I noticed most literatures on mimo channel capacity focused on flat fading channel. I want to know if any one interested in the capacity of MIMO frequency selective channel, or any literature to this problem? why so few literatures in this problem? it is because it is very complex or any other reasons? Any ideas are welcome!! Thank you!
capacity of MIMO frequency selective channel
Started by ●December 6, 2003
Reply by ●December 6, 20032003-12-06
you can probably find an expression for it; but the problem is whether ou can compute it for a "good" channel model and get some intuitive understanding for it. as far as i know, there is no satisfying channel model for this kind of system yet, but i am not well-read in this area. for example, the expression for the capacity of multi-antenna flat fading systems is already known for a long time. it was not until telatar used results from random matrices, many of which you can find in alan adelman's phd thesis at mit, were people able to see that you get linear increase in capacity with increasing numbers of transmit and receive antennas. julius On Sat, 6 Dec 2003, Johnathn wrote:> I noticed most literatures on mimo channel capacity focused on flat > fading channel. I want to know if any one interested in the capacity > of MIMO frequency selective channel, or any literature to this > problem? why so few literatures in this problem? it is because it is > very complex or any other reasons? Any ideas are welcome!! > > Thank you! >-- The most rigorous proofs will be shown by vigorous handwaving. http://www.mit.edu/~kusuma opinion of author is not necessarily of the institute
Reply by ●December 6, 20032003-12-06
On 6 Dec 2003 04:48:23 -0800, frankerlin_peng@hotmail.com (Johnathn) wrote:>I want to know if any one interested in the capacity >of MIMO frequency selective channelA MIMO-OFDM looks like one of them. BR, ------ James K. (txdiversity@hotmail.com) - Any remarks, proposal and/or indicator would be greatly respected. - Private opinions: These are not the opinions from my affiliation. [Home] http://home.naver.com/txdiversity
Reply by ●December 6, 20032003-12-06
On Sat, 6 Dec 2003 12:51:17 -0500, Julius Kusuma <kusuma@mit.edu> wrote:>it was not until telatar used >results from random matrices, many of which you can find in alan adelman's >phd thesis at mit, were people able to see that you get linear increase in >capacity with increasing numbers of transmit and receive antennas.By adding Alan Adelman's phd thesis, now I have many papers of MIMO initiation. Please let me know which one I have to read first as a beginner. These are list of items what I have taken: - MIMO capacity: Alan Adelman's paper, Telatar's paper, ... - MIMO system: A. J. Paulraj and T. Kailath 's DT/DR, ... - To achieve MIMO capacity in Rx only coordinated systems: G. J. Foschini's BLAST, ... - To achieve MIMO capacity in Tx only coordinated systems: M.H.M. Costa's Dirty paper coding, ... - MU-MIMO with space-time scheduling: ... BR, ------ James K. (txdiversity@hotmail.com) - Any remarks, proposal and/or indicator would be greatly respected. - Private opinions: These are not the opinions from my affiliation. [Home] http://home.naver.com/txdiversity
Reply by ●December 7, 20032003-12-07
i should state again that i'm not an expert in this area. i'm sure other posters here can make a better recommendation. On Sun, 7 Dec 2003, James K. wrote:> By adding Alan Adelman's phd thesis, now I have many papers of MIMO > initiation. Please let me know which one I have to read first as a > beginner. These are list of items what I have taken: > - MIMO capacity: Alan Adelman's paper, Telatar's paper, ... > - MIMO system: A. J. Paulraj and T. Kailath 's DT/DR, ... > - To achieve MIMO capacity in Rx only coordinated systems: > G. J. Foschini's BLAST, ...what about the papers from tarokh? the 1998 paper gives a really nice evaluation criterion. i think the recent paper by jafarkhani gives a very nice constructive way of designing space-time codes for this type of systems.> - To achieve MIMO capacity in Tx only coordinated systems: > M.H.M. Costa's Dirty paper coding, ... > - MU-MIMO with space-time scheduling: ... >start from the vishwanath/tse/laroiya paper, it's very well-written. plus you should read zheng/tse's paper on the tradeoff between capacity and diversity, which is also very well-written. hope that helps, julius -- The most rigorous proofs will be shown by vigorous handwaving. http://www.mit.edu/~kusuma opinion of author is not necessarily of the institute
Reply by ●December 7, 20032003-12-07
James K. <txdiversity@hotmail.com> wrote in message news:<i355tvokgg0cm39h8gl9g0s1u9rpvq8voo@4ax.com>...> On 6 Dec 2003 04:48:23 -0800, frankerlin_peng@hotmail.com (Johnathn) > wrote: > > >I want to know if any one interested in the capacity > >of MIMO frequency selective channel > > A MIMO-OFDM looks like one of them. >To say exactly, i mean if we can find some results on capacity limits of MIMO frequency selective channel like what G. J. Foschini and M. J. Gans has done on flat fading channel MIMO. BTW: Where can I find Alan Adelman's phd thesis?
