Speech Transcript - AN EFFICIENT VARIABLE STEP-SIZE PROPORTIONATE AFFINE PROJECTION ALGORITHM

0:00:13	we got than
0:00:14	uh my name is
0:00:15	that was that in a little to and the to get that with the professor of S
0:00:20	from a you know that's
0:00:21	okay
0:00:22	and our team of
0:00:24	what what are you can
0:00:26	would like to present to a variable step-size the proposed and make a a type of in which we call
0:00:32	that
0:00:33	yeah or a solution for echo cancellation
0:00:37	uh
0:00:38	is the outline
0:00:39	as annotation
0:00:41	we can see
0:00:42	a what the production then uh
0:00:45	as the basis
0:00:47	of the proposed to eight of find projection
0:00:49	followed you followed by a
0:00:51	our proposed a and we and we
0:00:53	simulation up
0:00:54	company
0:00:56	now a sense to the nice presentation
0:01:00	yeah i
0:01:02	a scale but mission if we
0:01:04	if using production
0:01:06	basically we we deal with the same echo cancellation problem
0:01:09	we in fact is a
0:01:11	uh
0:01:12	system identification by with some challenge
0:01:15	this challenging in uh i have a union our maybe
0:01:19	is that a a long line
0:01:21	or the equal parts so a lot no think what they are not
0:01:24	if if you that and
0:01:25	maybe the double talk situations
0:01:28	see
0:01:29	is much
0:01:29	a challenging in there
0:01:31	a right
0:01:33	a this specific problem we
0:01:35	the the more give a task for some special Y
0:01:38	for example
0:01:39	if we want to
0:01:41	uh a faster
0:01:43	again and then choose the family of affine projection
0:01:46	oh
0:01:47	which we know that the
0:01:49	ah the
0:01:50	more efficient from this point of us compare
0:01:53	and that a man
0:01:54	and we also if we we won
0:01:56	to increase the robustness to double talk
0:01:59	we can use the body of a step size
0:02:01	we will see in the presentation
0:02:03	of course in general the as
0:02:05	a echo canceller
0:02:06	and keep with a little of detector but
0:02:09	yeah very useful
0:02:10	you is yeah that we've algorithm it somehow
0:02:13	oh was
0:02:13	but seven to that
0:02:16	and uh we have some of the hints let's say
0:02:20	uh
0:02:21	because course is the system we need to identify which are be
0:02:25	a a i i i
0:02:27	make is that the my is it
0:02:29	so it would be useful to the use
0:02:32	but to admit
0:02:33	i
0:02:34	adaptive of body
0:02:36	i i don't by means this three each with result
0:02:39	uh a the present a
0:02:45	now just the
0:02:47	oh
0:02:48	but if for the each of a you of the problem
0:02:50	uh this is the general
0:02:52	okay
0:02:52	separation
0:02:53	patient
0:02:54	what additional so
0:02:56	and the a lot of course
0:02:57	can be expressed in of a a ways for example from that use the point of view was the main
0:03:02	but
0:03:03	is to
0:03:04	but couple but C know the near a signal in the all yeah that
0:03:09	of course
0:03:10	for all a point of from the application point of view we have to cancel this K
0:03:15	well you not know what we have to like that if i is equal uh so this is the basic
0:03:20	and a the
0:03:22	application one
0:03:25	now i is a
0:03:27	uh talk uh and that the is the affine projection of what a a a a at may from the
0:03:33	convergence point of view
0:03:35	uh uh they but for very where especially we
0:03:38	the in it
0:03:39	signal inputs like speech
0:03:41	uh yeah creation
0:03:43	or the class
0:03:44	a find projection of are
0:03:46	you but yeah
0:03:48	uh
0:03:51	this is uh
0:03:52	it true signal vector but this as the input
0:03:54	signal signal my
0:03:56	and
0:03:56	most important this part i mean that you know the projection all that if you can see when P E
0:04:02	close to one
0:04:03	this is we used to a a lot and elements
0:04:06	this is a a a a if you and and
0:04:09	this is the step size for it that which we uh
0:04:12	the following
0:04:14	are those of its
0:04:15	H
0:04:16	now is that problem to me
0:04:18	a fine projection of what you can you thing by extending the idea of pnlms
0:04:24	in the same manner
0:04:26	as
0:04:26	we be form and lms the pnlms
0:04:29	we can do for
0:04:30	a yeah two
0:04:31	well it's it yeah
0:04:33	uh
0:04:35	it up yes this
0:04:36	that's a proper a marketing
0:04:39	which in fact is that i i i not automatic speech a lost to
0:04:43	a just just the step
0:04:45	for each the
0:04:46	in V but feel that way fish
0:04:49	if you can see here
0:04:51	let us denote by P of and is my
0:04:53	it would be very computationally efficient to compute a in the class that way
