0:00:13 | a a good afternoon |
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0:00:15 | welcome come to my presentation and thus and hunt this work is dry need done with my P H Ds |

0:00:19 | of so |

0:00:20 | oh by serving can ma we are from the chinese university of hong kong |

0:00:26 | is is the how night of my presentation in the first parts i we first |

0:00:30 | read three introduce a let this be and |

0:00:33 | and multi rate our proposed method |

0:00:36 | the a one and you relaxation based that is cold and method |

0:00:40 | and then i we use |

0:00:41 | the simulation to use them as during the performance of our proposed method |

0:00:46 | and the final part is summary in is engines |

0:00:51 | these these the then that my most no model |

0:00:55 | as the hearing use the transmit this simple which is transformed that the channel make H C |

0:01:00 | and it's cool up the by don't noise |

0:01:03 | do |

0:01:04 | and be the gold here he's that that's we want to detect the transmitted symbols as the from the receive |

0:01:10 | six |

0:01:10 | we they've signal Y the if and that's been all the channel matrix |

0:01:14 | it |

0:01:15 | no model capture many applications like spatial multiplexing |

0:01:19 | multiuser cdma and many many they |

0:01:22 | applications |

0:01:23 | you one important thing is that |

0:01:25 | the constellation of the transmit it |

0:01:28 | both |

0:01:29 | as the is |

0:01:30 | well |

0:01:30 | which means that |

0:01:32 | the real part and a J of up from this that all |

0:01:35 | plus all one possible all models three up to pass on you you you used and all lump |

0:01:42 | and i to compress |

0:01:44 | model to a and you cleanse real model |

0:01:47 | and the i missions of these matrix and four |

0:01:50 | and |

0:01:52 | but there's a pose |

0:01:54 | wrist you have these |

0:01:56 | model |

0:01:57 | yeah you can |

0:01:58 | why can be is a and B in and C is as the constellation that in this form |

0:02:03 | you one is and are when vector |

0:02:06 | and is |

0:02:07 | where a is and it mice where and also the in you quality is an element-wise |

0:02:12 | you quality |

0:02:14 | so as is and all integer vector |

0:02:17 | and each any month is found between to as you and you |

0:02:21 | is these the symbol bound |

0:02:24 | is this the optimum |

0:02:26 | maximum the mom like lip detection this is that mean the structure a little bit |

0:02:30 | first |

0:02:31 | i is is the and all integer but the |

0:02:33 | these like all or in you read integer but the used transformed it by the channel H |

0:02:38 | and become a chance lady pig |

0:02:41 | also each any month these |

0:02:42 | in the |

0:02:43 | between the symbol bound |

0:02:45 | so what the |

0:02:46 | miss some likelihood detection does is to find and at this point in find the simple font |

0:02:51 | this is it to the this this don't Y |

0:02:55 | is |

0:02:55 | ml detection can be efficiently computed by the bias be a decoder |

0:03:00 | but actually is problem is an np-hard problem |

0:03:04 | the compress the is is well so it in the |

0:03:07 | a one size and which means that we can not quite a efficient to come this |

0:03:12 | the patient up i one size is large |

0:03:14 | it describe our loans that's the |

0:03:16 | um the of those be a decoder that rely a relies heavily on the condition number of the channel H |

0:03:23 | if the channel use better conditions |

0:03:25 | the compress the of the edge |

0:03:27 | to to be a decoder is old |

0:03:30 | so to make the channel become that the |

0:03:32 | one that that is to use the so called that is the reduction |

0:03:36 | that this reduction is to find a a T model to make use you |

0:03:40 | you're |

0:03:40 | such that the formed |

0:03:42 | channel make use |

0:03:44 | you H become better |

0:03:46 | yeah i is and |

0:03:47 | to time mention them is them well |

0:03:50 | is H one and H two out two columns of the original channel make H |

0:03:55 | you can see that they are |

0:03:57 | quite close to each other |

0:03:59 | but up the the chairs formation of the |

0:04:02 | that is to be options |

0:04:03 | the new channel with there's become wealthy of all the no |

0:04:07 | which means that |

0:04:08 | now the channel is become better and the compressed the of be a decoder is no war |

0:04:14 | but |

0:04:16 | the change formation of the you more do i make use you |

0:04:19 | also makes things to complicated or region the we we only have these |

0:04:23 | quite simple |

0:04:24 | why simple symbol bound |

0:04:26 | well after the transformation of the you model make shoes |

0:04:29 | the simple bound to be this |

0:04:31 | a but that out well |

0:04:33 | the comments be at it called that cannot handle this |

0:04:37 | symbol bound so it is just this it in the soul court now net is than |

0:04:44 | a life if that these decoding just want to buy and let this point |

0:04:48 | close to the wrist signal no method read that it is inside the symbol bound or outside a simple bound |