Reply by ●December 7, 20032003-12-07
This is a multi-part message in MIME format. ------=_NextPart_000_001F_01C3BD86.0D3A7CB0 Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable "Johnathn" <frankerlin_peng@hotmail.com> wrote in message = news:dd6ca172.0312071742.35fa9515@posting.google.com...> To say exactly, i mean if we can find some results on capacity limits > of MIMO frequency selective channel like what G. J. Foschini and M. J. > Gans has done on flat fading channel MIMO.I thought that you wanted to see just some applications of MIMO on the = frequency selective channel. Regarding to the capacity of MIMO on the = frequency selective channel, it looks like really new area. As matter of = fact, the capacity of even single path MIMO channel seems to have more = things to be researched, yet. In practice, as far as I know, they (G. J. Foschini and M. J., Gans) = researched starting from the ergodic capacity so I'm not sure yet about = its exact formulae for instatant case. The ergodic capacity is =20 E[C] =3D E[Sum[Log[2,1+(P/N)*r[i]]],{i,1,min[M,N]}], -- (1) where E[.] is the expectation function, Sum[.,{i,1,min[M,N]}] is the = sumation operator ranging i=3D1 to minimum value of [M,N], Log[2,.] is = the logarithm function with base 2, P is SNR (Signal to Noise power = Ratio) when the noise distribution is normalized to ~N(0,1), r[i] is = i-th eigen value of the channel matrix multiple H'H, and M, N are the = number of Rx and Tx antenna elements, respectively. This equation (1) is = simply solved to the equation (2) when we assume M=3DN, E[C] =3D Integrate[N*Log[2,1+(P/N)*r]*p(r), {r,0,Infinity}], -- (2) =20 where surprisingly p(r) is the general pdf of SNR for the single path = Rayleigh channel. For the instant channel, we need to know values of not = only 1st moment but also other higher order moment. Thus, this case is = not clear yet to me. In brief, I have seen a study of the capacity formulae in SISO frequncy = selective channel, e.g. OFDM analysis. Its extention to MIMO supposed to = be still *Big Deal* for us to study, as it was noted by Johnathn. BR, ------ James K. (txdiversity@hotmail.com) - Any remarks, proposal and/or indicator would be greatly respected. - Private opinions: These are not the opinions from my affiliation. [Home] http://home.naver.com/txdiversity ------=_NextPart_000_001F_01C3BD86.0D3A7CB0 Content-Type: text/html; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=3DContent-Type content=3D"text/html; = charset=3Diso-8859-1"> <META content=3D"MSHTML 6.00.2800.1276" name=3DGENERATOR> <STYLE></STYLE> </HEAD> <BODY> <DIV><FONT face=3D굴림 size=3D2>"Johnathn" <</FONT><A=20 href=3D"mailto:frankerlin_peng@hotmail.com"><FONT = face=3D굴림=20 size=3D2>frankerlin_peng@hotmail.com</FONT></A><FONT = face=3D굴림 size=3D2>> wrote in=20 message </FONT><A=20 href=3D"news:dd6ca172.0312071742.35fa9515@posting.google.com"><FONT = face=3D굴림=20 size=3D2>news:dd6ca172.0312071742.35fa9515@posting.google.com</FONT></A><= FONT=20 face=3D굴림 size=3D2>...</FONT></DIV> <DIV><FONT face=3D굴림 size=3D2>> To say exactly, i mean = if we can find some=20 results on capacity limits<BR>> of MIMO frequency selective channel = like what=20 G. J. Foschini and M. J.<BR>> Gans has done on flat fading channel=20 MIMO.<BR></FONT></DIV> <DIV><FONT face=3D굴림 size=3D2>I thought that you wanted to = see just some=20 applications of MIMO on the frequency selective channel. Regarding to = the=20 capacity of MIMO on the frequency selective channel, it looks like = really new=20 area. As matter of fact, the capacity of even single path MIMO channel = seems to=20 have more things to be researched, yet.