0:04:58	detection
0:04:59	we can take advantage of the i are gonna a kind of of this matter
0:05:03	and we can uh a process that it is yeah
0:05:07	this um
0:05:09	in this way
0:05:11	uh so here
0:05:13	B are not that sign
0:05:14	set
0:05:15	point
0:05:17	vector
0:05:18	is not the issue for a high number of do
0:05:20	so we can come
0:05:22	uh
0:05:23	so uh
0:05:23	P
0:05:25	and market
0:05:26	i simply multiplying
0:05:28	is a a a a a a a vector of the proper five
0:05:31	element by element with a vector or so
0:05:35	yeah these not means element by element multiplication between
0:05:39	these two but
0:05:41	as we can see
0:05:42	uh
0:05:43	the classical for more sound but they simple color the content
0:05:47	uh or what to make five
0:05:51	recently recently we proposed a soul call member
0:05:55	uh pop up to an the final projection of what
0:05:58	which
0:05:58	uh face into account not only the content
0:06:02	factors bar
0:06:03	that's that's study of these fact
0:06:05	and most important than
0:06:07	and uh
0:06:09	besides the fact that used are going to achieve
0:06:12	but that
0:06:12	performance in at instant
0:06:14	guess score that is that egg are i
0:06:17	it is more computation
0:06:19	efficient because
0:06:20	if you
0:06:21	take a look at C
0:06:23	uh
0:06:23	i
0:06:24	we need to compute or is the first
0:06:27	and N
0:06:28	the first
0:06:29	column
0:06:30	and to use
0:06:31	the out that form the previous
0:06:32	it that nation and and do the same
0:06:34	form for this map
0:06:36	this can be a a you know that if you should manner of my
0:06:40	computing or needs the first column and the first
0:06:42	which is not the case here
0:06:47	uh uh
0:06:48	you you the
0:06:49	it's uh
0:06:49	each of which you more plates
0:06:51	the uh
0:06:53	a
0:06:54	is that a on
0:06:55	uh medical many complex
0:06:56	that
0:06:57	patient
0:06:58	addition
0:06:59	uh there a class a lot of loading and our proposed a
0:07:03	of course
0:07:04	uh
0:07:06	yep and each becomes more smaller back and when we is the projection the
0:07:13	and uh
0:07:14	the next step
0:07:15	but what ones
0:07:16	which was to develop a of a step size
0:07:19	fashion for this
0:07:21	member in
0:07:22	uh uh how you
0:07:24	we we i here
0:07:25	uh uh it's a eight
0:07:28	and
0:07:29	again it is the step size mean
0:07:31	and is the we know
0:07:34	always
0:07:35	we have a complete think requirements
0:07:38	when we have to choose
0:07:39	the step size parameter because we have to compromise between combat
0:07:44	and misadjustment well
0:07:45	uh
0:07:46	the bit rate in
0:07:48	the double talk of who's that so
0:07:50	the you know that two
0:07:52	uh let's see
0:07:53	compromise is used the
0:07:56	and for out it yeah
0:07:57	it would be nice to use a body a step size the
0:08:02	and uh we start a lot development
0:08:05	by rewriting and it will be
0:08:07	this for a
0:08:09	uh using
0:08:11	uh a to use force the
0:08:13	step side
0:08:15	as as you can see
0:08:16	from these two
0:08:18	creations from this plot but it
0:08:20	if
0:08:21	we use
0:08:22	uh is the same but for all
0:08:25	and i and
0:08:26	we can get a each step size are working
0:08:29	which is
0:08:30	you can here
0:08:31	now
0:08:33	if we take a look
0:08:34	at a
0:08:36	a a posteriori a vector or not you are here a the which are you bring yeah
0:08:41	these these easy to uh what they no relation in these two that
0:08:46	using these two and a
0:08:49	a a of the seattle
0:08:51	now we can see is a relation and if we we remember that to the basic i
0:08:56	as you can find projection on reading once to chance and
0:09:00	be a posteriori here
0:09:01	the core we should
0:09:02	slides seas
0:09:04	assuming what was it
0:09:05	man
0:09:06	not well
0:09:07	we will get
0:09:08	a simple solution
0:09:10	which means that all the step size should be about one
0:09:14	unfortunately fortunately this holds already means absence of the nodes because is you remember from the
0:09:19	for
0:09:20	a
0:09:21	in the echo cancellation problem
0:09:23	we do not want to guess so
0:09:25	yeah
0:09:25	yeah are that if you don't by to recover is that near end signal
0:09:29	from these and so we modify
0:09:31	quantization
0:09:32	and we it i
0:09:33	uh
0:09:35	this is the
0:09:36	calculation that
0:09:38	that
0:09:38	then
0:09:39	we take the might or might have a
0:09:41	dictation
0:09:43	and the we get the
0:09:45	for
0:09:45	as a a a a a step size
0:09:48	of formal a like this
0:09:50	which yeah we have
