Polarization Covariance Matrix
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From: Madhu on 2 Jan 2007 12:22 Thanks for your responses, Andy and Clay. > http://www.dsprelated.com/showmessage/69440/1.php > > you have come to the wrong group- first off, your acronyms might as well > be a foreign language. The work I'm doing is in dsp and wireless comm mainly. The polarization aspect to channel modeling is new to me. So after not getting help from pure dsp guys in comp.dsp, I decided to cross post to the physics forum as well and it worked. >You will get more useful help if you can more > clearly explain what you are trying to do. sorry about that. will try to explain my questions better. Known facts/concepts: --------------------------------- XPD: cross polarization discrimination = ratio of co-polarized power to cross-polarized power i.e. XPD: ratio of channel power between identically polarized elements to power of channel between cross polarized elements. MIMO : multiple input, multiple output systems. They have multiple antennas at both transmit and receive ends. Notation; a system with m transmit and n receive antennas is called an n x m system. Spatial correlation matrix : has dimension mn x mn. It models the correlation between the channels (for different antenna receiver combinations) Questions: ------------- In the 3GPP document R4-060334, (located at http://www.3gpp.org/ftp/tsg_ran/WG4_Radio/tsgr4_38/Docs/R4-060334.zip ) polarization covariance matrices are used to model the channel. The following formulation is used to obtain the spatial covariance matrix. In the paper, R_tap = p_tap . g_BS_tap . g_MS_tap .A (kron) POL_COV (kron) B (i) where, (kron) : kronecker product POL_COV : polarization covariance matrix R_tap : spatial covariance matrix A, B : BS, MS spatial correlation matrices p_tap : tap power (scalar) g_BS_tap, g_MS_tap : BS, MS antenna gains (scalar) Now, the following formula has been used to obtain spatial CORRelation matrices in literature and have been proved valid: Spatial Corr matrix = A (kron) B (ii) The introduction of the polarization covariance matrix in (i) has been done in this paper and that is what seems suspect and weird to me. The dimension of the resulting covariance matrix will be incorrect, if the normal definitions apply to the matrices A and B in (i). So there seems to have been an implicit change in the defn of A and B in (i). I was hoping that understanding what the elements in the POL_COV matrix mean, would help me better interpret the logic behind this formulation. The polarization covariance matrices are provided for two types of systems : I )(2 x 2) 2 transmit antennas(1V, 1H polarized), 2 receive antennas (1V, 1H polarized) II )(2 x 4) 2 transmit antennas(1V, 1H polarized), 4 receive antennas (2V, 2H polarized) The respective polarization covariance matrices: I) POL_COV= [0.5953 0.1936 0.0000 0.1831 0.1936 0.5953 0.1831 0.0000 0.0000 0.1831 0.2976 -0.0968 0.1831 0.0000 -0.0968 0.2976] II) POL_COV = [ 0.5953 0.4047 0 0; 0.4047 0.5953 0 0; 0 0 0.5953 -0.4047; 0 0 -0.4047 0.5953] I'm trying to figure out why the POL_COV matrices are 4x4 in dimension. As per what you'd stated and the little I understand about polarization, they should be 2x2 matrices. Observe the following, and please shed some light on why they are so, if you can make sense out of them. In the POL_COV matrix for system type (I) , the elements in the bottom right 2x2 block are twice (with -ve sign for cross diagonal elements) those in the top left 2x2 block. In the POL_COV matrix for system type (II) , the elements in the bottom right 2x2 block are equal (with -ve sign for cross diagonal elements) to those in the top left 2x2 block. Also, the top right and bottom left 2x2 blocks are all zeros. Thanks again to all of you for your help so far. Madhu
