Speech Transcript - DETECTION DIVERSITY OF MULTIANTENNA SPECTRUM SENSORS

0:00:13	hello everyone
0:00:15	a here i will be presenting a high during the work between the university of people and to feel it's
0:00:20	set
0:00:21	in the netherlands
0:00:24	okay
0:00:25	here it will be a speaking about the concept of a detection like diversity
0:00:30	in one can to
0:00:31	spectrum sense
0:00:33	as we will see
0:00:36	a a a a a you is pretty minds the concept of type are T A we all know from
0:00:41	communication
0:00:43	and here a is that would like to a person
0:00:46	first
0:00:48	i will be introducing the concept of a a type are T
0:00:52	may in communications
0:00:54	probably due are or familiar
0:00:56	with it but uh it just one is light
0:00:58	and then i will be presenting
0:01:01	the a
0:01:03	this set that we will be can is here to form we can't that i detection
0:01:08	oh will be paired very simple
0:01:10	simple model but the is enough for our corporate part
0:01:15	and
0:01:16	then i'm willing to use the concept of type are T first percent it by that kind of map
0:01:22	in their a context of for uh that networks and we we see that it applies to was spectrum sensing
0:01:28	and i with if few nice the presentation with some results
0:01:32	and they find out
0:01:33	please
0:01:36	first
0:01:37	and the concept of diversity in wireless communications
0:01:41	yeah
0:01:43	it's a a like a
0:01:45	we have a a a bit error rate cool
0:01:48	usually a a a and these behaviour in the high snr regime
0:01:53	that it's a we have here um with if you got that that it's sort which were usually colour
0:01:58	a coding gain of quickly to now that
0:02:00	i one
0:02:01	and to a we have here i'm X point
0:02:04	that it is that are secure
0:02:07	a by using different coding scheme so we can
0:02:10	a a move this course down but this no is kind of their as file they died are secure that
0:02:15	of the is
0:02:17	and a
0:02:18	the was Q means a if we can in probably a similar scheme in
0:02:23	in a
0:02:24	that a the spectrum sense
0:02:26	and we would see that a a yes
0:02:28	but
0:02:29	we have we must have into account that in communications
0:02:33	okay we use when move far from this point so that
0:02:37	we use the
0:02:39	usually go to the bit error rates are um to ten to the minor to your ten to the minus
0:02:44	four
0:02:45	and
0:02:46	a a a a use could be not the case in the case of the spend to sense
0:02:51	a here we have the model that we we can see there here in a spectrum sensing
0:02:56	a a a a a simple in the sense that a will be considered
0:03:00	both the spatial and a both temporal
0:03:04	while
0:03:05	signal
0:03:06	and nodes
0:03:08	and to
0:03:09	here we will have that the noise he's can see there are uncorrelated that first antennas same with the same
0:03:14	part
0:03:15	we should we be assumed no
0:03:17	and the signal it would be a a run one in
0:03:21	that T
0:03:22	a a is the same signal
0:03:23	seeing told antennas
0:03:25	yes multiplied by a company
0:03:26	five
0:03:29	and a we we consider here are some more
0:03:34	under this model it's easy to see that the hypothesis that dustin problem is given by the eye what this
0:03:40	is there
0:03:41	that a
0:03:43	no no memory usage is present
0:03:45	that is the the same to say that H sequence either
0:03:49	yeah hypothesis one it's different from zero
0:03:52	and to as detection schemes
0:03:54	we we can see there a a a three C
0:03:57	the first one is that year are clear that the talk but you're not i a generalized likelihood
0:04:02	racial test
0:04:03	for a say and more that we present before
0:04:06	and in this case we have that in this a is that vector or response to the largest eigenvalue of
0:04:12	the spatial covariance
0:04:15	mesh sure
0:04:16	spatial covariance
0:04:17	and then
0:04:18	these detector
0:04:19	choirs the cross-correlation terms between the different a
0:04:24	and see it's not a very useful for for to put the
0:04:28	implementation
0:04:30	then we have a the detection that just mesh are spent at the at each of and then S
0:04:35	some C
0:04:36	i
0:04:36	and compress it seconds set their score
0:04:39	and a finally we will have a a a fully these two would
0:04:44	a a or we sure that
0:04:46	a a a a and that test
