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