of uh
0:05:58be the signals that you're not trying to S
0:06:01um but it can suffer for when um
0:06:06when you uh
0:06:07it britain T or all in the direction of the that the signal you're trying to test
0:06:14so and then so some of the challenges he list here or one on that the parametric models on available
0:06:20the signal
0:06:24and we don't know where so mean that we don't know anything about the source
0:06:31in total though the blind processing need to rely on relatively mild assumption
0:06:37so this is the summary of the existing approaches for uh
0:06:42blind deconvolution and blind source separation
0:06:45um and he's broken them down in
0:06:47in this this high R here
0:06:50where um
0:06:51they're blind source or source separation techniques that are based on a meetings source props some source properties
0:06:58yeah um or a blind source separation techniques that are based on assuming some channel characteristic prop
0:07:07this method for as to this assumption this this
0:07:11part of a tree about as to mean some mild conditions about the channel characteristics
0:07:15and about the the multipath
0:07:17and by
0:07:19in particular
0:07:20it's going to uh
0:07:21and describe the uh channel in terms of time delays and and doppler shift
0:07:31so uh uh that of a breeze your calls out for than that the gems algorithm
0:07:36and uh i believe that stands for generalized estimation of multipath signals
0:07:41and so the idea is to construct this
0:07:44uh this cost function
0:07:47where um
0:07:49the uh the variables over which the cost function varies R
0:07:53uh delay
0:07:54and and doppler
0:07:56so the cost function is constructed by take uh
0:08:00oh can take this matrix a
0:08:03which consists of
0:08:05K a a snapshot
0:08:08um um and then in addition and auxiliary matrix is formed uh you which consist of
0:08:15or a snapshots that are
0:08:17the and doppler shift
0:08:22a the uh
0:08:23the cost is parameterized by
0:08:26these two sets of weights what he calls a reference weights and on weight
0:08:30and each of these weights is actually private eyes by i
0:08:35delay and doppler shifts
0:08:36so this this total
0:08:38squared error
0:08:39cost function is
0:08:41parameterized by uh uh delay
0:08:43and uh doppler shift
0:08:47and doing to map you can re formulate the problem
0:08:52and it and this matter
0:08:54and number to here
0:08:55and you can and uh come up with a a uh
0:08:59close form solution
0:09:03that uh describes the uh
0:09:08the the solution to this problem
0:09:15algorithm the the
0:09:17we're team works by take you or snapshot vectors
0:09:24the and doppler shift in them to give you an auxiliary vector you
0:09:31that goes into this this jen they they go to this uh jan
0:09:35gems optimization techniques
0:09:37and uh
0:09:39you the outputs
0:09:42get the
0:09:44some here
0:09:45and you looking at all squared error
0:09:47and uh
0:09:49but just
0:09:50you just this this this uh routine for different delay and doppler shifts than that adjust your troll squared error
0:09:55matt error metric
0:09:57and you look for a minimum of this
0:09:59and that gives you um
0:10:01in in L and V to use
0:10:03uh in this side of the chain and to produce an estimate of the uh
0:10:08the signal snapshot
0:10:10um um
0:10:11so basically the main points are summarise the bottom it so there's a close form solution for
0:10:17this technique can much is combined with a grid search procedure over delay and doppler
0:10:22which produces to different weight vectors
0:10:25and uh
0:10:29you can actually start this procedure by um can mean it from a and order ambiguity
0:10:36so you can you the delay and doppler search in this manner
0:10:41so this is this is now now now has some examples of this data being drawn on
0:10:47uh i to each a data collected with they yeah and experimental
0:10:51or a
0:10:52um in in northern australia
0:10:56um a rated to collected this data way is a a two dimensional L shape to write
0:11:00it's is in a protocol model poles
0:11:02and is a did the receiver per element
0:11:04uh there sixteen
0:11:06um model elements
0:11:08and uh the B and with
0:11:10collected was uh sticks
0:11:11six Q point five dollar
0:11:16so uh the picture on the lab shows be uh a um
0:11:21it's actually a um at them C W waveform form
