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