0:04:54 | is these then relaxation because it this got the symbol bounds |

0:04:59 | this the relaxation you |

0:05:00 | it where the |

0:05:02 | error rates performance |

0:05:03 | sometimes the |

0:05:05 | lost in rates performance can be large |

0:05:07 | it is shown that |

0:05:09 | this these flight this people that may not a chip the |

0:05:12 | optimal T mote iris the multiplexing train off |

0:05:14 | so was to be due to improve the performance of this life let this be that we cannot just is |

0:05:20 | based they city at that the symbol on |

0:05:24 | yeah i i is |

0:05:25 | regularization |

0:05:26 | this root term is and regularization term he's he's that pretty or the that and it make checks |

0:05:33 | this regularization beep you know the simple as that is far away from the are region |

0:05:37 | so you meet case the |

0:05:39 | our our symbol you bites and also improve the symbol error rate |

0:05:44 | i sup rising city is |

0:05:46 | regular wise let this be called then |

0:05:49 | and a achieve the optimal i was T multi posting to you know |

0:05:52 | and you one more supplies and see a low compress the approximation to these |

0:05:57 | that these people the postal word |

0:05:59 | that is the reduction at |

0:06:01 | but that can also a achieve the optimal was be multi train |

0:06:06 | one common choice of these |

0:06:08 | and mse oh sorry one how much choice of these regular station make use T |

0:06:13 | is the mmse regularization |

0:06:15 | it is a scaled version of their identity matrix |

0:06:20 | other other then this mmse regularization the lot the regularization use or for the in the literature |

0:06:25 | so we want to find a that the regularization |

0:06:28 | to improve the performance of the mmse for guys station |

0:06:33 | that is because all that |

0:06:36 | is this the key idea of of our proposed method the lot one in or relaxation |

0:06:41 | based let these be cold and method |

0:06:43 | oh you first |

0:06:44 | one relates the log one and two relaxation of the ml mimo problem |

0:06:48 | in this formulation i would would the rack of ice like this decoding as |

0:06:53 | from the real points of a like what in the right if here |

0:06:56 | then i we use the old to the up a method to solve this lot point and will and station |

0:07:01 | in the hope to find a better regularization |

0:07:05 | this approach it is separate them |

0:07:06 | method has a right a nice interpretation of |

0:07:09 | adaptive |

0:07:10 | regularization |

0:07:12 | to crunch all the symbol bound |

0:07:15 | is these the primal problem the all region though ml problem |

0:07:19 | oh i be by the problem won't may as piece |

0:07:22 | all integer vectors that's |

0:07:24 | these days |

0:07:25 | the major difference speech |

0:07:26 | a between our |

0:07:28 | but that's and other relaxation method like semidefinite relaxation |

0:07:32 | in semidefinite every relaxation the |

0:07:35 | i one till may use uh can there's those space |

0:07:38 | it is also because all these |

0:07:40 | this problem to make that conditions that our formulation can preserve the structure of that is the code then |

0:07:48 | now for and those then that that point directly yeah we we defined the lot one you're function with a |

0:07:53 | lot negative |

0:07:54 | long that |

0:07:55 | sometimes times the |

0:07:57 | like one a multiplier |

0:07:58 | yeah the um that use that diagonal make |

0:08:01 | with the small and biking is tiger knows |

0:08:03 | and we minimize the lot don't function |

0:08:07 | a well or |

0:08:09 | or long all integer vectors |

0:08:11 | and these the um that is the dual function |

0:08:15 | or or a like a non-negative long that this you number |

0:08:18 | is that as |

0:08:19 | well what of the optimal objective value of the primal problem |

0:08:23 | so we maximise is |

0:08:25 | to a function or well |

0:08:27 | non-negative negative number |

0:08:29 | now we have a next mean not that button to relaxation problems |

0:08:33 | you can see that the last term is in relevance in that you know the minimization so we just move |

0:08:39 | house not |

0:08:40 | i think for these in the minimization violent but |

0:08:44 | so we have the of the laplacian pungent do where X there's in in this for |

