0:00:14 | sure |
---|---|

0:00:17 | so my name is same and are this is the joint work with |

0:00:20 | uh |

0:00:21 | most of these is due to me and my supervisor pure just an |

0:00:25 | i'm K H or is to to technology in stockholm |

0:00:29 | i'm here to talk about channel one station the sign |

0:00:31 | not to use my i'm system |

0:00:33 | and we will look at this problem both a simple to go em with um |

0:00:37 | practical to go or or it's immolation |

0:00:42 | so as an direction |

0:00:44 | we will look at multiuser user mimo |

0:00:46 | a one recent |

0:00:48 | working can with multi as my ways is that you can get the good |

0:00:50 | the multiplexing gain |

0:00:52 | but we also look at what happened with the multiplexing gain if we have |

0:00:56 | uh on channels sir can do what is the impact |

0:01:00 | and talking about the channels this kind of channel information we can divide into different categories |

0:01:05 | we can look at the directional information which we |

0:01:08 | have the improve relation C the i |

0:01:11 | and the quality information which could be the the warm some of to measure of the cold channel |

0:01:15 | and we will roll right this |

0:01:17 | C Q |

0:01:19 | and that there's a basic a trade off between the directional and the quality information |

0:01:23 | since the |

0:01:25 | if we estimate the channel them to feedback |

0:01:28 | we have a limited number of feedback bits |

0:01:30 | a question is how should we divide is between direction and the quality |

0:01:34 | and is there an impact of having spatial correlation just system or having many users |

0:01:40 | well of the pen this |

0:01:42 | this is things to be are trying to look at |

0:01:45 | use some asymptotic analysis |

0:01:47 | and we try to confirm them using simulations on the what we can |

0:01:51 | practical condition |

0:01:54 | so we look at the downlink transmission system |

0:01:56 | we have a base station here with and then us |

0:01:59 | we have many users here with one antenna each |

0:02:02 | and there are more |

0:02:03 | it user stunned |

0:02:05 | yeah and ten |

0:02:06 | equal |

0:02:08 | and there is some kind of constraint on two |

0:02:10 | how |

0:02:13 | and we serve them use space division multiple access as to make so we select someone the users and we |

0:02:18 | transmit and at the same time |

0:02:22 | and why do we look at as T make |

0:02:24 | well we if we look at the asymptotic but on this kind of system there's something called the multiplexing gain |

0:02:29 | which says that the sum rate |

0:02:30 | the sum of the rates the different do uses would get at high snr will look like a are which |

0:02:35 | is a multiplexing gain times a log of the snr |

0:02:38 | a seconds |

0:02:40 | which basically means that if a look at the slow in the curve here with a not in the B |

0:02:45 | and the sum rate over we here |

0:02:46 | then having a slow problem means that at high as will go like this line and not ties now we |

0:02:52 | would go |

0:02:53 | it this line if we also still |

0:02:56 | and as they may improve the multiplacing gain sense |

0:02:59 | uh the base again is more or less the number of interference free streams that because that so we just |

0:03:04 | a |

0:03:04 | the may we can in principle get the number of transmit ten |

0:03:08 | it's |

0:03:08 | and if we as the one used would one on ten not that we can all and one screen to |

0:03:12 | the use |

0:03:15 | but this analysis here is |

0:03:17 | and that when we have perfect channel state information |

0:03:20 | so but in practice we will have to estimate the channel |

0:03:23 | have to compress it and feed back to do |

0:03:25 | base station using you |

0:03:27 | and |

0:03:28 | i and limited number of bits |

0:03:30 | what least we need to do this |

0:03:31 | in and |

0:03:32 | if you D C's them in a T D system uh at some estimation error |

0:03:37 | uh |

0:03:37 | but this |

0:03:38 | is more like an F system |

0:03:40 | so in practical system will have some kind of channel a certain |

0:03:45 | a S maybe requires very actual channel state information |

0:03:48 | in a to control the co used interference that will have a didn't kind of system |

0:03:52 | to jen was shown in two does a six use in there a got some rate |

0:03:56 | that the model in game with the bound the by one on the contest |

0:03:59 | as C is i if we haven't limited number of bits we can't increase |

0:04:06 | and |

0:04:07 | i |

0:04:08 | look and this curve are this will be an S to make a with ten last here were single user |

