a Q mister chain um a break go

up up the ladies and gentlemen my name is challenging light and it's my honour to present to you

the design of robust the of a broadband beam formers

right the microphone gain in base error of right there is day

now during the course of my presentation of first find the problem that

we want to solve

and then now move

to discuss about the array geometry that we use for all beamformer design

after that out top some up just the of a broadband beamformer structure use and robust design formulation

then out

a provide us

sign example and finally out close my presentation

now in speech acquisition as applications such a

teleconferencing and audio surveillance

it is likely that the speaker a time was to move around the room

so

you be best if we have a

beamformer form that can be steel to the directions of the speaker

in order to acquire the speech signal

and because we are dealing with a

speech signal here which use of rock band we want

our be former to have a a frequency invariant property

and lastly

we want our beamformer to robot

um

to be robust to microphones errors and

i the deviation

so in other what's these three

card to stick is what we are trying to achieve a our design

and in these presentations

only meet the discussion in the five few more that you as you move and only

but it should be not that

it can be these design can be easily tend to the knee a few more than

not the original tree that we propose here is what we call the spider a i'm alright right

basically is the mouth you reading can are right

where

if we can see the that for example

um

uh

michael here for the first all of the zero already

and then

the microphone at the first three and the next ring we can see that

you've form the spiral um

and the next one is well so that the reason by would call it

the spiral i'm a

now

one of the good properties of this

spire i'm i race that's it has

uh circular symmetric properties which we we can exploit

in order to have a three hundred and sixty degrees during compatibility

not the

it response of

these microphone are rate is given by these equations

where the in that

C and K

we was to the K microphone

in the P three

and the only got are represent a frequency

five represent a as he move and a

our P P we present the radius of the P reading a C is the

speech of the propagating eighteen

where

now as for the steerable a broadband beamformer structures

i'm we are using the farrow structures at each of the microphone

so here we can use the for you by bill from the far all structures

do not that has

the thought here

the all main B

and the patient is given by these

so basically

the side here represent the

steering and a and a

sign met

here is the maximum steering range

so basically these inspirations

is just to scale the

theory and a to be we in the range of plus minus the a five for the five

farrow structure

no do not mean a beam pattern of these

beamformer structure is given by these inspiration

which can be written compactly in terms of

but the form

where the back the a a and a

ah

C K and and times one long vector

wait P C is the number of reading

K is the number of microphone re

and mine one he's the order of farrow structure

and and is the number of

tech

for the if a a few of

now in print um in print car environment

we always has some deviations from the idea more

and this

deviations can come from

a so such as

mismatches between microphone elements

not i knew characteristic of the microphones

positions a those in the microphones

elements and also low cost get bring effect

so

if we want to

um have uh a robust side of being form of then we need to include

some sort of error of modeling into our design

so if we include the

error modelling into our design then we have

oh but to alima response people by D K

where

cut a here

we present the gain

deviations for each microphone and

gamma

we present the face deviations for each microphone

and if we use these but to my element rest balls then will have

the beam paid them with but the element response given by D

which we can use then use this

in our design

now for the robust design we and to optimize the design based on the mean of the deviations

which is basically the S but the value you of how a deviation

not if we formulate our design in least ways formulation as we have

the cost functions people by these

what the compute the side we present the desired steering range

the tape make a

we present the

frequency range of interest and the to

Y represent present a

as a move in of interest

and it is well known that

these these where cost function can be written in a compact

matrix form given by these

where the element is

uh the matrix

chi bet the P

but the B and a D is given by these

now the mean error terms

is given by

the matrix

you bob L talk and

B

but the tar

and

there are and a into the metric

Q you

and that the B

as you can see here

you but with the robust

sorry

if but with the robust

these i'm formulations with do you have this and that

form of these ways formulations

this mean that this means that to solve this formulations we can still use this then that these squares