0:11:24um and
0:11:26the uh
0:11:27the data was collected such that there was only one signal being
0:11:32one signal
0:11:39and in the second example but he shows a are there's going to be two signals there is and F
0:11:44M C W signal
0:11:46overlapping with a a a and brought guess
0:11:49uh so the idea is we run the out where them and we're gonna extra
0:11:53uh the different way four
0:11:57so here's an example of
0:12:01the uh
0:12:02the the first case which is actually a F I R C mo case because there's a single input waveform
0:12:07a single um
0:12:08F M C W away for
0:12:10and this is an ink this is the uh and example the channel scattering function for that case
0:12:15so we have
0:12:17the delay on the right a a the delay on the lab and doppler shift on the right
0:12:21on the on the bottom mean
0:12:23uh and what you can see is that uh
0:12:26there are multiple model
0:12:28as and
0:12:28within this
0:12:30source to receiver channel
0:12:32and you can see that but had there's a several different peaks and delay doppler space
0:12:37so basically there's these uh different
0:12:40um multi modes and they all exhibit different uh
0:12:44delay and doppler ships
0:12:47and the rows and
0:12:48because of that
0:12:50you get distortions of the wavefront
0:12:53with with respect to the normal plane wave propagation
0:12:57so on the on this graphic here on the right
0:12:59each showing uh the the amplitude distortion of cross the receiver index
0:13:07the blue is mode one
0:13:09and the the red is mode to and this is
0:13:12plot with respect to uh
0:13:14the uh
0:13:15what would be expected for a plane
0:13:18similarly on the right you showing uh
0:13:21the doppler spectrum
0:13:23for these two different mode
0:13:25and um on the right on here on the bottom he showing the uh
0:13:30a distortion for these two different modes
0:13:36a basically this is this is same the channel composed of
0:13:41multipath and actually some mike or multipath
0:13:45the the distortion here is caused by a or multi but within each of these
0:13:50delay doppler
0:13:54so uh to compare this
0:13:56could to compare the a signal estimation technique
0:14:01what he's done is
0:14:05uh looked at the uh the waveform output
0:14:10in comparison to the that to when known the known reference signal so in this case you know what the
0:14:15the rubber single was it's a of of them C W waveform so
0:14:19uh uh uh estimate
0:14:33yes okay
0:14:34so this would be as a standard technique
0:14:37uh just trying to do uh
0:14:41uh trying to steer beam towards the direction of the known reference signal
0:14:48see that the uh the reference way we form
0:14:51a a should have a a uh
0:14:55a a a uh
0:14:56signal that looks like the black
0:14:58a black line
0:15:01uh when you that we trying to steer beam towards the uh the no
0:15:06signal direction
0:15:08you get a a a uh
0:15:09you get an estimate of the wave form but highly distort
0:15:15now if you quite is this gems technique
0:15:19if we work at that the bottom right picture you get a much better estimate of the uh of the
0:15:24signal waveform so again in black show on the reference signal and green actually show the estimate of the uh
0:15:30of the source a
0:15:33and and what he showing here on the top of the of the page is the uh
0:15:37the gems cost function
0:15:39and delay doppler space
0:15:44just for comparison he showing the uh auto and but you would you function
0:15:52so he's also done some complexity analysis
0:15:55uh to determine how costly it is to run the routine
0:15:59not gonna go through all of this
0:16:04joe will be here later so when he shows up you can ask a question
0:16:09but last example he has is for uh the multiple
0:16:13signal in case so is the F I R my
0:16:18um um
0:16:20a basically if you look at the uh so it's old but on the right is the a uh music
0:16:26and one is showing is the elevation as it
0:16:30directional spectrum for this
0:16:32the uh
0:16:33the source waveforms that are and you know near right
0:16:36in what you can see is that they're two sources the F M C W source and the a and
0:16:40modulation sure source
0:16:42coming from um
0:16:44different spatial location
0:16:50at the bottom
0:16:53the uh
0:16:59uh the signal estimates
0:17:02uh in red is a single receiver