0:04:48	performed is in each of the nodes and then just the decisions are right
0:04:52	send
0:04:53	to the fashion
0:04:54	which one send
0:04:56	and the
0:04:59	as you can see these say that the are a better
0:05:02	in terms of their complexity
0:05:04	first we have these that they are requires that they only got ten S are located
0:05:09	this one requires to there's meet then or you seen by each of the that top say here we have
0:05:14	they or for sure
0:05:16	and
0:05:17	as performers formers tick we will use a a day usual probably lead your sound and
0:05:22	and the probability of detection that it's equal want to a one minute the probability of
0:05:28	and the we are considering here a a fading the fading case
0:05:32	we are that a a bit channel coefficient and coefficient H
0:05:37	is not the state it is not a deterministic but a a a a presents that are and fading
0:05:43	in this case we have that they produce the of false alarm
0:05:46	it depends only on the on this is zero and does it and doesn't depend on the right stations of
0:05:52	they
0:05:52	of the channel
0:05:55	and then we
0:05:57	we have that the a a a it's a also that are used
0:06:01	can in the following we will consider probability of false alarm fixed
0:06:05	and we will focus on the became your of the probability of detection and probability of missed detection
0:06:11	that the columns a random body
0:06:14	can we talk about the and they were set in this case
0:06:17	and that's there is a a a a a two
0:06:19	if we plot
0:06:22	directly they a their behaviour of the different detectors
0:06:26	for a different number of antennas
0:06:29	yeah we brought in the average means that the probability
0:06:33	this already average over a a fading right S H M so the channel are going to be average a
0:06:38	signal of the channel
0:06:39	and we can see that a a week come bound
0:06:42	all the behaviour of detectors
0:06:44	and the same definition of in the communications a scheme apply
0:06:49	that be say here we have that the slope of the cool
0:06:52	a corresponds to my and the number of and
0:06:57	however that was to me a does it makes sense to consider these
0:07:01	this performance metric
0:07:03	in
0:07:04	in the spectrum sensing
0:07:07	because here if we will look quite these axes
0:07:10	we see that a we yeah we if they asymptotic really in a signals larger than C
0:07:16	but we are interested more in the behaviour of if you for and the schemes here and use be you
0:07:22	where a
0:07:23	these behavior is
0:07:24	you sent a fully described by this is no
0:07:29	hence can a we have that
0:07:33	in in
0:07:34	in
0:07:35	a spectrum sensing we are more interested
0:07:38	you know in these two point
0:07:40	i mean a a a a at what point
0:07:42	that that vectors are just working with
0:07:44	and how fast
0:07:46	these that the door
0:07:47	a
0:07:49	i achieves
0:07:50	asymptotic asymptotic rate
0:07:53	in this case a
0:07:55	we we can think
0:07:57	if
0:07:58	if the a previous method a couple i can describe this
0:08:01	features and a we say that we can see that and that a a a
0:08:06	detection by their city as seen in communications just described the behaviour of the course
0:08:11	cool
0:08:12	here
0:08:13	when the probability of rich probably get detection was close to one
0:08:18	but a ever this problem or ready yeah there you four
0:08:21	in there are that work
0:08:22	and they here we are going to use a a summer results
0:08:26	first present it by that i don't have
0:08:30	in the feed it of a product networks
0:08:33	and a but you also have the same problem that the and they are actual definition of type are you
0:08:38	that's an but i directly to a to the sense
0:08:44	a spectrum sense
0:08:45	in this case they are there as they T by two permit
0:08:49	a they define that may more iteration of a signal
0:08:54	a
0:08:55	crowbar bar star
0:08:56	that it's here and you'd say and the point where they
0:09:00	average probably the of detection it was point five
0:09:04	that it's a and the point
0:09:06	from which they that vectors that's working well
0:09:11	this corpus
0:09:12	all i always assumes that the probably you of false alarm is fixed
0:09:16	a case a fixed for
0:09:19	and the the second a
0:09:21	metric take they use
0:09:23	to characterise the