0:09:52	the the elements of C L vector a
0:09:55	since is this is a very of but it is easy to estimate is this five
0:09:59	but unfortunately the problem but it mice
0:10:02	the estimate of the power
0:10:04	well of the near and
0:10:06	uh as the problems comes from the fact that the near end signal is in fact a combination P the
0:10:11	back noise and then you in speech
0:10:14	you when is two pass are uncorrelated heat so we can write as this relation
0:10:19	and even if we would basically to make this part and silence as for example
0:10:24	it is difficult to have an expression for this
0:10:27	uh
0:10:27	i
0:10:28	so
0:10:30	you know that to solve this problem
0:10:33	i i think that yeah that's that echo cancellation a configuration
0:10:38	so uh
0:10:41	we can express as you circulation in better
0:10:43	of
0:10:44	expectation
0:10:46	one and that of our
0:10:48	and now we will use a very strong assumption
0:10:52	which is that is yeah now if you that has come back somehow list and uh
0:10:56	get
0:10:58	in this case if if you make a a a a a a is this the assumption of this relation
0:11:03	can me
0:11:03	really then
0:11:05	axes
0:11:06	of course
0:11:07	as is this is a strong assumption because the
0:11:10	i'm i'm for example is the beginning of the adaptation one but i
0:11:15	station
0:11:16	it may not hold by
0:11:18	see E my the simulation that
0:11:20	so uh
0:11:21	oh performance a out of the fine
0:11:24	right would
0:11:25	uh uh most important
0:11:27	if we take a look at these the relation to this estimate all this
0:11:31	signal
0:11:32	all this uh measure are available because we only use
0:11:35	the signals
0:11:36	from the that if you that that that that is that i know and
0:11:40	it's all
0:11:41	oh from this point of view it would be a dark
0:11:44	a the solution
0:11:45	so the answer to our problem is
0:11:48	a state
0:11:49	step size of a space
0:11:50	step size
0:11:51	which look like to use of course
0:11:53	i i can be made
0:11:55	in the same or
0:11:56	say say that
0:11:58	and the finally
0:12:00	uh
0:12:02	we do show some uh
0:12:04	simulation results presented
0:12:06	you know a network echo cancellation problem
0:12:09	with a few that a lack of five and
0:12:11	the the wave actions
0:12:13	um the input will be you do white gaussian noise of speech
0:12:18	and a the the performance measure
0:12:21	a a a a a of the normalized means alignment or a according loss
0:12:25	a
0:12:26	and we will compare three at of buttons
0:12:31	our proposed or the last one
0:12:33	and
0:12:34	it's a uh uh a fixed stepsize action
0:12:38	uh uh as you can do these up here we do not mention anything about the alternate an eight five
0:12:43	you at can be we can was any what what's an eight back what
0:12:47	for
0:12:48	i
0:12:49	now uh you know uh i the experiment which is their i the elements of what in it's
0:12:56	what what and fact factor
0:12:57	was also presented by a monaural
0:13:00	before
0:13:01	uh in as
0:13:02	our simulation they'd
0:13:04	the bible
0:13:04	i mean
0:13:05	but is also
0:13:06	the the trans
0:13:08	and we compare
0:13:09	uh is this struggling in with
0:13:11	is that a have the step size
0:13:13	non proposed at that should the action
0:13:16	which is
0:13:17	uh
0:13:18	or they need to remove the
0:13:20	for puts an eight might from these
0:13:22	the ah
0:13:24	in the first
0:13:24	speed man
0:13:25	we compare the variable step that should with a fixed at signs
0:13:29	that's and was to
0:13:31	a fighting for the step size as we can see
0:13:34	uh as the body of the step size that's and combat almost as fast as
0:13:38	the
0:13:40	each step side that's start with a lot
0:13:42	size
0:13:43	but achieve a much lower miss i'm and close
0:13:46	and that
0:13:47	situation
0:13:49	in this case we use the
0:13:51	an input signal
0:13:53	uh
0:13:54	white gaussian noise
0:13:56	then
0:13:56	we uh are an snr all
0:13:59	uh
0:14:01	assuming that uh
0:14:03	try
0:14:04	patient the mean that
0:14:05	relation
0:14:06	and we compare our algorithm with a
0:14:08	none of course but may action
0:14:11	we can see that
0:14:12	i'll hope of that
0:14:13	is expected somehow
0:14:15	a of problems
0:14:16	a class L
0:14:18	action
0:14:18	in that of well convergence it
0:14:22	or that just
0:14:23	this alignment
0:14:24	and finally
0:14:26	uh uh you know that what looks and i not
0:14:29	uh
0:14:30	we compare at all
0:14:32	the three hour
0:14:34	and uh we see that for this point of view from that was to double a point of
0:14:39	our our that it's