0:04:11 | case once slow for slope |

0:04:15 | and what have as if we introduce some kind of channel uncertainty here |

0:04:19 | well the single user a case here is quite robust we can't in really see the difference here between the |

0:04:23 | black and a blue curve |

0:04:25 | and we will use slit the bits since we don't know or channel perfectly but it's quite robust to have |

0:04:29 | a channels are |

0:04:30 | wow as they may is very sensitive since we need is information to be able to separate use |

0:04:36 | do if we just proceed with transmitting for screens |

0:04:39 | then we will come interference limited in yet |

0:04:41 | and of course we can switch off use few of yours streams and and just one screen |

0:04:46 | one one user |

0:04:47 | and for a single speaker |

0:04:51 | so what do some i mode contest feedback if we have just |

0:04:54 | B bits per user the not low large there is no point of using as team may since |

0:04:59 | uh |

0:05:00 | the low while the sex will only depend |

0:05:02 | look like X so it's |

0:05:04 | no |

0:05:04 | point to make in yeah how in ministry |

0:05:07 | and at high snr as may will come interference limit |

0:05:11 | so sort is basically an interval here a medium snrs where it's reasonable to work with estimate |

0:05:16 | and if we increase the number of bits that we having the system them we can perhaps increase this interval |

0:05:20 | but |

0:05:21 | in the end we will always |

0:05:22 | have an bomb where there's no point of |

0:05:24 | using as they in more since we don't have and |

0:05:27 | feed |

0:05:28 | sir |

0:05:32 | and before we and a i things here |

0:05:34 | and the question is how do we evaluate before and in kind of systems |

0:05:38 | and one way would be the actual some rates this is a sum rate that we |

0:05:42 | yeah it she would our precoders are so if we would know exactly what what the channels |

0:05:47 | but the problem is we don't know the channel so there's no point of a can this one since we |

0:05:51 | can't really select the right rate |

0:05:53 | and transmit with them |

0:05:55 | another approach would be to use the goal dig summary |

0:05:58 | a |

0:05:59 | that would mean that we it use a some that will uh |

0:06:02 | be the |

0:06:03 | the meeting over all channel real sections |

0:06:05 | but the problem is that we were like to have a short delay student transmission will like to select the |

0:06:10 | uses all the time so we can't really do this with short terms to get schedule |

0:06:14 | still these are the performance measure the people are using a literature pretty can just |

0:06:19 | but two |

0:06:20 | but i claim here is that this is infeasible that we have |

0:06:23 | the what more lot look like this that first we |

0:06:26 | estimate the channel then we quantized it's |

0:06:28 | and feed it back and then we just use a selection transmission for a while |

0:06:31 | until list |

0:06:32 | information is up eight uh we do over again |

0:06:36 | but we need to use in this can system is quite to explore its the of information to select |

0:06:41 | uh |

0:06:42 | a some kind of of rate that support that with high probability |

0:06:47 | and the way that we're doing this is |

0:06:48 | use F some out that's right |

0:06:50 | cool call it are K out |

0:06:52 | and this is the rate |

0:06:53 | that |

0:06:54 | is always larger than the actual rate |

0:06:56 | with a probability that's a |

0:06:59 | a a and we won't types of useful |

0:07:01 | and our proposed performance measure here's then |

0:07:04 | if so to some way we some up this out the rates for for use |

0:07:10 | and in order to analyse this we need to have some assumptions |

0:07:13 | we assume that we have B bits for feedback for user |

0:07:16 | i want to use them efficiently |

0:07:18 | well to maximise that's non out it's |

0:07:20 | some right |

0:07:21 | we assume rayleigh fading channels |

0:07:23 | so there |

0:07:24 | channel vector which |

0:07:25 | zero mean and some alone |

0:07:27 | covariance matrix E which in general will not be an |

0:07:30 | i don't |

0:07:32 | and is two categories some channels that information |

0:07:34 | i can get to rate |

0:07:35 | right it's like this the direction of one more less be that |

0:07:38 | normalize vector |

0:07:40 | and we want to use it to select users that are in different directions |