0:17:11of the blue was a single receiver
0:17:15well go
0:17:18so uh
0:17:19if you run the gems his is uh
0:17:22so uh estimation uh
0:17:24method that on this these two overlapping signals
0:17:29you get a a um
0:17:32a cost function that looks like
0:17:34like this with two different minimum in it
0:17:37and uh
0:17:39one of the minimum corresponds to one of the source signals and the one of the other minimums corresponds to
0:17:45the second source signal
0:17:49and he shown here on the bottom be estimated uh and them C W source signal
0:17:56again in black is the true source signal
0:18:01in blue is is
0:18:02uh jen's estimation technique
0:18:05and uh
0:18:08the uh the the red is a uh
0:18:12a traditional
0:18:13spatial only estimate
0:18:15of the source signal
0:18:17um and then on the right is uh in estimate of the and broadcast signal
0:18:24um and you can see that the the gems technique
0:18:27gives you fairly
0:18:29actually rather good estimate of the this a and broadcast
0:18:32in the F M C W signal on multi
0:18:37um so in conclusion
0:18:40this uh gender technique can with separate multiple sources and multicast components by spatial processing
0:18:48in incorporates multipath structure and way for wavefront front calls
0:18:53into the um
0:18:55that the channel model
0:18:58it the uh the form lady here enables a relevant practise problem to you dressed in a novel way
0:19:06other lines
0:19:07spatial processing techniques not is on the same so so it's
0:19:10it basically designed under different channel assumptions
0:19:17he's saying that uh it provides a in the van capability for this
0:19:21F I R
0:19:22uh my no problem
0:19:26and i think that he can
0:19:27uh is looking to continue look you know the points out or them to um
0:19:31different datasets not limited just to the H
0:19:38okay K it there any questions
0:19:40thank you not
0:19:48the yeah that quickly did you do the uh X number i no estimation and the doppler and delay estimation
0:19:54separately because you show this the music spectrum first
0:19:57and then later on the uh as to um the doppler um
0:20:01and apple delay plane
0:20:03yes what i believe what we did in that is
0:20:07sort of two
0:20:08just to illustrate that the two sources and that the coming from different directions
0:20:12just produce the traditional music okay
0:20:15but can't to incorporate an it i and then to have a like a dimension estimation and that would have
0:20:20a high resolution probably right
0:20:22if you um an estimate the nation and doppler shift and delay jointly
0:20:31i i think i believe varied in the routine he's somehow doing a joint
0:20:36but this is a different technique as music right this is nice i and so that a showing in the
0:20:40the space role
0:20:42okay um
0:20:43to uh
0:20:45the recover the waveforms
0:20:49instructing in this
0:20:50this cost function that
0:20:52is parameterized by delay and doppler but within that delay doppler space there
0:20:58also estimate in the uh source direction
0:21:01okay because because you point than out there and yeah the model
0:21:05and you that's what is doing and it does you only allow for integer delay an integer future uh a
0:21:11doppler shift in and the and your with data model
0:21:14um i believe so i think he's is so mean that the uh uh the sources is oversampled hmmm
0:21:21you can approximate of by integer
0:21:25more yes place
0:21:28you take a mic
0:21:31i see from the uh six a bit the sources is a vector shot
0:21:37so E i E i to some stranger
0:21:41to so i have a now to the
0:21:45but i
0:21:47we we have a this it in the sprite that is a a a a a is a you
0:21:54so oh
0:21:55i i i i have some problem uh a complete your
0:22:00you but for me the were your uh
0:22:02a a fine so you're of the correlation so that we could expect spectrum
0:22:06well uh yeah it was it seems that
0:22:09well uh you know i i i is it we have been so i'm are even in the team uh
0:22:14in some level even a a a a really low bit the are have so a little bit are we
0:22:19have so
0:22:20E E a single was uh
0:22:24just like a reference
0:22:27it can be done a seven or a a of me check at the base of um the algorithms
0:22:33in the a the estimate estimator
0:22:36uh i a billy that the a
0:22:40is a the problem of the also be uh for the
0:22:43but i i E um