</FONT></DIV> <DIV><FONT face=3D굴림 size=3D2></FONT> </DIV> <DIV><FONT face=3D굴림 size=3D2>In practice, as far as I = know, they (G. J. Foschini=20 and M. J., Gans) researched starting from the ergodic capacity = so I'm not=20 sure yet about its exact formulae for instatant case. The = ergodic=20 capacity is </FONT></DIV> <DIV><FONT face=3D굴림 size=3D2></FONT> </DIV> <DIV><FONT face=3D굴림 size=3D2> E[C] =3D=20 E[Sum[Log[2,1+(P/N)*r[i]]],{i,1,min[M,N]}], -- (1)</FONT></DIV> <DIV><FONT face=3D굴림 size=3D2></FONT> </DIV> <DIV><FONT face=3D굴림 size=3D2>where E[.] is the = expectation function,=20 Sum[.,{i,1,min[M,N]}] is the sumation operator ranging i=3D1 to = minimum value=20 of [M,N], Log[2,.] is the logarithm function with base 2, P is SNR = (Signal to=20 Noise power Ratio) when the noise distribution is normalized to=20 ~N(0,1), r[i] is i-th eigen value of the channel matrix multiple = H'H, and=20 M, N are the number of Rx and Tx antenna elements, respectively. This = equation=20 (1) is simply solved to the equation (2) when we assume = M=3DN,</FONT></DIV> <DIV><FONT face=3D굴림 size=3D2></FONT> </DIV> <DIV><FONT face=3D굴림 size=3D2> E[C] =3D = Integrate[N*Log[2,1+(P/N)*r]*p(r),=20 {r,0,Infinity}], -- (2)</FONT></DIV> <DIV><FONT face=3D굴림=20 size=3D2> &nbs= p;  = ; =20 </FONT></DIV> <DIV><FONT face=3D굴림 size=3D2>where surprisingly p(r) = is the general pdf of SNR=20 for the single path Rayleigh channel. For the instant channel, we need = to know=20 values of not only 1st moment but also other higher order = moment.=20 Thus, this case is not clear yet to me.</FONT></DIV> <DIV><FONT face=3D굴림 size=3D2></FONT> </DIV> <DIV><FONT face=3D굴림 size=3D2>In brief, I have = seen a study of the=20 capacity formulae in SISO frequncy selective channel, e.g. OFDM = analysis.=20 Its extention to MIMO supposed to be still *Big Deal* for us to study, = as it was=20 noted by Johnathn.</FONT></DIV> <DIV><FONT face=3D굴림 size=3D2></FONT> </DIV> <DIV><FONT face=3D굴림 size=3D2>BR,<BR>------<BR>James K. = (</FONT><A=20 href=3D"mailto:txdiversity@hotmail.com"><FONT face=3D굴림=20 size=3D2>txdiversity@hotmail.com</FONT></A><FONT face=3D굴림 = size=3D2>)<BR>- Any=20 remarks, proposal and/or indicator would be greatly respected.<BR>- = Private=20 opinions: These are not the opinions from my = affiliation.<BR><STRONG><FONT=20 color=3D#ff0000>[Home]</FONT></STRONG> </FONT><A=20 href=3D"http://home.naver.com/txdiversity"><FONT face=3D굴림 = size=3D2>http://home.naver.com/txdiversity</FONT></A></DIV></BODY></HTML>= ------=_NextPart_000_001F_01C3BD86.0D3A7CB0--
Reply by ●December 8, 20032003-12-08
On Sun, 7 Dec 2003 19:33:50 -0500, Julius Kusuma <kusuma@mit.edu> wrote:> >i should state again that i'm not an expert in this area. >i'm sure other posters here can make a better recommendation.I dunno, Julius, you can scan a related paper and distill it to points like this better than most, and you seem to be scanning all the right papers. I find few that get these issues as well as you seem to, so please don't hesitate to post on stuff like this. Eric Jacobsen Minister of Algorithms, Intel Corp. My opinions may not be Intel's opinions. http://www.ericjacobsen.org
Reply by ●December 8, 20032003-12-08
Julius Kusuma <kusuma@mit.edu> wrote in message news:<Pine.GSO.4.55L.0312061248090.17845@department-of-alchemy.mit.edu>...> > for example, the expression for the capacity of multi-antenna flat fading > systems is already known for a long time. it was not until telatar used > results from random matrices, many of which you can find in alan adelman's > phd thesis at mit,alan adelman? do you refer a right name? I try to search it in Google, but can not find. Peng http://cn.geocities.com/frankerlin/
Reply by ●December 8, 20032003-12-08
On Mon, 8 Dec 2003, Johnathn wrote:> Julius Kusuma <kusuma@mit.edu> wrote in message news:<Pine.GSO.4.55L.0312061248090.17845@department-of-alchemy.mit.edu>... > > > > for example, the expression for the capacity of multi-antenna flat fading > > systems is already known for a long time. it was not until telatar used > > results from random matrices, many of which you can find in alan adelman's > > phd thesis at mit, > > alan adelman? do you refer a right name? I try to search it in > Google, but can not find. > > > Peng > > http://cn.geocities.com/frankerlin/ >if you had looked in telatar's paper, you will have found that i indeed mispelled "alan edelman". julius -- The most rigorous proofs will be shown by vigorous handwaving. http://www.mit.edu/~kusuma opinion of author is not necessarily of the institute