0:07:44 | i well to use to just transmit in those direction would be four |

0:07:47 | and the quality information want to use them to select you just a strong channel four moments are we |

0:07:53 | a good channel properties |

0:07:54 | and then select maps and a discrete |

0:07:56 | and with |

0:07:57 | that is high |

0:07:59 | there's basically in trade of them |

0:08:01 | yeah how i certainly do we want to be about the direction and about the quality |

0:08:06 | which is often disregarded in different papers just assume that one of these ones are perfectly known and the other |

0:08:11 | one is |

0:08:13 | but the |

0:08:14 | the question we trying to answer is how do we divide B bits per user |

0:08:18 | between direction for information |

0:08:21 | and purse will do this using some asymptotic an L |

0:08:25 | and the first of the asymptotic observation we have space the following |

0:08:29 | it should be absent here was something wrong there's a bullet inside of it |

0:08:33 | but it is up so i'll sum rate it behaves |

0:08:36 | like and T time slot obvious nor seconds like meaning that is |

0:08:39 | we assume the full multiplexing gain of and T |

0:08:43 | when snr goes to infinity for is all |

0:08:45 | if we know that directional information |

0:08:48 | the normalized vector for users |

0:08:51 | perfect |

0:08:53 | and the proof i is quite similar to what in do use when you work with their go like |

0:08:57 | yeah some some rate |

0:08:59 | we can do is force beamforming since |

0:09:01 | zero for means we want to know |

0:09:03 | the of total space of the channel |

0:09:05 | and no in the direction and or knowing you |

0:09:08 | along that |

0:09:09 | that the channel or it doesn't matter we have the same in space |

0:09:13 | and then we can select and nap some out a rate based on statistics that we know channel and cheap |

0:09:18 | source a |

0:09:20 | the indication of this results look like that the the most important thing here is that we have a direction |

0:09:25 | information |

0:09:26 | and |

0:09:27 | but we don't know really at what this say for practical snrs this is all the when a snore scroll |

0:09:32 | up |

0:09:35 | but this this they the true |

0:09:36 | well |

0:09:37 | there is another kind of observation what we can make |

0:09:39 | saying that the abs out to sum rate will assume this multiplexing gain of T |

0:09:43 | when the snug as affinity for an well |

0:09:46 | if we know that |

0:09:47 | quality of them information of the channel |

0:09:50 | perfectly for users and this is not exactly normal vector this is metric and indicate that we have in the |

0:09:55 | paper which is |

0:09:57 | a a little bit base some directions to |

0:09:59 | and |

0:10:00 | this happens if the number of users is large so should increase with as an R such that it's not |

0:10:06 | a by log K |

0:10:08 | uh them or you just an goes to a that comes |

0:10:12 | and the proof idea here is that |

0:10:14 | we select strong users based on these |

0:10:16 | holding |

0:10:17 | information |

0:10:18 | and |

0:10:19 | if we have a non id channel we need to have a low |

0:10:22 | we can't have an I D but if we have a what just a little |

0:10:25 | with the |

0:10:26 | correlation here's a one on that |

0:10:28 | directions it is these different beams there indicate the a strong different eigen directions |

0:10:33 | if just one of them is large another one and we that the strong |

0:10:36 | select the use a strong then with high probability it would be the strong as eigen direction that we can |

0:10:41 | take |

0:10:42 | yeah power channel |

0:10:47 | so the indication of this kind of result |

0:10:50 | uh with it proof use some uh |

0:10:52 | a large number |

0:10:54 | uh results uh |

0:10:56 | is that it seems like we only need quality information insist |

0:10:59 | as one where many users so the quest is how many use do we need to practise the C kind |

