i Q so yeah i will be presenting this on behalf of um E U and the other corridors um you had some visa issues and um kind of be here today um so um for this presentation we will consider the problem of precoding selection um for multicast systems um first will um motivate the work give some preliminaries and background and then we'll introduce the major contribution of uh this paper which is a set of probabilistic algorithms over the precoding matrices to improve the packet drop rate um given some um performance goals um and then we'll give some detailed um simulations of this work so the um the motivation is that most wireless was systems use some kind of feedback usually to um provide channel state information um to the transmitter um new systems um and emergent system such as all T um rely heavily on this kind of feedback um two um facilitate the growth and data rates due to smart from traffic and other um wireless devices with large data need um and so but we don't wanna do is to send back fee um quantized the channel state information because we want to minimize the number of bits so we are using and so we instead choose a small number of precoding matrices um at the transmitter and then the individual receivers um take the channel state information that they measure um choose the i'd the optimal precoding matrix and then um send back the um index of that matrix to the transmitter and so this method provides a feedback provides gains in beamforming well also minimizing the number of feedback bits um so but this is beyond the scope of the talk today but um another work we have shown that predicted performance gains based on um the instantaneous feedback are largely preserved if you consider um feed that um if you make long range predictions based on rapidly time-varying um fading channels and so here the user will predict where the channel B in two to five millisecond and um assuming the accuracy of jakes model the performance gains are larger you preserved even for user travelling in a car it's say sixty miles an hour and so the focus of today's talk will be how to accommodate um multicast where the transmitter receives um limited feedback from the users about different preferred channels that they have so our assumptions um each um so each user's treated equally in the important um the important thing will be the geometry of our precoding matrices and so by understanding this geometry we can and for a partial ordering on the preferences of the users um and and their most preferred matrix so this opens the door to many different um global optimization functions um that focus and but we focus on minimizing the outage probability for each of the users channels so the framework is general is general but to a were also focus on and L T environment um where each base station has two transmit antennas and each user has to receive antennas um so that each um point to point link is a to by two system and we also consider the standard L T precoding codebook which will um come up later in the talk so the um the system model that we have is each user um each um user receives a a message from the transmitter that's um where the precoding matrix P um shapes the message to be sent and then it goes to the channel H for each receiver um and it's corrupted by some noise and um and here we just combine um each of the channels for each receiver into one combined system um we also have for the the standard mmse capacity um um between each uh between the base station and each user um given right here and so we're interested in maximizing the channel capacity for each um for each user here's a um a representation of the problem we have um five users where um user one and user to both um select the um precoding matrix one as the optimal and the other users all choose a different um precoding matrix as the optimal so there's a few different ways to um make this selection of the optimal precoding matrix and um one is um we can do random selection or a round robin or a majority rule um the question is does the choice make a difference and in short it does if the goal involves quality of service um if we were only looking to maximise the sum rate capacity then we will only see incremental improvement but because we are choosing um other goals um the sum rate capacity than um we find that it does make um a different and so here's are prop are um problem formulation we want to minimize the average drop rate that each user sees and so um and outage happens if the capacity of the channel is below the rate that the transmitters trying to send to the user um captured right here and um and so we want to and so we want to find the precoding matrix that minimises the um some of all the drop rates of each user and the problem with this um formulation is that the the transmitter requires instantaneous channel state information um which will not be available um in this situation and so we re formulate the problem um two um minimize the expected drop rate um based on the um the previous channel um channel state information fed back from the users so if we only have a finitely many precoding matrices to choose from then this optimization problem is feasible and we can um and it's given by this expected value right here which we can pretty um pretty compute yeah are transmitter um assuming that we have a um stationary channel so um to um for this um computation we um create this matrix a a given right here um and it looks like this where um um and then for to make a decision we create this vector V which is just a collection of the number of users that voted for um the precoding matrix indexed by J and so to make are um our decision for the optimal precoding matrix we just um take the largest entry of the product um a times B so now let's introduce are um are L T precoding matrices um we see that these rank one matrices right here are optimal in the low snr regime and the rank two matrices are optimal in the high snr regime and um we wanna look at the situation where um the channel is both both stationary and non-stationary so if it stationary like i said we can pretty calculate R matrix a a and keep it at the transmitter but at the channel is not stationary or unknown um then we must do adaptive learning of a and so for um for this but for this talk we consider the um low as an region so where selecting these um rank one matrices and um and so we will consider how to construct are matrix a um in this case so um we see that you have and so the the important thing to note is that um these matrices are given in three N T pablo pairs and so for example if uh matrix Q one is the optimal then Q two is many times the worst matrix um to choose and the other four are in some sense um have roughly the same offer the same perform so we can um reduce the parameterization or matrix a um to to parameters given by a and B and if we subtract it from the all one matrix then we um can further reduce it to parameterisation by a single parameter C and this parameter C um is determined by the um the rate lambda the that we're trying to send um to each of the users or excuse use me the lemme is the outage rate of the channel and so here we see that um when if the outage rate is low which means that are value of C is close to zero then um Q one is the preferred precoder um and um Q three four five and six well all be um greatly um preferred over the anti pa um matrix Q two um but we see that if the outage probability is hi um make you want is preferred then the remaining um will be treated roughly equal and so um if the channel is non-stationary then we need to learn this matrix a a um and so how what we do that um we proposed this adaptive algorithm which is similar to simulated annealing um and the the basic idea is that we introduce a a a perturbation to um the parameter and then if that perturbation helps to improve the drop rate then we update the parameter um if it doesn't then we randomly update the parameter with some probability and so we also um pick a a um a service that were um a service such as voice there were trying to optimize over so the packet drop rate will greatly affect the um quality of a voice call um and so you but you also want to minimize the delay in that link and so um one provisioning of service um user utility is measured by this are factor um and i just want to emphasise a we could've picked um other sit other services with the more stringent quality of service like video or gaming um but the important point here is that we're connecting the channels to channel statistics two the um to the to the measured quality of the service so um in this situation we simulated uh system with eight users and compare our scheme as shown here in black against the um scheme and read without any precoding and also the round robin scheme and we see that the our scheme is close to the optimal with just the optimal is computed um assuming that you have perfect channel state information at the transmitter and we also see that we have a um similar improvement on the R factor um where where closer is closer to the um optimal um than the other two schemes and so um finally um we assume that the channel is stationary and also show that if we use are adaptive algorithm then we um perform very close to um the fixed algorithm that involves pretty computing the matrix a at the transmitter and so the shows that we um we don't need to necessarily compute R matrix a um we can just use the adaptive algorithm and get um nearly as good performance um and so we won't have to store um are matrix and so um i hope that this talk is convinced you and peaked your curiosity about using um limited feedback um information in wireless multicast system thank you right oh i i can try to answer some questions for you i you this one uh_huh i i i um i i'm not sure myself sorry sorry