0:08:49 | yeah the |

0:08:50 | in the minimization is uh i can only regular wise like this decoding |

0:08:54 | it on that is that i go metric |

0:08:57 | the lot one to an excitation |

0:08:59 | try |

0:08:59 | control the |

0:09:01 | the the web or on that |

0:09:03 | with which means that you control the regularization |

0:09:06 | a one to do realisation station trying to find the X |

0:09:09 | i i regularization to a makes the ml problem |

0:09:14 | or or if let this the cold and not that use just the or no regularization |

0:09:19 | or mmse regularization |

0:09:21 | not that use the scale version of |

0:09:23 | all one but uh |

0:09:24 | so |

0:09:25 | the life let this people then an mmse a this coding can be you as but because a instance |

0:09:31 | or our a point to dual relaxation |

0:09:35 | the lap one and you relaxation trying to find a text |

0:09:38 | i i no regularization |

0:09:39 | so |

0:09:40 | to |

0:09:41 | by stop this |

0:09:42 | not point it the relaxation we can get up at a regularization |

0:09:47 | yeah you'll on back is that and long differentiable function |

0:09:50 | one one but to do with this kind of blondie price so miss them i'm so and use the |

0:09:55 | of that this up where the methods |

0:09:58 | this block diagram shows the three steps in |

0:10:01 | each iteration stop the old to this up way a method |

0:10:05 | a post now we are at the k-th iteration and you have a number K |

0:10:09 | then be even is |

0:10:10 | the two function you long time and that K |

0:10:14 | i |

0:10:14 | in in and the regular was let this be called and regular wise by the |

0:10:20 | oh |

0:10:21 | regularization |

0:10:22 | our ml problem that K |

0:10:24 | then we have the solution escape of the let this be calling problem |

0:10:28 | then we use this as K to calculate the stuff radians |

0:10:32 | and then update the doable i'm that K |

0:10:36 | yeah the insights behind this whole justice supporting the methods that |

0:10:39 | is supported as a way to map the ester actually is an adaptive regularization update and the double available |

0:10:46 | according to the quality of the solution as K |

0:10:53 | this equation solver |

0:10:54 | how we updates the doable about case suppose now we aren't and number okay then we walk along the subgradient |

0:11:00 | direction with a predefined |

0:11:02 | that's nice i like a then we make a projection to the lawn they get it open |

0:11:07 | because love that is non-negative |

0:11:10 | and that's we have already of the |

0:11:14 | the let this the them problem make a wise by on that case |

0:11:18 | we can actually maybe D calculates the sub gradient she case |

0:11:22 | it i |

0:11:22 | it can be just |

0:11:24 | computed by this be creation as is the solution of the let this be cold and problem |

0:11:31 | our oh do this up with them at that has the right nice interpretation of |

0:11:35 | at that they've symbol on controlled |

0:11:38 | this |

0:11:39 | oh the three step you have just seen in the in one iteration |

0:11:43 | suppose now we are and that K and S K use the solution of the wreck |

0:11:47 | provides that this be cold in problem |

0:11:50 | if one and months of this solution is outside the symbol box which means that this is where you just |

0:11:55 | block are then used where |

0:11:57 | then that elements of the stuff we then it's not larger than zero |

0:12:00 | and |

0:12:01 | but |

0:12:01 | regularization station is |

0:12:03 | larger |

0:12:04 | which means that you want to add more P normalization in the out that's |

0:12:08 | at next iteration the solution of the let these be code and you be inside the symbol but |

0:12:15 | a only if one and M as is inside the symbol bounds |

0:12:19 | the regularization is decrease |

0:12:23 | everything seems to read relies so far |

0:12:26 | but |

0:12:26 | actually is like this be colin problem is an and P ha |

0:12:30 | problem |

0:12:31 | watching in C |

0:12:32 | yeah many you come as the soap based the K D |

0:12:35 | approximation to the net these speak in problem |

0:12:38 | to lay a feel |

0:12:40 | then in back to two thousand two |

0:12:42 | yeah has been proposed |

0:12:44 | oh this |

0:12:45 | like this reduction at |

0:12:47 | method has been proposed |

0:12:48 | to a pasta makes the let these be call problem |

0:12:51 | note that |

0:12:52 | this method combined with the regularization |

0:12:55 | K is so one to a chip the optimal die was in multi you or you know |

0:13:00 | to for there we use the compress the we can it be minute the lattice this reduction and just use |

0:13:06 | the |

0:13:06 | decision feedback |

0:13:08 | yeah i also many are the approximations |

0:13:11 | for a re sensor wait please refer to this |

0:13:13 | a paper |

0:13:17 | in our simulation we used these to stopping point your we are first i that the maximum number all be |