0:11:04 | with it |

0:11:05 | a also another objection might be that's |

0:11:07 | well |

0:11:08 | it the rayleigh fading channel isn't |

0:11:10 | perfect does a model |

0:11:12 | uh there is a small small probability |

0:11:14 | that the channel will become infinitely strong |

0:11:17 | but if we have many used in sect strong one we might |

0:11:20 | uh and up |

0:11:21 | operating in those take which is |

0:11:23 | and modeling or to factor or the fading distribution |

0:11:28 | and a weight this is |

0:11:29 | one of the a simple to so we can G |

0:11:32 | third a simple to get result say the following that we can is you |

0:11:36 | the so some rate will achieve the full multiplexing gain pen |

0:11:39 | a not goes to infinity and that's a |

0:11:41 | if we have a large |

0:11:43 | spatial correlation |

0:11:44 | and we can't to grow right this |

0:11:46 | you |

0:11:46 | characterised this using the two largest eigenvalues of the covariance matrix |

0:11:51 | take a large one divided by that |

0:11:53 | second are just |

0:11:54 | and we want this |

0:11:55 | uh uh |

0:11:57 | become large such size this an are divided by a goes to to con |

0:12:02 | and a proof D is that we have a |

0:12:04 | high spatial correlation that means that the strong as eigen direction will contain more more uh a percentage of that |

0:12:11 | top power and then with the channel direction is known to line almost of direction |

0:12:16 | so an indication of this a simple to results that's set |

0:12:18 | we need really need no feedback make a as long as we have a local spatial correlation just |

0:12:24 | what was the summer here |

0:12:26 | well the conclusion for a a simple can analysis is that |

0:12:29 | we can very diverse observations |

0:12:31 | one says that only directional information is sufficient |

0:12:35 | uh one says that only quality information sufficient as long as we have many users |

0:12:39 | a was says the we don't thing in the V back at all as long as we make sure that |

0:12:43 | we have a |

0:12:44 | high spatial correlation channel |

0:12:46 | but which one or |

0:12:48 | or multiple of these ones that actually applying a practical scenarios |

0:12:51 | this is something that we tried to |

0:12:53 | illustrate i've simulation |

0:12:58 | and we you just look at the simple as they make a C with one i feedback |

0:13:01 | we use a D bits for direction and we use a meaning code book that's been at that |

0:13:06 | uh in a simple way for correlation |

0:13:09 | and we have a cube bits |

0:13:10 | for dixie C Q i and we use and be maximizing code |

0:13:14 | and of course we can have better co which we can you |

0:13:16 | used a log codebook the optimization here but we want something that's simple |

0:13:21 | and we can these or or or or separate |

0:13:23 | that's as still |

0:13:24 | as soon as we |

0:13:26 | have some kind of correlation |

0:13:28 | a |

0:13:29 | we actually want to have a a combined book |

0:13:31 | since |

0:13:32 | for every direction we have |

0:13:34 | the distribution of the game will be look but different |

0:13:37 | but we have separate here |

0:13:38 | simple |

0:13:40 | i we have fixed number bits B |

0:13:43 | it to the of Q |

0:13:45 | and we assume perfect csi at receiver it's only the conversation that's great |

0:13:49 | error |

0:13:51 | average as our location we have four and as |

0:13:54 | and the transmitter |

0:13:55 | we |

0:13:56 | i look we have a a are used as randomly look at on the circles that have the same |

0:14:00 | oh close just make things very simple |

0:14:03 | and uh we select a this this getting alley were done that i board from |

0:14:06 | a paper from |

0:14:07 | a lot the |

0:14:08 | no seven |

0:14:09 | just to |

0:14:10 | i |

0:14:11 | that's the most simple greedy i wouldn't you can |

0:14:13 | imagine |

0:14:14 | but he works well |

0:14:16 | and |

0:14:17 | we calculate an approximate lower bound on a sign are using these |

0:14:21 | feedback like information |

0:14:22 | it's more or less |

0:14:24 | averaging |

0:14:25 | uh |

0:14:26 | the error |

0:14:27 | uh a one station |

0:14:30 | and to since this estimate isn't perfect and we want to |

0:14:33 | uh achieve a certain the |

0:14:35 | if some out just |

0:14:36 | performance formants we have to have a fate |

0:14:38 | margin |

0:14:39 | out |

0:14:40 | so we multiply out uh |

0:14:43 | with |

0:14:43 | that's sign are we have a cheap |

0:14:45 | and we select and i'll but such that |

0:14:47 | probability that |

0:14:48 | this estimate the sign are it's larger than actual snr is small |

0:14:52 | five percent |

0:14:57 | and the first simulation results here is for uncorrelated channel I D |

