a a good afternoon
welcome come to my presentation and thus and hunt this work is dry need done with my P H Ds
of so
oh by serving can ma we are from the chinese university of hong kong
is is the how night of my presentation in the first parts i we first
read three introduce a let this be and
and multi rate our proposed method
the a one and you relaxation based that is cold and method
and then i we use
the simulation to use them as during the performance of our proposed method
and the final part is summary in is engines
these these the then that my most no model
as the hearing use the transmit this simple which is transformed that the channel make H C
and it's cool up the by don't noise
do
and be the gold here he's that that's we want to detect the transmitted symbols as the from the receive
six
we they've signal Y the if and that's been all the channel matrix
it
no model capture many applications like spatial multiplexing
multiuser cdma and many many they
applications
you one important thing is that
the constellation of the transmit it
both
as the is
well
which means that
the real part and a J of up from this that all
plus all one possible all models three up to pass on you you you used and all lump
and i to compress
model to a and you cleanse real model
and the i missions of these matrix and four
and
but there's a pose
wrist you have these
model
yeah you can
why can be is a and B in and C is as the constellation that in this form
you one is and are when vector
and is
where a is and it mice where and also the in you quality is an element-wise
you quality
so as is and all integer vector
and each any month is found between to as you and you
is these the symbol bound
is this the optimum
maximum the mom like lip detection this is that mean the structure a little bit
first
i is is the and all integer but the
these like all or in you read integer but the used transformed it by the channel H
and become a chance lady pig
also each any month these
in the
between the symbol bound
so what the
miss some likelihood detection does is to find and at this point in find the simple font
this is it to the this this don't Y
is
ml detection can be efficiently computed by the bias be a decoder
but actually is problem is an np-hard problem
the compress the is is well so it in the
a one size and which means that we can not quite a efficient to come this
the patient up i one size is large
it describe our loans that's the
um the of those be a decoder that rely a relies heavily on the condition number of the channel H
if the channel use better conditions
the compress the of the edge
to to be a decoder is old
so to make the channel become that the
one that that is to use the so called that is the reduction
that this reduction is to find a a T model to make use you
you're
such that the formed
channel make use
you H become better
yeah i is and
to time mention them is them well
is H one and H two out two columns of the original channel make H
you can see that they are
quite close to each other
but up the the chairs formation of the
that is to be options
the new channel with there's become wealthy of all the no
which means that
now the channel is become better and the compressed the of be a decoder is no war
but
the change formation of the you more do i make use you
also makes things to complicated or region the we we only have these
quite simple
why simple symbol bound
well after the transformation of the you model make shoes
the simple bound to be this
a but that out well
the comments be at it called that cannot handle this
symbol bound so it is just this it in the soul court now net is than
a life if that these decoding just want to buy and let this point
close to the wrist signal no method read that it is inside the symbol bound or outside a simple bound
is these then relaxation because it this got the symbol bounds
this the relaxation you
it where the
error rates performance
sometimes the
lost in rates performance can be large
it is shown that
this these flight this people that may not a chip the
optimal T mote iris the multiplexing train off
so was to be due to improve the performance of this life let this be that we cannot just is
based they city at that the symbol on
yeah i i is
regularization
this root term is and regularization term he's he's that pretty or the that and it make checks
this regularization beep you know the simple as that is far away from the are region
so you meet case the
our our symbol you bites and also improve the symbol error rate
i sup rising city is
regular wise let this be called then
and a achieve the optimal i was T multi posting to you know
and you one more supplies and see a low compress the approximation to these
that these people the postal word
that is the reduction at
but that can also a achieve the optimal was be multi train
one common choice of these
and mse oh sorry one how much choice of these regular station make use T
is the mmse regularization
it is a scaled version of their identity matrix
other other then this mmse regularization the lot the regularization use or for the in the literature
so we want to find a that the regularization
to improve the performance of the mmse for guys station
that is because all that
is this the key idea of of our proposed method the lot one in or relaxation
based let these be cold and method
oh you first
one relates the log one and two relaxation of the ml mimo problem
in this formulation i would would the rack of ice like this decoding as
from the real points of a like what in the right if here
then i we use the old to the up a method to solve this lot point and will and station
in the hope to find a better regularization
this approach it is separate them
method has a right a nice interpretation of
adaptive
regularization
to crunch all the symbol bound
is these the primal problem the all region though ml problem
oh i be by the problem won't may as piece
all integer vectors that's
these days
the major difference speech
a between our
but that's and other relaxation method like semidefinite relaxation
in semidefinite every relaxation the
i one till may use uh can there's those space
it is also because all these
this problem to make that conditions that our formulation can preserve the structure of that is the code then
now for and those then that that point directly yeah we we defined the lot one you're function with a
lot negative
long that
sometimes times the
like one a multiplier
yeah the um that use that diagonal make
with the small and biking is tiger knows
and we minimize the lot don't function
a well or
or long all integer vectors
and these the um that is the dual function
or or a like a non-negative long that this you number
is that as
well what of the optimal objective value of the primal problem
so we maximise is
to a function or well
non-negative negative number
now we have a next mean not that button to relaxation problems
you can see that the last term is in relevance in that you know the minimization so we just move
house not
i think for these in the minimization violent but
so we have the of the laplacian pungent do where X there's in in this for
