0:00:13 | i Q so yeah i will be presenting this on behalf of um |
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0:00:16 | E U and the other corridors um you had some visa issues and um kind of be here today |

0:00:22 | um so |

0:00:24 | um for this presentation we will consider the problem of precoding selection um for multicast systems |

0:00:31 | um first will |

0:00:32 | um motivate the work give some preliminaries and background |

0:00:36 | and then we'll introduce the major contribution of |

0:00:39 | uh this paper which is a set of probabilistic algorithms |

0:00:43 | over the precoding matrices |

0:00:45 | to improve the packet drop rate |

0:00:47 | um given some um performance goals |

0:00:51 | um and then we'll give some detailed um simulations of this work |

0:00:55 | so the |

0:00:58 | um the motivation is that most wireless was systems use some kind of feedback usually to um provide channel state |

0:01:05 | information |

0:01:06 | um to the transmitter um new systems um and emergent system such as all T |

0:01:12 | um rely heavily on this kind of feedback |

0:01:14 | um |

0:01:15 | two |

0:01:16 | um facilitate the growth and data rates due to smart from traffic and other |

0:01:22 | um wireless devices with large data need |

0:01:26 | um and so but we don't wanna do is to send back fee um quantized the channel state information |

0:01:32 | because we want to minimize the number of bits so we are using |

0:01:36 | and so |

0:01:36 | we instead choose a small number of precoding matrices |

0:01:40 | um |

0:01:41 | at the transmitter and then the individual receivers um take the channel state information that they measure |

0:01:47 | um choose the i'd the optimal |

0:01:51 | precoding matrix and then um send back the |

0:01:54 | um index of that matrix to the transmitter |

0:01:57 | and so this method provides |

0:02:00 | a feedback provides |

0:02:01 | gains in beamforming well also minimizing the number of feedback bits |

0:02:07 | um so but this is beyond the scope of the talk today but |

0:02:10 | um another work we have shown that predicted performance gains based on |

0:02:15 | um the instantaneous feedback are largely preserved if you consider um |

0:02:21 | feed that um if you make long range predictions based on rapidly time-varying um fading channels |

0:02:28 | and so |

0:02:30 | here the user will predict where the channel B in two to five millisecond |

0:02:35 | and um |

0:02:36 | assuming the accuracy of jakes model the performance gains are larger you preserved |

0:02:41 | even for user travelling in a car it's say sixty miles an hour |

0:02:47 | and so the focus of today's talk will be how to accommodate um multicast |

0:02:52 | where the transmitter receives |

0:02:53 | um limited feedback from the users |

0:02:56 | about different preferred channels that they have |

0:02:59 | so our assumptions um each |

0:03:09 | um so each user's treated equally in the important um |

0:03:13 | the important thing will be the geometry of our precoding matrices |

0:03:17 | and so by understanding this geometry we can and for a partial ordering |

0:03:21 | on the preferences of the users |

0:03:25 | um and |

0:03:26 | and their most preferred matrix |

0:03:28 | so this opens the door to many different um global optimization functions |

0:03:33 | um that focus and but we focus on minimizing the outage probability for each of the users channels |

0:03:41 | so the framework is general |

0:03:43 | is general but to a were also focus on and L T environment |

0:03:47 | um where each base station has two transmit antennas and each user has to receive antennas |

