0:00:13i Q so yeah i will be presenting this on behalf of um
0:00:16E U and the other corridors um you had some visa issues and um kind of be here today
0:00:22um so
0:00:24um for this presentation we will consider the problem of precoding selection um for multicast systems
0:00:31um first will
0:00:32um motivate the work give some preliminaries and background
0:00:36and then we'll introduce the major contribution of
0:00:39uh this paper which is a set of probabilistic algorithms
0:00:43over the precoding matrices
0:00:45to improve the packet drop rate
0:00:47um given some um performance goals
0:00:51um and then we'll give some detailed um simulations of this work
0:00:55so the
0:00:58um the motivation is that most wireless was systems use some kind of feedback usually to um provide channel state
0:01:06um to the transmitter um new systems um and emergent system such as all T
0:01:12um rely heavily on this kind of feedback
0:01:16um facilitate the growth and data rates due to smart from traffic and other
0:01:22um wireless devices with large data need
0:01:26um and so but we don't wanna do is to send back fee um quantized the channel state information
0:01:32because we want to minimize the number of bits so we are using
0:01:36and so
0:01:36we instead choose a small number of precoding matrices
0:01:41at the transmitter and then the individual receivers um take the channel state information that they measure
0:01:47um choose the i'd the optimal
0:01:51precoding matrix and then um send back the
0:01:54um index of that matrix to the transmitter
0:01:57and so this method provides
0:02:00a feedback provides
0:02:01gains in beamforming well also minimizing the number of feedback bits
0:02:07um so but this is beyond the scope of the talk today but
0:02:10um another work we have shown that predicted performance gains based on
0:02:15um the instantaneous feedback are largely preserved if you consider um
0:02:21feed that um if you make long range predictions based on rapidly time-varying um fading channels
0:02:28and so
0:02:30here the user will predict where the channel B in two to five millisecond
0:02:35and um
0:02:36assuming the accuracy of jakes model the performance gains are larger you preserved
0:02:41even for user travelling in a car it's say sixty miles an hour
0:02:47and so the focus of today's talk will be how to accommodate um multicast
0:02:52where the transmitter receives
0:02:53um limited feedback from the users
0:02:56about different preferred channels that they have
0:02:59so our assumptions um each
0:03:09um so each user's treated equally in the important um
0:03:13the important thing will be the geometry of our precoding matrices
0:03:17and so by understanding this geometry we can and for a partial ordering
0:03:21on the preferences of the users
0:03:25um and
0:03:26and their most preferred matrix
0:03:28so this opens the door to many different um global optimization functions
0:03:33um that focus and but we focus on minimizing the outage probability for each of the users channels
0:03:41so the framework is general
0:03:43is general but to a were also focus on and L T environment
0:03:47um where each base station has two transmit antennas and each user has to receive antennas
0:03:53um so that each um point to point link is a to by two system
0:03:57and we also consider the standard L T precoding codebook
0:04:02which will um come up later in the talk
0:04:06so the
0:04:08the system model that we have is each user
0:04:13each um user receives
0:04:15a a message from the transmitter that's
0:04:19where the precoding matrix P
0:04:21um shapes the message to be sent
0:04:24and then it goes to the channel H for each receiver
0:04:28um and it's corrupted by some noise
0:04:30and um and here we just combine
0:04:33um each of the channels for each receiver into one combined system
0:04:38um we also have for the
0:04:41the standard mmse capacity
0:04:46um between each uh between the base station and each user
0:04:50um given
0:04:51right here
0:04:54and so we're interested in maximizing the channel capacity for each
0:04:58um for each user
0:05:01here's a um a representation of the problem
0:05:04we have um five users where um user one and user to both
0:05:10um select the um precoding matrix one as the optimal
0:05:14and the other users all choose a different
0:05:17um precoding matrix as the optimal
0:05:19so there's a few different ways to
0:05:22um make this selection of the optimal precoding matrix
0:05:26and um one is um we can do random selection or
0:05:31a round robin or a majority rule
0:05:34um the question is does the choice make a difference
0:05:39in short it does if the goal involves quality of service
0:05:43um if we were only looking to maximise the sum rate capacity
0:05:47then we will only see incremental improvement
0:05:50but because we are choosing um other goals
0:05:53um the sum rate capacity than um
0:05:56we find that it does make
0:05:58um a different
0:06:01and so here's are prop are um problem formulation we want to
0:06:05minimize the average drop rate
0:06:07that each user sees
0:06:09and so um and outage happens if the capacity of the channel is below the rate that the transmitters trying
0:06:16to send to the user
0:06:18um captured right here
0:06:20and um
0:06:23and so we want to
0:06:27and so we want to find the precoding matrix that minimises
0:06:32um some of all the drop rates of each user
0:06:39and the problem with this
0:06:41um formulation is that the
0:06:43the transmitter requires instantaneous channel state information
0:06:48um which will not be available
0:06:51in this situation
0:06:53and so we re formulate the problem
0:06:55um two
