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