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