0:15:02 | on the y-axis we have that some out it's some rate |

0:15:05 | here we have a |

0:15:06 | that's an art up to varying and we have twenty users |

0:15:09 | on the right care |

0:15:10 | here we have |

0:15:11 | varying the number of users and we have fixed an are ten db |

0:15:15 | and |

0:15:16 | here we have a talk a twelve bits |

0:15:18 | well bits |

0:15:19 | and the lower to ones are eight bits and total make bits in total and of course |

0:15:23 | these |

0:15:24 | represent different locations |

0:15:26 | and what we can see here is that the top most curves here are when we take to |

0:15:31 | a bits per use or for the information and the remaining one directional information |

0:15:36 | and we can see here that these two curves here they are going little bit together someone we increase number |

0:15:41 | of users it seems like having a hold information |

0:15:44 | becomes slightly more important |

0:15:46 | but uh still |

0:15:47 | this always |

0:15:49 | in these simulations best to |

0:15:51 | is |

0:15:51 | it's |

0:15:52 | information |

0:15:55 | this increase quite well with the first a simple to summation at we have that |

0:15:58 | or to it that directional information is the most important thing |

0:16:03 | but what happens when we |

0:16:04 | yeah introduced some spatial correlation |

0:16:07 | well we use is simple model here |

0:16:10 | where the angle spread represents a spatial correlation so angle spread is the |

0:16:14 | uh average direction and |

0:16:17 | angle angle direction where |

0:16:18 | it should transmit an or for |

0:16:20 | it to C |

0:16:21 | but the user |

0:16:24 | so having a small angle spread means that have high correlation and |

0:16:28 | a week increase we the correlation and we we increase it we decrease the like so it's not direction |

0:16:34 | and we have a tend to be that's an hour and twenty years |

0:16:38 | and it's very hard to read anything at all here about the sure of the |

0:16:42 | so that we can gain a little bit here when we have a very high correlation |

0:16:46 | and by |

0:16:47 | allocating locating that bit more bits for cold information |

0:16:50 | but the difference where small and that's in as we increase and |

0:16:53 | to an angle spread of ten to fifty |

0:16:55 | reese for example |

0:16:56 | and once again see that which should allocate the but to to free bits |

0:17:00 | for for the information the rest of for direction |

0:17:05 | so this also reach quite well with the |

0:17:07 | with asymptotic observation while that if you bits |

0:17:10 | for called information and the rest of direction |

0:17:14 | as a summer here |

0:17:15 | we look that multi use a mimo which and show excellent performance if we have perfect channel |

0:17:20 | they'd information |

0:17:22 | but in practice limit by have a feedback station |

0:17:25 | and we |

0:17:26 | this guest how to compress the channel |

0:17:28 | and there's a tradeoff between the cold information and the direction information |

0:17:32 | and we'll try to or was the relative importance between a |

0:17:36 | and when we look at some topic |

0:17:38 | they were |

0:17:39 | very different thing we can show we can show and |

0:17:41 | and anything |

0:17:42 | do we did have them the asymptotic to what we K |

0:17:45 | but |

0:17:45 | but B look |

0:17:46 | that's simulations with saw but to to free bits for user should use but quality and the remaining money direction |

0:17:51 | is is very important |

0:17:53 | to have |

0:17:53 | a good |

0:17:55 | yeah |

0:17:55 | control of interfere |

0:17:57 | and if you compare is with L D's done as for example where we have a codebook of four bits |

0:18:01 | per user for old information |

0:18:03 | we see here that |

0:18:05 | we can decrease at a the bit but a since we know channel statistics |

0:18:09 | to we all the use of portion of which for example |

0:18:12 | we not |

0:18:12 | strong channel |

0:18:14 | i have a |

0:18:16 | and in fact of spatial correlation and the number of uses is quite small |

0:18:20 | and |

0:18:22 | our simulations agrees with one of a simple cells which |

0:18:25 | probably the most recent |

0:18:26 | well |

0:18:28 | so we like to thank you for listening |

0:18:30 | my paper some presentation available on |

0:18:33 | and i will let also question |

0:18:37 | i |

0:18:47 | yes so have a a question or |

0:18:49 | or maybe some or multiple questions depending oh what other people wanna ask um |

