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