0:22:46the much it should
0:22:48the processing
0:22:50yeah why the
0:22:52these uh a uh uh a a little shopping to two
0:22:56that have uh and uh uh a a and i of a and in the say
0:23:00a a combine the sum of of the up with some clever she is the um do this discrete in
0:23:07science i'm i'm or
0:23:08this is a is possible in the existing so that techniques of of some memories
0:23:14you you need to to a a sort the tool blind separation
0:23:22i'll try is answer
0:23:23can can
0:23:24is that there is it is a problem
0:23:26i i i i
0:23:28a from mister still
0:23:32i whatever or a i E
0:23:35we can can so we can see some some things
0:23:39the the the the sprite exist
0:23:43time right
0:23:44is that
0:23:46scale some of the from the some the action
0:23:50yes yeah so walks
0:23:57well to use the fact that a peaks a shot again
0:24:03well that there i okay
0:24:08but the six Q you can be seen
0:24:12five that
0:24:21you sort of a yeah i the directions a right not with the have no need to should original use
0:24:28fine i'm yeah should i mean you also him uh you the in this manner
0:24:33a a in assume that the the is that the steering vector a is a like one okay
0:24:40is was like to wind the for example
0:24:42the but the but the prince you public gimmick has have set in parts a distribution since
0:24:48a a a a a a lack uh function
0:24:52a a a a we win the word
0:24:54so that they have a set of of them up it was uh a to me yeah my strike and
0:25:00the last
0:25:02is the can
0:25:04"'kay" thank you common
0:25:08maybe the best thing is when when doctor for busy gets you
0:25:11discuss a okay we sure i i can say is that
0:25:14you know think the idea is to describe
0:25:17the uh uh
0:25:19eight distinct multipath mode by a
0:25:22so like a quickly wavefront
0:25:24because within that single to the rain mode
0:25:28um there's your resolve able
0:25:31um um
0:25:32plane wave from
0:25:33but the did you rate that you're trying to sample the but not to the the with from but you
0:25:37you you are you
0:25:38you have mixing it to have moments
0:25:41the source scroll relation
0:25:44this was of addition
0:25:46and and the the initial was uh out of time have a clue to the to this
0:25:52mode sort of plan at this is that possible position on or my plane waves
0:25:57shall speech
0:25:59use scriptures as
0:26:00so the problem is and have it signal and the all not the sprite
0:26:06and that's right
0:26:07yes but was what
0:26:08but the sprite that
0:26:09i for the by different the your might trying to combine as um
0:26:16oh or back up with the scene you have a that publish you to come to be the exactly you
0:26:21know now or but the but the should not
0:26:24but the the and those provide that for an G for what a metric care meet me minimum minima sure
0:26:30meant them uh image and of the source
0:26:32can be and said that but i the by should the kings
0:26:37which you need so that even in this case should but like two that's some shown might yeah but
0:26:43a block or race in coming to from are i one that's a set thing the uh the action right
0:26:49a of the components you could do that you can model below that i was uh ba
0:26:55by a robust to beamformer sense yeah
0:26:58think it's not it's not a but music yeah is use a is a robust is based on a robust
0:27:02to beamforming your is story got show this okay goes
0:27:07performs what
0:27:08so but but also been farmers should perform well
0:27:12okay yeah
0:27:13so the the the the techniques are not mutually exclusive the mean in some sense it's sort of like an
0:27:18approximation to a match field technique i i can
0:27:20i think that that is
0:27:22but there's some relation there
0:27:24the second thing is that it this is not just about there
0:27:27as as the in direction of arrival
0:27:29it's about estimating the source wave for
0:27:33so it's not enough to just get a gross estimate of where the signals the coming from
0:27:37you have to have a good idea of what that mike or multi that is like
0:27:41so that you can
0:27:44as an eight oh what is supposed to be a plane white
0:27:48okay okay but to can discuss discussed this with the a
0:27:52think that's a for four a to come coming to the to thank you marry much for your a questions
0:27:58and and not this be a um for all the speakers thank