0:00:13a a good afternoon
0:00:15welcome come to my presentation and thus and hunt this work is dry need done with my P H Ds
0:00:19of so
0:00:20oh by serving can ma we are from the chinese university of hong kong
0:00:26is is the how night of my presentation in the first parts i we first
0:00:30read three introduce a let this be and
0:00:33and multi rate our proposed method
0:00:36the a one and you relaxation based that is cold and method
0:00:40and then i we use
0:00:41the simulation to use them as during the performance of our proposed method
0:00:46and the final part is summary in is engines
0:00:51these these the then that my most no model
0:00:55as the hearing use the transmit this simple which is transformed that the channel make H C
0:01:00and it's cool up the by don't noise
0:01:04and be the gold here he's that that's we want to detect the transmitted symbols as the from the receive
0:01:10we they've signal Y the if and that's been all the channel matrix
0:01:15no model capture many applications like spatial multiplexing
0:01:19multiuser cdma and many many they
0:01:23you one important thing is that
0:01:25the constellation of the transmit it
0:01:29as the is
0:01:30which means that
0:01:32the real part and a J of up from this that all
0:01:35plus all one possible all models three up to pass on you you you used and all lump
0:01:42and i to compress
0:01:44model to a and you cleanse real model
0:01:47and the i missions of these matrix and four
0:01:52but there's a pose
0:01:54wrist you have these
0:01:57yeah you can
0:01:58why can be is a and B in and C is as the constellation that in this form
0:02:03you one is and are when vector
0:02:06and is
0:02:07where a is and it mice where and also the in you quality is an element-wise
0:02:12you quality
0:02:14so as is and all integer vector
0:02:17and each any month is found between to as you and you
0:02:21is these the symbol bound
0:02:24is this the optimum
0:02:26maximum the mom like lip detection this is that mean the structure a little bit
0:02:31i is is the and all integer but the
0:02:33these like all or in you read integer but the used transformed it by the channel H
0:02:38and become a chance lady pig
0:02:41also each any month these
0:02:42in the
0:02:43between the symbol bound
0:02:45so what the
0:02:46miss some likelihood detection does is to find and at this point in find the simple font
0:02:51this is it to the this this don't Y
0:02:55ml detection can be efficiently computed by the bias be a decoder
0:03:00but actually is problem is an np-hard problem
0:03:04the compress the is is well so it in the
0:03:07a one size and which means that we can not quite a efficient to come this
0:03:12the patient up i one size is large
0:03:14it describe our loans that's the
0:03:16um the of those be a decoder that rely a relies heavily on the condition number of the channel H
0:03:23if the channel use better conditions
0:03:25the compress the of the edge
0:03:27to to be a decoder is old
0:03:30so to make the channel become that the
0:03:32one that that is to use the so called that is the reduction
0:03:36that this reduction is to find a a T model to make use you
0:03:40such that the formed
0:03:42channel make use
0:03:44you H become better
0:03:46yeah i is and
0:03:47to time mention them is them well
0:03:50is H one and H two out two columns of the original channel make H
0:03:55you can see that they are
0:03:57quite close to each other
0:03:59but up the the chairs formation of the
0:04:02that is to be options
0:04:03the new channel with there's become wealthy of all the no
0:04:07which means that
0:04:08now the channel is become better and the compressed the of be a decoder is no war
0:04:16the change formation of the you more do i make use you
0:04:19also makes things to complicated or region the we we only have these
0:04:23quite simple
0:04:24why simple symbol bound
0:04:26well after the transformation of the you model make shoes
0:04:29the simple bound to be this
0:04:31a but that out well
0:04:33the comments be at it called that cannot handle this
0:04:37symbol bound so it is just this it in the soul court now net is than
0:04:44a life if that these decoding just want to buy and let this point
0:04:48close to the wrist signal no method read that it is inside the symbol bound or outside a simple bound
0:04:54is these then relaxation because it this got the symbol bounds
0:04:59this the relaxation you
0:05:00it where the
0:05:02error rates performance
0:05:03sometimes the
0:05:05lost in rates performance can be large
0:05:07it is shown that
0:05:09this these flight this people that may not a chip the
0:05:12optimal T mote iris the multiplexing train off
0:05:14so was to be due to improve the performance of this life let this be that we cannot just is
0:05:20based they city at that the symbol on
0:05:24yeah i i is
0:05:26this root term is and regularization term he's he's that pretty or the that and it make checks
0:05:33this regularization beep you know the simple as that is far away from the are region
0:05:37so you meet case the
0:05:39our our symbol you bites and also improve the symbol error rate
0:05:44i sup rising city is
0:05:46regular wise let this be called then
0:05:49and a achieve the optimal i was T multi posting to you know
0:05:52and you one more supplies and see a low compress the approximation to these
0:05:57that these people the postal word
0:05:59that is the reduction at