0:06:56um minimize the expected drop rate
0:06:59um based on the
0:07:03the previous channel um channel state information fed back from the users
0:07:10so if we only have a finitely many precoding matrices to choose from
0:07:14then this optimization problem is feasible
0:07:19we can um
0:07:21and it's given by this expected value right here
0:07:24which we can pretty um pretty compute
0:07:28yeah are transmitter
0:07:29um assuming that we have a
0:07:31um stationary channel
0:07:35so um
0:07:37to um for this um computation we
0:07:40um create this matrix a a
0:07:42given right here
0:07:43um and it looks like this
0:07:46where um
0:07:51um and then
0:07:53for to make a decision we create this vector V which is just a collection of
0:07:59the number of users that voted for
0:08:04the precoding matrix indexed by J
0:08:07and so to make are um our decision for the optimal precoding matrix
0:08:12we just um take the largest
0:08:15entry of the product um a times B
0:08:20so now let's introduce are um
0:08:23are L T precoding matrices
0:08:26um we see that
0:08:28rank one matrices right here are optimal in the low snr regime
0:08:32and the rank two matrices are optimal in the high snr regime
0:08:38um we wanna look at the situation where
0:08:40um the channel is both
0:08:43stationary and non-stationary
0:08:45so if it stationary like i said we can pretty calculate
0:08:48R matrix a a
0:08:49and keep it at the transmitter
0:08:51but at the channel is not stationary or unknown
0:08:54um then we must do adaptive learning of a
0:09:15and so for um for this but for this talk we consider the
0:09:18um low as an region so where
0:09:21selecting these um rank one matrices
0:09:24and um
0:09:28and so we will consider how to construct are matrix a
0:09:31um in this case
0:09:36um we see that you have and so the
0:09:39the important thing to note is that
0:09:42um these matrices are given in three N T pablo pairs
0:09:46and so for example if uh matrix Q one
0:09:50is the optimal then Q two is many times the worst matrix
0:09:54um to choose
0:09:55and the other four are in some sense um
0:10:00roughly the same offer the same perform
0:10:02so we can um reduce
0:10:04the parameterization or matrix a
0:10:07um to to parameters given by
0:10:10a and B
0:10:12and if we subtract it from the all one matrix then
0:10:16we um can further reduce it to parameterisation by a single parameter C
0:10:22and this parameter C
0:10:26um is determined by the um the rate lambda the that we're trying to send
0:10:32um to each of the users
0:10:34or excuse use me the
0:10:36lemme is the outage rate of the channel
0:10:40and so here we see that um when if the outage rate is low
0:10:45which means that are value of C is close to zero
0:10:48then um Q one is the preferred
0:10:51precoder um
0:10:55Q three four five and six well all be um
0:10:59greatly um preferred over the anti pa
0:11:02um matrix
0:11:04Q two
0:11:05um but we see that if the outage probability is
0:11:09hi um make you want is preferred
0:11:11then the remaining um will be treated roughly equal
0:11:19and so um
0:11:20if the channel is non-stationary then we need to learn this matrix a a
0:11:25um and so how what we do that
0:11:28um we proposed this adaptive algorithm which is similar to
0:11:32simulated annealing
0:11:34um and the the basic idea is that we introduce a a a perturbation
0:11:38to um the parameter
0:11:41and then if that perturbation helps to improve the drop rate then we update the parameter
0:11:46um if it doesn't then we randomly update the parameter with some probability
0:11:54and so we also um
0:11:57a a um a service that were um
0:12:02a service such as voice there were trying to optimize over
0:12:05so the packet drop rate will greatly affect the
0:12:08um quality of a voice call
0:12:11um and so you
0:12:12but you also want to minimize the delay
0:12:15in that link
0:12:17and so um one provisioning of service um user utility is measured by this are factor
0:12:24um and i just want to emphasise a we could've picked
0:12:28um other sit other services with the more stringent quality of service like video or gaming
0:12:33um but the important point here is that we're connecting the channels to channel statistics
0:12:39the um to the to the measured quality of the service
0:12:44so um in this situation we simulated
0:12:48uh system with eight users
0:12:50and compare our scheme as shown here in black
0:12:53against the um scheme and read without any precoding
0:12:57and also the round robin scheme
0:12:59and we see that the our scheme is close to the optimal
0:13:04with just the optimal is computed um assuming that you have perfect channel state information at the transmitter
0:13:11and we also see that we have a um similar
0:13:14improvement on the R factor
0:13:17um where where closer is closer to the
0:13:22um than the other two schemes
0:13:31and so um finally
0:13:33um we assume that the channel is stationary
0:13:36and also show that if we use
0:13:38are adaptive algorithm
0:13:40then we
0:13:44perform very close to
0:13:46um the fixed algorithm that involves pretty computing the matrix a at the transmitter
0:13:51and so the shows that we um
0:13:54we don't need to necessarily compute R matrix a um we can just use the adaptive algorithm and get um
0:14:00nearly as good performance
0:14:02um and so we won't have to store
0:14:05um are matrix
0:14:07and so um i hope that this
0:14:10talk is
0:14:11convinced you and peaked your curiosity about using um limited feedback
0:14:16um information in wireless multicast system
0:14:20thank you
0:14:36i can try to answer some questions for you
0:14:58this one
0:15:22i'm not sure
0:15:24myself sorry