this i'm at

not as and

design example suppose that we want to design

a being and that can be as a from minus the T six degree tools the T six degree

and you has a

spectral pass band

from two hundred to three thousand and eight hundred uh

and you has a fall

reading

we've the ring id given by these

and for each

reading we have four five

microphone and the order of fire structure is four and the number of you that the is study two

now

or the microphone gain deviations we use the rally

our rally

distribution we've sick my was to one and for the slice deviations we use a uniform K

a

we've the actual minus

pile but to to pile over two

in order to illustrate last the robustness of our design

we introduced two types of perturbation

to our

um

beam patterns

the first but the nations

we want to model the bees mismatch between michael

so here each of the microphone is more than the as the fifty texts band pass if i a people

talk

and then the coefficients of this field those is perturbed by

uniform random form random was given by D

so as can be seen here the two graph here we represent a

frequency response of the microphones where the first

the left hand graph represent the microphone case and uh right

graph we present the microphone groups delay

now each line here

give the response of

each of the microphone elements used

as can be seen from these two graph

we can see that

for all the michael form in them once we do not have i you

microphone characteristic and

a microphone elements

ah

not match

with each other

not on top of that

we introduced in either the perturbations

which is

to model the

error in the microphone

a positions

so here

the X and Y coding net of all microphone uses

is put up with zero-mean gaussian pdf with standard deviation of once same thing we do

now

this for graph shows the beam pattern all sparse are and

spectral response of a beamformer

the left column here shows the beam pattern them for the non robust design

yeah et

minus twenty degree and thirty five degree

the right

hence that here shows the beam pattern for the robust design

the a minus twenty green and the five degree

not a few comments here

for the robust design

we can see that

the beam pattern

you meant tend the properties that we

this or we and to design where

um why we have a frequency invariance property

and

just do you

it is you clear that the as a man being at the directions of

the steering and a we she's minus twenty degree his case and

the D five degree these case

now for the non robust design

or the only case do see some

beam but then

a sum

men be at the higher frequency and

but and the low frequency and

the beam but than just blows out

in the presence of perturbation

so this clearly shows that i'm the is improvement

in the robust design

no

these for beam pattern shows

the beam patterns without any perturbation

now if the is not that the missions then the non robust design

even

a a a at the left two graphs

in the perform better

as shown by the more was quite low

where for the robust designs

we have

a be high side not

so this is the tradeoff off between

have been a lot was

a low side and the robust design

so in order to achieve

robust design we need to trail

the side lot level

i as

compared to the previous slide we can see that for the robust design

the beam pattern is maintain

even

in the presence of perturbation

now to conclude

we have proposed a robust steerable broadband beamformer design

and the steering capability is achieved by using the pharaohs if few those structure

not the robust

formulations is more though using stochastic model

and it is optimized for the mean performance

and from the design example us

it is clearly show that

um the robust design achieve the tree

i to the that initially we set up to solve

namely

it has a steering actually T

and it has a frequency variance

properties

and lastly it is robust against the perturbations

not with these i and my

presentation and thank you for your attention

questions

use use the mac

a case you for in simply we don't and

some a question is that the is so i look but you corporate thing to be to to control to

the microphone again and and arrow

can be a a a a uh a peak move for

the the raise

for instance here you you use a like a spider of um race where yes

but yes S is a a a few cable for linear or

no the right

yes um this that can be applicable to any other the

um array geometry that in that we need to modify is the a response

functions

a on the uh original array three that we you uh we design or

i guess

okay thank you

um as you know we the more the average response

it could still happen that for some special division of giving and

uh a actually there is a a large deviation for the we won

you can comment on that and do you also look at worst case optimization performance

okay um

if

if the error a D too much from the nominal mean a value of than definitely the you know what

think for or if you trim a the mean the average performing sparse specific

or additional doing and the is it could go can for the specific variation yeah

that a diffusion is very large but still on average is good performance

but did you also look at its worst case optimization

um we have a look at the worst case

a P my stations yet

currently we only look

look at the mean performance

thank you

and more questions

thank you