0:03:53 | um so that each um point to point link is a to by two system |

0:03:57 | and we also consider the standard L T precoding codebook |

0:04:02 | which will um come up later in the talk |

0:04:06 | so the |

0:04:07 | um |

0:04:08 | the system model that we have is each user |

0:04:12 | um |

0:04:13 | each um user receives |

0:04:15 | a a message from the transmitter that's |

0:04:18 | um |

0:04:19 | where the precoding matrix P |

0:04:21 | um shapes the message to be sent |

0:04:24 | and then it goes to the channel H for each receiver |

0:04:28 | um and it's corrupted by some noise |

0:04:30 | and um and here we just combine |

0:04:33 | um each of the channels for each receiver into one combined system |

0:04:38 | um we also have for the |

0:04:41 | the standard mmse capacity |

0:04:43 | um |

0:04:46 | um between each uh between the base station and each user |

0:04:50 | um given |

0:04:51 | right here |

0:04:54 | and so we're interested in maximizing the channel capacity for each |

0:04:58 | um for each user |

0:05:01 | here's a um a representation of the problem |

0:05:04 | we have um five users where um user one and user to both |

0:05:10 | um select the um precoding matrix one as the optimal |

0:05:14 | and the other users all choose a different |

0:05:17 | um precoding matrix as the optimal |

0:05:19 | so there's a few different ways to |

0:05:22 | um make this selection of the optimal precoding matrix |

0:05:26 | and um one is um we can do random selection or |

0:05:31 | a round robin or a majority rule |

0:05:34 | um the question is does the choice make a difference |

0:05:38 | and |

0:05:39 | in short it does if the goal involves quality of service |

0:05:43 | um if we were only looking to maximise the sum rate capacity |

0:05:47 | then we will only see incremental improvement |

0:05:50 | but because we are choosing um other goals |

0:05:53 | um the sum rate capacity than um |

0:05:56 | we find that it does make |

0:05:58 | um a different |

0:06:01 | and so here's are prop are um problem formulation we want to |

0:06:05 | minimize the average drop rate |

0:06:07 | that each user sees |

0:06:09 | and so um and outage happens if the capacity of the channel is below the rate that the transmitters trying |

0:06:16 | to send to the user |

0:06:18 | um captured right here |

0:06:20 | and um |

0:06:23 | and so we want to |

0:06:27 | and so we want to find the precoding matrix that minimises |

0:06:31 | the |

0:06:32 | um some of all the drop rates of each user |

0:06:39 | and the problem with this |

0:06:41 | um formulation is that the |

0:06:43 | the transmitter requires instantaneous channel state information |

0:06:48 | um which will not be available |

0:06:50 | um |

0:06:51 | in this situation |

0:06:53 | and so we re formulate the problem |

0:06:55 | um two |

0:06:56 | um minimize the expected drop rate |

0:06:59 | um based on the |

0:07:02 | um |

0:07:03 | the previous channel um channel state information fed back from the users |

0:07:10 | so if we only have a finitely many precoding matrices to choose from |

0:07:14 | then this optimization problem is feasible |

0:07:17 | and |

0:07:19 | we can um |

0:07:21 | and it's given by this expected value right here |

0:07:24 | which we can pretty um pretty compute |

0:07:28 | yeah are transmitter |

0:07:29 | um assuming that we have a |

0:07:31 | um stationary channel |

0:07:35 | so um |

0:07:37 | to um for this um computation we |

0:07:40 | um create this matrix a a |

0:07:42 | given right here |

0:07:43 | um and it looks like this |

0:07:46 | where um |

0:07:51 | um and then |

0:07:53 | for to make a decision we create this vector V which is just a collection of |

0:07:59 | the number of users that voted for |

0:08:03 | um |

0:08:04 | the precoding matrix indexed by J |

0:08:07 | and so to make are um our decision for the optimal precoding matrix |

0:08:12 | we just um take the largest |

0:08:15 | entry of the product um a times B |

0:08:20 | so now let's introduce are um |

0:08:23 | are L T precoding matrices |

0:08:26 | um we see that |

0:08:28 | these |

0:08:28 | rank one matrices right here are optimal in the low snr regime |

0:08:32 | and the rank two matrices are optimal in the high snr regime |

0:08:37 | and |

0:08:38 | um we wanna look at the situation where |

0:08:40 | um the channel is both |

0:08:42 | both |

0:08:43 | stationary and non-stationary |

0:08:45 | so if it stationary like i said we can pretty calculate |

0:08:48 | R matrix a a |

0:08:49 | and keep it at the transmitter |

0:08:51 | but at the channel is not stationary or unknown |

0:08:54 | um then we must do adaptive learning of a |

0:09:15 | and so for um for this but for this talk we consider the |

0:09:18 | um low as an region so where |

0:09:21 | selecting these um rank one matrices |

0:09:24 | and um |

0:09:28 | and so we will consider how to construct are matrix a |

0:09:31 | um in this case |

0:09:35 | so |

0:09:36 | um we see that you have and so the |

0:09:39 | the important thing to note is that |

0:09:42 | um these matrices are given in three N T pablo pairs |

0:09:46 | and so for example if uh matrix Q one |

0:09:50 | is the optimal then Q two is many times the worst matrix |

0:09:54 | um to choose |

0:09:55 | and the other four are in some sense um |

0:09:59 | have |

0:10:00 | roughly the same offer the same perform |

0:10:02 | so we can um reduce |

0:10:04 | the parameterization or matrix a |

0:10:07 | um to to parameters given by |

0:10:10 | a and B |

0:10:12 | and if we subtract it from the all one matrix then |

0:10:16 | we um can further reduce it to parameterisation by a single parameter C |