0:09:25	the performance
0:09:27	is that they are secure the or that or that a i'm not a bit by are T
0:09:31	that in this case is defined as a is slow
0:09:35	of a
0:09:36	average average probability of detection at this point that we have seen before
0:09:41	that to use a a a a a prop
0:09:43	the performance of kind of a eyes by
0:09:46	these
0:09:47	like that i wrote he
0:09:54	a a in their case
0:09:56	this this that they pretty they use a is very similar to that one may we have seen
0:10:01	in five to this equation
0:10:03	i really is complete with the more they like percent at to be in this talk
0:10:08	the only difference that it's a big difference
0:10:11	is that a you know for rather
0:10:13	the vector direct X
0:10:14	these assumed to be known
0:10:17	and the seems the that already
0:10:19	it's assumed to be no
0:10:21	a
0:10:21	why even if fading
0:10:23	it can be seen as a option
0:10:26	a random variable
0:10:27	because we have here i i wish and noise last
0:10:30	the for a
0:10:31	what features of the channel that is also about the case of raid five fading
0:10:36	and then thing
0:10:38	this um is
0:10:39	also about
0:10:40	and then
0:10:41	they derive the diversity order
0:10:45	as defined by
0:10:47	i is the mutual we have seen before
0:10:51	a for a three different detectors high percentage before
0:10:54	for the idea that they they think that they or their grows
0:10:58	linear with the number of antennas
0:11:01	energy detection we could also with
0:11:03	the square root of a
0:11:05	and they are function i a
0:11:08	it grows with a a low you mean
0:11:11	of the number of and can spend taking of the cases it's proportional to the number of some
0:11:16	we have a from each of them then
0:11:19	but a a however in a spectrum sensing a a we have
0:11:23	that a
0:11:25	just go here
0:11:26	we have to be
0:11:27	the transmitted signal by the primary system is not no
0:11:31	in this case a we have here i wish we could like biology
0:11:35	yeah
0:11:36	something
0:11:37	and here we have another option
0:11:40	a it's is
0:11:42	something in difficult to deal with
0:11:44	and a in five
0:11:45	we have a
0:11:49	the a
0:11:50	the probability of the detection
0:11:52	without
0:11:53	i
0:11:54	having the average
0:11:56	i mean a we have this i mean close form but we need one but it with respect to the
0:12:01	fading of the channel
0:12:04	a a this is a difficult
0:12:06	and a a a at least a
0:12:09	a a in order to get some
0:12:11	close form results as we have to resort to approximations
0:12:16	and they inspired by the problem and a actually definition of a C you by that do not
0:12:21	we propose the following approximation
0:12:24	here a i'm not in their joint probability of detection
0:12:28	that's a before they title
0:12:32	average
0:12:33	a a with respect
0:12:34	to this thing
0:12:35	to the extent and
0:12:36	as
0:12:37	and we approximate it by a piecewise linear
0:12:40	function
0:12:41	that a a a a a has there right the slope but the point
0:12:44	so your point five
0:12:45	and then
0:12:47	you
0:12:48	you from a point and before a point it
0:12:51	zero and one
0:12:54	this looks like a rough approximation but they are there are writing with respect to
0:13:00	to the a
0:13:01	to a rayleigh fading we see that and a
0:13:05	the approximation a
0:13:07	fits speed you we pretty well with they a with N P D rock salt
0:13:12	and more if we look at the point of interest that it's are around
0:13:17	where the probability of detection is a point five the average probability of detection is point
0:13:24	and a
0:13:25	using this a this approximation we we where you want to thing
0:13:30	the same type of the order that
0:13:32	i in the case of for other
0:13:34	but a a for our to
0:13:36	this is already the a and that her and then at their type of C by that's that you are
0:13:40	for spectrum send
0:13:42	a here we can see that a a there are stored sub time not quite similar to the to that
0:13:47	one simple of usually
0:13:49	and the
0:13:51	here we see that a a for the N or the we then in that uh a more of their
0:13:55	proportional to web
0:13:57	here are for an and you the texture the square root of ten
0:14:00	and for the or for sure
0:14:01	even using this approximations
0:14:04	we are not able to obtain now
