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