0:06:01but that can also a achieve the optimal was be multi train
0:06:06one common choice of these
0:06:08and mse oh sorry one how much choice of these regular station make use T
0:06:13is the mmse regularization
0:06:15it is a scaled version of their identity matrix
0:06:20other other then this mmse regularization the lot the regularization use or for the in the literature
0:06:25so we want to find a that the regularization
0:06:28to improve the performance of the mmse for guys station
0:06:33that is because all that
0:06:36is this the key idea of of our proposed method the lot one in or relaxation
0:06:41based let these be cold and method
0:06:43oh you first
0:06:44one relates the log one and two relaxation of the ml mimo problem
0:06:48in this formulation i would would the rack of ice like this decoding as
0:06:53from the real points of a like what in the right if here
0:06:56then i we use the old to the up a method to solve this lot point and will and station
0:07:01in the hope to find a better regularization
0:07:05this approach it is separate them
0:07:06method has a right a nice interpretation of
0:07:12to crunch all the symbol bound
0:07:15is these the primal problem the all region though ml problem
0:07:19oh i be by the problem won't may as piece
0:07:22all integer vectors that's
0:07:24these days
0:07:25the major difference speech
0:07:26a between our
0:07:28but that's and other relaxation method like semidefinite relaxation
0:07:32in semidefinite every relaxation the
0:07:35i one till may use uh can there's those space
0:07:38it is also because all these
0:07:40this problem to make that conditions that our formulation can preserve the structure of that is the code then
0:07:48now for and those then that that point directly yeah we we defined the lot one you're function with a
0:07:53lot negative
0:07:54long that
0:07:55sometimes times the
0:07:57like one a multiplier
0:07:58yeah the um that use that diagonal make
0:08:01with the small and biking is tiger knows
0:08:03and we minimize the lot don't function
0:08:07a well or
0:08:09or long all integer vectors
0:08:11and these the um that is the dual function
0:08:15or or a like a non-negative long that this you number
0:08:18is that as
0:08:19well what of the optimal objective value of the primal problem
0:08:23so we maximise is
0:08:25to a function or well
0:08:27non-negative negative number
0:08:29now we have a next mean not that button to relaxation problems
0:08:33you can see that the last term is in relevance in that you know the minimization so we just move
0:08:39house not
0:08:40i think for these in the minimization violent but
0:08:44so we have the of the laplacian pungent do where X there's in in this for
0:08:49yeah the
0:08:50in the minimization is uh i can only regular wise like this decoding
0:08:54it on that is that i go metric
0:08:57the lot one to an excitation
0:08:59control the
0:09:01the the web or on that
0:09:03with which means that you control the regularization
0:09:06a one to do realisation station trying to find the X
0:09:09i i regularization to a makes the ml problem
0:09:14or or if let this the cold and not that use just the or no regularization
0:09:19or mmse regularization
0:09:21not that use the scale version of
0:09:23all one but uh
0:09:25the life let this people then an mmse a this coding can be you as but because a instance
0:09:31or our a point to dual relaxation
0:09:35the lap one and you relaxation trying to find a text
0:09:38i i no regularization
0:09:41by stop this
0:09:42not point it the relaxation we can get up at a regularization
0:09:47yeah you'll on back is that and long differentiable function
0:09:50one one but to do with this kind of blondie price so miss them i'm so and use the
0:09:55of that this up where the methods
0:09:58this block diagram shows the three steps in
0:10:01each iteration stop the old to this up way a method
0:10:05a post now we are at the k-th iteration and you have a number K
0:10:09then be even is
0:10:10the two function you long time and that K
0:10:14in in and the regular was let this be called and regular wise by the
0:10:22our ml problem that K
0:10:24then we have the solution escape of the let this be calling problem
0:10:28then we use this as K to calculate the stuff radians
0:10:32and then update the doable i'm that K
0:10:36yeah the insights behind this whole justice supporting the methods that
0:10:39is supported as a way to map the ester actually is an adaptive regularization update and the double available
0:10:46according to the quality of the solution as K
0:10:53this equation solver
0:10:54how we updates the doable about case suppose now we aren't and number okay then we walk along the subgradient
0:11:00direction with a predefined
0:11:02that's nice i like a then we make a projection to the lawn they get it open
0:11:07because love that is non-negative
0:11:10and that's we have already of the
0:11:14the let this the them problem make a wise by on that case
0:11:18we can actually maybe D calculates the sub gradient she case
0:11:22it i
0:11:22it can be just
0:11:24computed by this be creation as is the solution of the let this be cold and problem
0:11:31our oh do this up with them at that has the right nice interpretation of
0:11:35at that they've symbol on controlled
0:11:39oh the three step you have just seen in the in one iteration
0:11:43suppose now we are and that K and S K use the solution of the wreck