0:18:53 | so yeah i i mean i like the comparison and the |

0:18:56 | the asymptotic messages is kind of interesting um |

0:18:59 | so i guess i wanna push back a little bit on your epsilon |

0:19:02 | because |

0:19:03 | my understanding is that |

0:19:05 | normally the rate |

0:19:07 | the the issue is uncertainty about the rate you don't know what log of one plus S and Rs which |

0:19:11 | you quantized the thing and S and R yeah but my understanding is normally that's this is what the use |

0:19:15 | this fast hybrid really or Q for |

0:19:17 | to kind of fix that |

0:19:19 | so |

0:19:20 | that's what every time i talk to someone an industry were some three D B P that's all so i |

0:19:23 | guess i'm wondering like |

0:19:25 | do you have any results that show that doing the apps line gives you something |

0:19:30 | in that's not captured by |

0:19:32 | just using the log one process and are "'cause" i didn't |

0:19:35 | and see that can person |

0:19:37 | is it is central to we to what you did |

0:19:40 | well at the same time this say when the in the standard that they should |

0:19:43 | a a the having a maps so that about ten percent |

0:19:46 | uh |

0:19:47 | but uh |

0:19:49 | we are not really taking care of the the errors that that we gets a with five percent |

0:19:53 | these are run reasonable |

0:19:55 | numbers that we add up |

0:19:56 | to it but um |

0:19:58 | and |

0:20:01 | it's hard to i |

0:20:03 | yeah i guess you yeah need to run simulations to see how large absolute you can accept in or to |

0:20:07 | take care of the rest of their or student using have but i yeah Q but i'm quite sure that |

0:20:12 | you |

0:20:12 | you can't take care of everything you |

0:20:16 | yeah you |

0:20:16 | yeah mean there's always some more errors i guess i'm wondering go |

0:20:19 | some of these results depend on that |

0:20:22 | measure of performance as opposed to |

0:20:25 | yeah i that that's basically what model but i guess of that's the case then you would not have the |

0:20:29 | quality |

0:20:31 | Q i would probably not place what role |

0:20:33 | i think if we won't do anything able |

0:20:36 | here for example uh that we will have a fifty percent |

0:20:40 | probability of the uh |

0:20:42 | a getting now each and taken care to this with |

0:20:45 | a a a a to is not really what was meant for for the beginning again |

0:20:50 | i mean a hybrid are who you're gonna get sums of these things you're going to get |

0:20:54 | i mean |

0:20:55 | it does appear a little bit of the way a kind of |

0:20:58 | goes away |

0:21:01 | or |

0:21:01 | yeah or are alright |

0:21:12 | as |

0:21:12 | i |

0:21:14 | but |

0:21:15 | uh |

0:21:16 | so |

0:21:17 | the |

0:21:19 | i |

0:21:20 | oh |

0:21:20 | oh |

0:21:21 | oh |

0:21:23 | no |

0:21:24 | oh |

0:21:28 | i |

0:21:34 | oh |

0:21:34 | oh |

0:21:35 | i |

0:21:39 | i |

0:21:39 | so basically we made the |

0:21:41 | those assumptions stuff was the |

0:21:43 | uh |

0:21:44 | need in nor to |

0:21:45 | if fixed do proofs of this free a simple tick things in the and i guess paper but the i |

0:21:50 | think we we can |

0:21:51 | yeah |

0:21:52 | expand things there are quite a lot uh minute of these of may should could be proved |

0:21:57 | uh asymptotic asymptotically an |

0:21:58 | for |

0:21:59 | different user |

0:22:01 | fusion |

0:22:05 | that |

0:22:06 | but but but not not only set we need it is not a very hard to prove that you see |

0:22:10 | that |

0:22:10 | yeah |

0:22:11 | don't to most basic in the constant to come very large should use |

0:22:14 | is proofs are more based on of this quite easy to prove |

0:22:22 | okay |

0:22:23 | um |

0:22:24 | okay |

0:22:25 | okay |