Speech Transcript - EXPLOITING MULTIPATH FOR BLIND SOURCE SEPARATION WITH SENSOR ARRAYS

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

EXPLOITING MULTIPATH FOR BLIND SOURCE SEPARATION WITH SENSOR ARRAYS

Signal Separation

Presented by: Giuseppe Fabrizio, Author(s): Giuseppe Fabrizio, Defence Science and Technology Organisation, Australia; Alfonso Farina, Selex Sistemi Integrati, Italy