0:11:47provides that this be cold in problem
0:11:50if one and months of this solution is outside the symbol box which means that this is where you just
0:11:55block are then used where
0:11:57then that elements of the stuff we then it's not larger than zero
0:12:01regularization station is
0:12:04which means that you want to add more P normalization in the out that's
0:12:08at next iteration the solution of the let these be code and you be inside the symbol but
0:12:15a only if one and M as is inside the symbol bounds
0:12:19the regularization is decrease
0:12:23everything seems to read relies so far
0:12:26actually is like this be colin problem is an and P ha
0:12:31watching in C
0:12:32yeah many you come as the soap based the K D
0:12:35approximation to the net these speak in problem
0:12:38to lay a feel
0:12:40then in back to two thousand two
0:12:42yeah has been proposed
0:12:44oh this
0:12:45like this reduction at
0:12:47method has been proposed
0:12:48to a pasta makes the let these be call problem
0:12:51note that
0:12:52this method combined with the regularization
0:12:55K is so one to a chip the optimal die was in multi you or you know
0:13:00to for there we use the compress the we can it be minute the lattice this reduction and just use
0:13:06decision feedback
0:13:08yeah i also many are the approximations
0:13:11for a re sensor wait please refer to this
0:13:13a paper
0:13:17in our simulation we used these to stopping point your we are first i that the maximum number all be
0:13:22iteration as ten
0:13:24and i also stop the
0:13:26and we're from the difference between two iteration
0:13:29is rather small
0:13:32yes so the symbol what a lm weights of the proposed method
0:13:35the problem size is this teen an the constellation is this thing form
0:13:40this right now i is the mmse that these be cold and
0:13:44and the point i is
0:13:45our proposed a method combined to brief neck he's cold and
0:13:49you can see that the mmse like this the is very close to optimal and our proposed method
0:13:55only give a a very small improve
0:13:59that's to
0:14:00they look at all
0:14:01the compressed the
0:14:03that as an i is trained to two T V the amount size ray be from two to thirty
0:14:09you can see that the compressed the of
0:14:10the ml speed at decoder increase
0:14:13very fast
0:14:14is for we actually passed
0:14:16the compressed the a black this speaker collins
0:14:19is much
0:14:20a what and the combines the of the ml
0:14:23sphere decoder called
0:14:25that's three to the approximation case
0:14:28this so our proposed method combined with the like this to be at B
0:14:33this is P at method this
0:14:36and our proposed method combined with a lacy this is M P band map is nine
0:14:41you can see that
0:14:42our proposed the method
0:14:44in give more than three db improvement compared to the conventional mmse counterpart
0:14:49and the compress the all of this but that's not just for the me
0:14:54and you can also see that that the compress the of our proposed method
0:14:58a two to ten times of the
0:15:01mmse on the past you make things that two to ten times out
0:15:05well maybe high
0:15:07take a look at the
0:15:09number of iterations
0:15:10the problem size is the oh sixteen
0:15:14um while they're we to a high snr from about twenty one db to thirty db our proposed method only
0:15:21requires a all for two
0:15:22two iterations
0:15:24which are quite small
0:15:28to conclude
0:15:30we a
0:15:31a a pose a lot one don't do relaxation based let these be code and
0:15:35but that
0:15:36and how a lot to do relaxation can incorporates the light if let this be code and and um
0:15:42and mmse like his be called then
0:15:44to get up but the regularization we use the palm to this up the method
0:15:48to solve the log what don't with relaxation
0:15:51and this
0:15:52to this up way them but the has a rabbit lies interpretation of
0:15:56at that pf
0:15:57symbol on control
0:15:59simulation shows that
0:16:00our method come
0:16:01find with the L T F and they C D at can give significant performance improve my
0:16:10these are
0:16:11from is thank that have been found
0:16:13we mainly focus on compressed the reduction
0:16:16actually we can find a better
0:16:18so than once ones
0:16:19then the mmse and the number but you to recent these almost one iteration is from more the we to
0:16:25a high as that not
0:16:27and we can also
0:16:29use the
0:16:30you formation of the purest iteration to compute
0:16:33the cup and iteration
0:16:35we can further reduce the compressed the by about thirty to forty percent
0:16:41and you
0:16:47okay we have uh a of time questions
0:17:01or um your of them um
0:17:03can you prior to constellations them into a a
0:17:10all our our our that
0:17:12but that use that based on that is because
0:17:15and all the
0:17:16gonna at the constellation it it cannot form that is um
0:17:21i things a days
0:17:23no good trying to
0:17:24i two
0:17:32in progress
0:17:37uh well saying is uh we have a little bit of time
0:17:40i think yeah i like to encourage you to look towards the front of your broke
0:17:44and you may find out present as a of uh
0:17:47at the front of the book as well as uh in the back on session because
0:17:51he was one of the uh we is of the student paper or a one for i cast
0:17:56so i
0:17:57i think we should make good use of this time and congratulating