yeah the
in the minimization is uh i can only regular wise like this decoding
it on that is that i go metric
the lot one to an excitation
try
control the
the the web or on that
with which means that you control the regularization
a one to do realisation station trying to find the X
i i regularization to a makes the ml problem
or or if let this the cold and not that use just the or no regularization
or mmse regularization
not that use the scale version of
all one but uh
so
the life let this people then an mmse a this coding can be you as but because a instance
or our a point to dual relaxation
the lap one and you relaxation trying to find a text
i i no regularization
so
to
by stop this
not point it the relaxation we can get up at a regularization
yeah you'll on back is that and long differentiable function
one one but to do with this kind of blondie price so miss them i'm so and use the
of that this up where the methods
this block diagram shows the three steps in
each iteration stop the old to this up way a method
a post now we are at the k-th iteration and you have a number K
then be even is
the two function you long time and that K
i
in in and the regular was let this be called and regular wise by the
oh
regularization
our ml problem that K
then we have the solution escape of the let this be calling problem
then we use this as K to calculate the stuff radians
and then update the doable i'm that K
yeah the insights behind this whole justice supporting the methods that
is supported as a way to map the ester actually is an adaptive regularization update and the double available
according to the quality of the solution as K
this equation solver
how we updates the doable about case suppose now we aren't and number okay then we walk along the subgradient
direction with a predefined
that's nice i like a then we make a projection to the lawn they get it open
because love that is non-negative
and that's we have already of the
the let this the them problem make a wise by on that case
we can actually maybe D calculates the sub gradient she case
it i
it can be just
computed by this be creation as is the solution of the let this be cold and problem
our oh do this up with them at that has the right nice interpretation of
at that they've symbol on controlled
this
oh the three step you have just seen in the in one iteration
suppose now we are and that K and S K use the solution of the wreck
provides that this be cold in problem
if one and months of this solution is outside the symbol box which means that this is where you just
block are then used where
then that elements of the stuff we then it's not larger than zero
and
but
regularization station is
larger
which means that you want to add more P normalization in the out that's
at next iteration the solution of the let these be code and you be inside the symbol but
a only if one and M as is inside the symbol bounds
the regularization is decrease
everything seems to read relies so far
but
actually is like this be colin problem is an and P ha
problem
watching in C
yeah many you come as the soap based the K D
approximation to the net these speak in problem
to lay a feel
then in back to two thousand two
yeah has been proposed
oh this
like this reduction at
method has been proposed
to a pasta makes the let these be call problem
note that
this method combined with the regularization
K is so one to a chip the optimal die was in multi you or you know
to for there we use the compress the we can it be minute the lattice this reduction and just use
the
decision feedback
yeah i also many are the approximations
for a re sensor wait please refer to this
a paper
in our simulation we used these to stopping point your we are first i that the maximum number all be
iteration as ten
and i also stop the
and we're from the difference between two iteration
is rather small
yes so the symbol what a lm weights of the proposed method
the problem size is this teen an the constellation is this thing form
this right now i is the mmse that these be cold and
and the point i is
our proposed a method combined to brief neck he's cold and
you can see that the mmse like this the is very close to optimal and our proposed method
only give a a very small improve
that's to
they look at all
the compressed the
that as an i is trained to two T V the amount size ray be from two to thirty
you can see that the compressed the of
the ml speed at decoder increase
very fast
is for we actually passed
the compressed the a black this speaker collins
is much
a what and the combines the of the ml
sphere decoder called
that's three to the approximation case
this so our proposed method combined with the like this to be at B
this is P at method this
line
and our proposed method combined with a lacy this is M P band map is nine
you can see that
our proposed the method
in give more than three db improvement compared to the conventional mmse counterpart
and the compress the all of this but that's not just for the me
and you can also see that that the compress the of our proposed method
a two to ten times of the
mmse on the past you make things that two to ten times out
well maybe high
but
take a look at the
number of iterations
the problem size is the oh sixteen
um while they're we to a high snr from about twenty one db to thirty db our proposed method only
requires a all for two
two iterations
which are quite small
to conclude
we a
a a pose a lot one don't do relaxation based let these be code and
but that
and how a lot to do relaxation can incorporates the light if let this be code and and um
and mmse like his be called then
to get up but the regularization we use the palm to this up the method
to solve the log what don't with relaxation
and this
to this up way them but the has a rabbit lies interpretation of
at that pf
symbol on control
simulation shows that
our method come
find with the L T F and they C D at can give significant performance improve my
these are
from is thank that have been found
we mainly focus on compressed the reduction
actually we can find a better
so than once ones
then the mmse and the number but you to recent these almost one iteration is from more the we to
a high as that not
and we can also
use the
you formation of the purest iteration to compute
the cup and iteration
we can further reduce the compressed the by about thirty to forty percent
and you
i
okay we have uh a of time questions
or um your of them um
can you prior to constellations them into a a
oh
all our our our that
but that use that based on that is because
and all the
gonna at the constellation it it cannot form that is um
i things a days
no good trying to
i two
that
"'cause"
in progress
uh well saying is uh we have a little bit of time
i think yeah i like to encourage you to look towards the front of your broke
and you may find out present as a of uh
at the front of the book as well as uh in the back on session because
he was one of the uh we is of the student paper or a one for i cast
so i
i think we should make good use of this time and congratulating
well
i
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