From: Andy Resnick on 3 Jan 2007 09:29 Madhu wrote: <snip> > > Questions: > ------------- > In the 3GPP document R4-060334, (located at > http://www.3gpp.org/ftp/tsg_ran/WG4_Radio/tsgr4_38/Docs/R4-060334.zip ) > polarization covariance matrices are used to model the channel. > > The following formulation is used to obtain the spatial covariance > matrix. <snip> > > The introduction of the polarization covariance matrix in (i) has been > done in this paper and that is what seems suspect and weird to me. The > dimension of the resulting covariance matrix will be incorrect, if the > normal definitions apply to the matrices A and B in (i). So there seems > to have been an implicit change in the defn of A and B in (i). <snip> > > I'm trying to figure out why the POL_COV matrices are 4x4 in dimension. > As per what you'd stated and the little I understand about > polarization, they should be 2x2 matrices. <snip> Ok, now I understand what you are asking- that's progress, right? :) I totally agree with you- the dimensions of the polarization covariance matrix (P) appear to be incorrect. I could understand if it had the same dimensions as A (kron) B, and there was some sort of "direct multiplication" implied- but that's not what the paper says. Unfortunately, I can't figure out what the paper is trying to say. Normally, at this point, for my own research, I contact the paper's author with my question(s), but there doesn't appear to be an author associated with this thing. It's a working group, and there must be some few people in charge, so if you can, try contacting them directly with your question- they are good questions, and perfectly reasonable. There's other annoying things in the paper- for example, the complex conjugate is switched between the definition of A and B in the paper and Annex B. And this whole Kronecker product doesn't make a lot of sense to me either. For what it's worth, there's very little physics in this model. -- Andrew Resnick, Ph.D. Department of Physiology and Biophysics Case Western Reserve University
From: Madhu on 4 Jan 2007 14:03 Andy Resnick wrote: > Unfortunately, I can't figure out what the paper is trying to say. > Normally, at this point, for my own research, I contact the paper's > author with my question(s), but there doesn't appear to be an author > associated with this thing. It's a working group, and there must be > some few people in charge, so if you can, try contacting them directly > with your question- they are good questions, and perfectly reasonable. Thanks Andy. I replied to your post yesterday but there seems to have been a mess up in beta groups or whatever; the post hasn't appeared yet. I have mailed a few IEEE paper authors who have published work on MIMO channel modeling, one of whom also handled polarization. Its been over a week now and I haven't received inputs from any of them. The one person who replied declined any comment on the subject. In the past, I have usually got replies to queries from authors within 5 days, so I don't expect to hear from them now. I am working to see if I can get hold of some contact in the working group that came up with the previously mentioned document. I will post back when I get things clarified by them. Thanks again to everyone. Madhu
From: smartWater on 2 Feb 2007 13:48 On Jan 4, 2:03 pm, "Madhu" <balding_spald...(a)inbox.com> wrote: > Andy Resnick wrote: > > Unfortunately, I can't figure out what the paper is trying to say. > > Normally, at this point, for my own research, I contact the paper's > > author with my question(s), but there doesn't appear to be an author > > associated with this thing. It's a working group, and there must be > > some few people in charge, so if you can, try contacting them directly > > with your question- they are good questions, and perfectly reasonable. > > Thanks Andy. I replied to your post yesterday but there seems to have > been a mess up in beta groups or whatever; the post hasn't appeared > yet. > > I have mailed a few IEEE paper authors who have published work on MIMO > channel modeling, one of whom also handledpolarization. Its been over > a week now and I haven't received inputs from any of them. The one > person who replied declined any comment on the subject. In the past, I > have usually got replies to queries from authors within 5 days, so I > don't expect to hear from them now. > > I am working to see if I can get hold of some contact in the working > group that came up with the previously mentioned document. I will post > back when I get things clarified by them. > > Thanks again to everyone. > > Madhu I have been grappling with this issue for a few day now. Its nasty that the suffcient refrences are too often not listed in standards contribution. After a somewhat painstaking search I ended with the following refrence that is very close to what you are looking for: Polarisation Diversity in MIMO radio channels: Experimental Validation of a stochatic model and performance Assessment: Proceedings of VTC, Fall 2001. Hope this helps! Kal
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