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