0:13:22 | iteration as ten |

0:13:24 | and i also stop the |

0:13:26 | and we're from the difference between two iteration |

0:13:29 | is rather small |

0:13:32 | yes so the symbol what a lm weights of the proposed method |

0:13:35 | the problem size is this teen an the constellation is this thing form |

0:13:40 | this right now i is the mmse that these be cold and |

0:13:44 | and the point i is |

0:13:45 | our proposed a method combined to brief neck he's cold and |

0:13:49 | you can see that the mmse like this the is very close to optimal and our proposed method |

0:13:55 | only give a a very small improve |

0:13:59 | that's to |

0:14:00 | they look at all |

0:14:01 | the compressed the |

0:14:03 | that as an i is trained to two T V the amount size ray be from two to thirty |

0:14:09 | you can see that the compressed the of |

0:14:10 | the ml speed at decoder increase |

0:14:13 | very fast |

0:14:14 | is for we actually passed |

0:14:16 | the compressed the a black this speaker collins |

0:14:19 | is much |

0:14:20 | a what and the combines the of the ml |

0:14:23 | sphere decoder called |

0:14:25 | that's three to the approximation case |

0:14:28 | this so our proposed method combined with the like this to be at B |

0:14:33 | this is P at method this |

0:14:35 | line |

0:14:36 | and our proposed method combined with a lacy this is M P band map is nine |

0:14:41 | you can see that |

0:14:42 | our proposed the method |

0:14:44 | in give more than three db improvement compared to the conventional mmse counterpart |

0:14:49 | and the compress the all of this but that's not just for the me |

0:14:54 | and you can also see that that the compress the of our proposed method |

0:14:58 | a two to ten times of the |

0:15:01 | mmse on the past you make things that two to ten times out |

0:15:05 | well maybe high |

0:15:07 | but |

0:15:07 | take a look at the |

0:15:09 | number of iterations |

0:15:10 | the problem size is the oh sixteen |

0:15:14 | um while they're we to a high snr from about twenty one db to thirty db our proposed method only |

0:15:21 | requires a all for two |

0:15:22 | two iterations |

0:15:24 | which are quite small |

0:15:28 | to conclude |

0:15:30 | we a |

0:15:31 | a a pose a lot one don't do relaxation based let these be code and |

0:15:35 | but that |

0:15:36 | and how a lot to do relaxation can incorporates the light if let this be code and and um |

0:15:42 | and mmse like his be called then |

0:15:44 | to get up but the regularization we use the palm to this up the method |

0:15:48 | to solve the log what don't with relaxation |

0:15:51 | and this |

0:15:52 | to this up way them but the has a rabbit lies interpretation of |

0:15:56 | at that pf |

0:15:57 | symbol on control |

0:15:59 | simulation shows that |

0:16:00 | our method come |

0:16:01 | find with the L T F and they C D at can give significant performance improve my |

0:16:10 | these are |

0:16:11 | from is thank that have been found |

0:16:13 | we mainly focus on compressed the reduction |

0:16:16 | actually we can find a better |

0:16:18 | so than once ones |

0:16:19 | then the mmse and the number but you to recent these almost one iteration is from more the we to |

0:16:25 | a high as that not |

0:16:27 | and we can also |

0:16:29 | use the |

0:16:30 | you formation of the purest iteration to compute |

0:16:33 | the cup and iteration |

0:16:35 | we can further reduce the compressed the by about thirty to forty percent |

0:16:41 | and you |

0:16:43 | i |

0:16:47 | okay we have uh a of time questions |

0:17:01 | or um your of them um |

0:17:03 | can you prior to constellations them into a a |

0:17:08 | oh |

0:17:10 | all our our our that |

0:17:12 | but that use that based on that is because |

0:17:15 | and all the |

0:17:16 | gonna at the constellation it it cannot form that is um |

0:17:21 | i things a days |

0:17:23 | no good trying to |

0:17:24 | i two |

0:17:25 | that |

0:17:26 | "'cause" |

0:17:32 | in progress |

0:17:37 | uh well saying is uh we have a little bit of time |

0:17:40 | i think yeah i like to encourage you to look towards the front of your broke |

0:17:44 | and you may find out present as a of uh |

0:17:47 | at the front of the book as well as uh in the back on session because |

0:17:51 | he was one of the uh we is of the student paper or a one for i cast |

0:17:56 | so i |

0:17:57 | i think we should make good use of this time and congratulating |

0:18:00 | well |

0:18:01 | i |

0:18:02 | i |