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

i