Speech Transcript - A LAGRANGIAN DUAL RELAXATION APPROACH TO ML MIMO DETECTION: REINTERPRETING REGULARIZED LATTICE DECODING

0:00:13	a a good afternoon
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

A LAGRANGIAN DUAL RELAXATION APPROACH TO ML MIMO DETECTION: REINTERPRETING REGULARIZED LATTICE DECODING

Beamforming and MIMO

Presented by: Jiaxian Pan, Author(s): Jiaxian Pan, Wing-Kin Ma, The Chinese University of Hong Kong, Hong Kong SAR of China