0:10:22 | and this parameter C |

0:10:26 | um is determined by the um the rate lambda the that we're trying to send |

0:10:32 | um to each of the users |

0:10:34 | or excuse use me the |

0:10:36 | lemme is the outage rate of the channel |

0:10:40 | and so here we see that um when if the outage rate is low |

0:10:45 | which means that are value of C is close to zero |

0:10:48 | then um Q one is the preferred |

0:10:51 | precoder um |

0:10:53 | and |

0:10:54 | um |

0:10:55 | Q three four five and six well all be um |

0:10:59 | greatly um preferred over the anti pa |

0:11:02 | um matrix |

0:11:04 | Q two |

0:11:05 | um but we see that if the outage probability is |

0:11:09 | hi um make you want is preferred |

0:11:11 | then the remaining um will be treated roughly equal |

0:11:19 | and so um |

0:11:20 | if the channel is non-stationary then we need to learn this matrix a a |

0:11:25 | um and so how what we do that |

0:11:28 | um we proposed this adaptive algorithm which is similar to |

0:11:32 | simulated annealing |

0:11:34 | um and the the basic idea is that we introduce a a a perturbation |

0:11:38 | to um the parameter |

0:11:41 | and then if that perturbation helps to improve the drop rate then we update the parameter |

0:11:46 | um if it doesn't then we randomly update the parameter with some probability |

0:11:54 | and so we also um |

0:11:56 | pick |

0:11:57 | a a um a service that were um |

0:12:02 | a service such as voice there were trying to optimize over |

0:12:05 | so the packet drop rate will greatly affect the |

0:12:08 | um quality of a voice call |

0:12:11 | um and so you |

0:12:12 | but you also want to minimize the delay |

0:12:15 | in that link |

0:12:17 | and so um one provisioning of service um user utility is measured by this are factor |

0:12:24 | um and i just want to emphasise a we could've picked |

0:12:28 | um other sit other services with the more stringent quality of service like video or gaming |

0:12:33 | um but the important point here is that we're connecting the channels to channel statistics |

0:12:38 | two |

0:12:39 | the um to the to the measured quality of the service |

0:12:44 | so um in this situation we simulated |

0:12:48 | uh system with eight users |

0:12:50 | and compare our scheme as shown here in black |

0:12:53 | against the um scheme and read without any precoding |

0:12:57 | and also the round robin scheme |

0:12:59 | and we see that the our scheme is close to the optimal |

0:13:04 | with just the optimal is computed um assuming that you have perfect channel state information at the transmitter |

0:13:11 | and we also see that we have a um similar |

0:13:14 | improvement on the R factor |

0:13:17 | um where where closer is closer to the |

0:13:20 | um |

0:13:21 | optimal |

0:13:22 | um than the other two schemes |

0:13:31 | and so um finally |

0:13:33 | um we assume that the channel is stationary |

0:13:36 | and also show that if we use |

0:13:38 | are adaptive algorithm |

0:13:40 | then we |

0:13:41 | um |

0:13:44 | perform very close to |

0:13:46 | um the fixed algorithm that involves pretty computing the matrix a at the transmitter |

0:13:51 | and so the shows that we um |

0:13:54 | we don't need to necessarily compute R matrix a um we can just use the adaptive algorithm and get um |

0:14:00 | nearly as good performance |

0:14:02 | um and so we won't have to store |

0:14:05 | um are matrix |

0:14:07 | and so um i hope that this |

0:14:10 | talk is |

0:14:11 | convinced you and peaked your curiosity about using um limited feedback |

0:14:16 | um information in wireless multicast system |

0:14:20 | thank you |

0:14:27 | right |

0:14:31 | oh |

0:14:34 | i |

0:14:36 | i can try to answer some questions for you |

0:14:54 | i |

0:14:55 | you |

0:14:58 | this one |

0:15:00 | uh_huh |

0:15:02 | i |

0:15:06 | i |

0:15:14 | i |

0:15:20 | um |

0:15:21 | i |

0:15:22 | i'm not sure |

0:15:24 | myself sorry |

0:15:32 | sorry |