0:14:41	much more what was as compare
0:14:43	yeah
0:14:44	at least is uh a non of a step size
0:14:48	yeah we use a a simple get about that that
0:14:51	a vector just two
0:14:53	and
0:14:53	the adaptation
0:14:55	double talk
0:14:59	i in it is a a a a few conclusion
0:15:01	so we propose
0:15:02	this out that point text of for echo cancellation
0:15:06	first
0:15:07	we can take advantage from a its computation of complex
0:15:11	T
0:15:12	which is low as from that is a class
0:15:15	second
0:15:16	we think that is important that the value of a step side
0:15:19	for
0:15:20	somehow somehow not about made
0:15:22	this means that we do not use any additional power uh
0:15:27	i'm sure one by one
0:15:30	and
0:15:31	we also note this is that
0:15:33	uh
0:15:34	these more what used to
0:15:36	uh near end signal evaluation
0:15:38	and most important to double
0:15:42	thank you very much earlier
0:15:51	for that
0:15:52	well we do you have some time for
0:15:53	i if anybody like
0:15:58	using again
0:16:02	you
0:16:03	presentation presentation just them curious about two
0:16:05	the step size it becomes negative when the values of the
0:16:08	design a value is a lot to than that of the there
0:16:12	yeah
0:16:13	so
0:16:17	in this problem
0:16:18	okay
0:16:19	this is a very nice for
0:16:21	because it we ski but it to meet some practical issues yeah
0:16:26	it is a recommended fast
0:16:28	to at
0:16:29	a small positive constant yeah
0:16:31	just to avoid you bytes
0:16:33	at most important
0:16:34	we should they is the absolute but
0:16:37	this a three star is then
0:16:39	the
0:16:40	but but what i
0:16:42	too much
0:16:43	but
0:16:44	if
0:16:51	inking your simulations used in order
0:16:53	a projection order
0:16:54	for for for yes
0:16:56	and is the method sense to the project no
0:16:59	no we just to choose this value
0:17:02	it's a for complex
0:17:03	but
0:17:04	we try was my
0:17:06	projection of
0:17:08	you have
0:17:09	and in your a personal experience
0:17:11	what projection order do you find is really the the right
0:17:14	and it to be working in
0:17:16	for for
0:17:18	uh
0:17:19	i think that uh to three we well we should not to take a larger than eight
0:17:25	that
0:17:26	but also because of the complexity issue you by that you for this these some uh
0:17:32	that's a diffusion map for completely because in a fine as the fine projection of what you
0:17:37	so main problem is how to invest
0:17:40	the out
0:17:41	i i have a project the higher projection of but we been blind or if you a quotation my
0:17:46	recently the as far as i
0:17:48	no was that are some more efficient manner
0:17:50	for example
0:17:52	you you all
0:17:53	because the models
0:17:55	i
0:17:56	or the might be end
0:17:57	variation of by
0:17:59	well also a
0:18:01	which she uh if you lead that for this operations so we can even go higher
0:18:05	a project
0:18:09	and other question
0:18:15	i think i have the opportunity to last one um
0:18:18	a more general question concerning the difference between acoustic echo cancellation
0:18:23	and network
0:18:25	and
0:18:26	could you clarify which
0:18:28	i think you first results at least as in the network
0:18:31	sure
0:18:32	yes
0:18:32	a the was the
0:18:34	so is the star
0:18:35	a point of
0:18:36	two and eight type of that if you that
0:18:39	oh
0:18:39	for a network that for consideration and respect to
0:18:43	that form but that's
0:18:44	send send you because of this i
0:18:47	of the
0:18:47	because i buy it can fall you by room acoustic a more cancellation if we properly choose
0:18:54	the proposed to eight five
0:18:55	this was that he's and defines the chose of the I the nlms out
0:18:59	which is
0:19:00	somehow of a host to this
0:19:02	ask
0:19:04	part think the
0:19:05	of course the
0:19:06	we can use for example a low as far as and uh as i
0:19:10	we proposed a few
0:19:12	a one year ago goes as the sparseness control coding which can
0:19:16	a beep on uh
0:19:18	well efficient as compared to ipnlms mess if we know as this from miss what it's to make some the
0:19:24	smell
0:19:25	so we is important to choose the proposed
0:19:30	well that's great thank you very much and

AN EFFICIENT VARIABLE STEP-SIZE PROPORTIONATE AFFINE PROJECTION ALGORITHM

Echo Cancellation

Presented by: Constantin Paleologu, Author(s): Constantin Paleologu, University Politehnica of Bucharest, Romania; Jacob Benesty, University of Quebec, Canada; Felix Albu, Silviu Ciochina, University Politehnica of Bucharest, Romania