0:14:06	a a closed-form expression for the
0:14:09	now i
0:14:12	in this case a we just show numerically that it's a smaller on the square
0:14:18	but they we believe
0:14:20	we believe that they in fact
0:14:23	i
0:14:23	it is
0:14:24	similar to the case of a rather think it's problem
0:14:28	brought proportional to look
0:14:32	and a which is the main difference
0:14:35	with respect to a rather that a here
0:14:37	if you if we all remember the the other perhaps you where
0:14:41	exactly like that
0:14:42	but we have a okay are and not just
0:14:46	uh i square root of K
0:14:49	this uh
0:14:52	is performance to a big keys
0:14:54	the comes from the fact that we don't know that with that C
0:14:58	you know rather that they know they
0:15:01	the vector
0:15:02	a
0:15:04	the transmitted signal
0:15:06	and then
0:15:08	they
0:15:08	a start
0:15:09	a like are or of the um we can do here the spectrum sin
0:15:16	and a to finish this presentation of just will percent here some
0:15:20	some numerical results
0:15:22	that we can not thing you see these
0:15:25	i
0:15:26	seem that more than
0:15:28	here we can see that the and the minimum operational snr
0:15:33	a
0:15:34	the D C with the number of antennas
0:15:37	and a we can see here that actually
0:15:40	there are a a a a a great of D is with respect
0:15:44	to the different
0:15:46	a a to the different that that
0:15:48	and the D R and yeah O T
0:15:50	or which performs best
0:15:51	but uh as we have seen it cannot be implement implement eating at least T would be man
0:15:57	and then are you X that
0:15:59	it performs a pretty you that are and day or for sure
0:16:03	and here we can see they behave you're right talk a lot before that if we look at the diapers
0:16:08	the or or than with respect to the number of antennas
0:16:11	the growth great
0:16:12	for the are to use mostly you
0:16:15	why a they one for day
0:16:17	and that you that they don't use a kind of a
0:16:21	following the square root of and
0:16:23	and he and or for sure
0:16:25	we can not think these numerical
0:16:28	for from the theoretical results
0:16:30	but we can not get that close form spanish pressure
0:16:34	a a to compute
0:16:35	some complete from
0:16:37	here i percent the concept of a a a a a that are not a they to T
0:16:42	and we have seen that it's meaningful
0:16:45	for spectrum size
0:16:46	this are that we use
0:16:48	a however
0:16:50	a a it's
0:16:51	white white and if you were to compute
0:16:54	a a and we need
0:16:55	to we sort
0:16:56	two approximations in model the too
0:16:59	do thing a close form
0:17:01	a
0:17:02	and a a i is to the racial set technique an approximation we some are we have four with
0:17:08	to take care about using approximations in these kind of
0:17:12	point
0:17:13	and as future work a yeah
0:17:16	the i just percent it one
0:17:18	not channel aggressive but but
0:17:20	maybe there is another one that is more
0:17:23	so double for our case
0:17:25	and a we may just than the press
0:17:28	a
0:17:30	that are
0:17:31	that are not
0:17:32	they a and not used
0:17:33	ooh more complex that the talks for all their fading standard
0:17:37	and we these uh i i finish my person take
0:17:40	or
0:17:44	so uh
0:17:45	there is a a question from the stage we have
0:17:48	four minutes so
0:17:49	we can take some question
0:17:55	okay if you don't have a question have one
0:17:57	uh
0:17:58	you told that's that's your results are based on a approximation
0:18:02	and and that you were working with the
0:18:04	fixed it probably to fonts and
0:18:07	so the question is is is your
0:18:09	approximation
0:18:10	batted than in your a is used for and it probably the found are i mean it's
0:18:14	what robust with
0:18:15	different probably the false or or or or
0:18:19	yeah
0:18:23	right
0:18:25	yeah
0:18:27	i
0:18:27	white
0:18:30	i
0:18:32	or
0:18:33	i
0:18:34	a
0:18:36	i
0:18:37	a
0:18:42	i
0:18:51	i
0:19:05	okay that's
0:19:07	and that a question
0:20:50	okay i use there is no hundred question list then the speaker
0:20:53	um

DETECTION DIVERSITY OF MULTIANTENNA SPECTRUM SENSORS

Spectrum Sensing for Cognitive Radio

Presented by: Gonzalo Vazquez-Vilar, Author(s): Gonzalo Vazquez-Vilar, Roberto Lopez-Valcarce, University of Vigo, Spain; Ashish Pandharipande, Philips Research, Netherlands