Polarization Covariance Matrix
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From: Madhu on 26 Dec 2006 17:18 Hi, I'm learning the basics of polarized antennas since I need it in my wireless channel modeling (MIMO) research. I would appreciate it if someone could help me understand a few concepts. 1. What do each of the elements in the polarization covariance matrix represent? 2. What is the relation between XPD and pol cov matrix? 3. What determines the dimensions of the pol cov matrix? Does it depend on the number of antennas at the transmit or receive end? 4. This question is more EE specific : If I have a spatial correlation matrix and pol cov matrix, what will be the spatial COVARIANCE matrix? Any help would be greatly appreciated. I have been grappling with these concepts for over 10 days now without making much headway. a google web search doesn't fetch any good results. Pointers to resources where I can learn about pol cov matrix would be great too. Thank you, Madhu
From: Clay on 26 Dec 2006 18:44 Madhu wrote: > Hi, > > I'm learning the basics of polarized antennas since I need it in my > wireless channel modeling (MIMO) research. I would appreciate it if > someone could help me understand a few concepts. > Hello Madhu, You may find some of your answers by looking up Stokes Parameters and the Mueller Calculus. While these were developed for dealing with light, they are useful for working with any E-M radiation. Clay
From: Madhu on 28 Dec 2006 13:44 > Hello Madhu, > > You may find some of your answers by looking up Stokes Parameters and > the Mueller Calculus. While these were developed for dealing with > light, they are useful for working with any E-M radiation. > > Clay Thanks Clay. On your suggestion, I read up on Stokes and Mueller Calculus. I find them too entrenched in Physics and a bit too rigorous. I'm looking for something a little more high level, that can help me understand what the elements in the polarization covariance matrix mean. Madhu
From: Andy Resnick on 28 Dec 2006 15:42 Madhu wrote: <snip> > > > Thanks Clay. On your suggestion, I read up on Stokes and Mueller > Calculus. I find them too entrenched in Physics and a bit too rigorous. > I'm looking for something a little more high level, that can help me > understand what the elements in the polarization covariance matrix > mean. Yeesh. Based on your other question: 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. You will get more useful help if you can more clearly explain what you are trying to do. Ugh... this brings back bad memories. I'll give it a shot. First, you asked 1. What do each of the elements in the polarization covariance matrix represent? 2. What is the relation between XPD and pol cov matrix? 3. What determines the dimensions of the pol cov matrix? Does it depend on the number of antennas at the transmit or receive end? 4. This question is more EE specific : If I have a spatial correlation matrix and pol cov matrix, what will be the spatial COVARIANCE matrix? As for #3- no, the matrices (or sub-blocks) are always 2x2, because using the Jones formulation for polarization (which is what your model seems to use), there are 2 orthogonal polarization states, here (V)ertical and (H)orizontal. So the diagonal elements VV and HH represent the unscattered signal, while the off-diagonal elements VH and HV are the cross-talk due to scattering from objects. #1- From the paper, "It is advantageous to separate the spatial domains and the polarization domain (which the SCM indeed allows), as this allows a more compact representation of the covariance matrix. The spatially separated elements are identical and will have equal power, thus it is sufficient to calculate a spatial correlation coefficient. This correlation coefficient is denoted a at the base station and b at the mobile station. The full covariance matrix is needed to describe the polarization domain, as the channel elements will not have equal power due to the channel XPD and rotations of the antennas. " Now I (sort of) understand what they are talking about: The covariance matrix is a 4x4 matrix, and Kronecker multiplication is a block multiplication. Why this particular formulation for polarization is used, I have no idea- it has nothing to do with the physics of polarization. The XPD (cross polarization something) tells you how much of your H signal ends up in your V channel due to scattering (and vice-versa), and should be a 2x2 matrix- and it looks like it's in each 2x2 block of the covariance matrix. The spatial correlation matrices have to do with (I think) the misorientation of the receiver antenna and transmission antenna. Good luck.... after reading all this stuff, I'm amazed you guys can make anything work... and I mean that in a good way. -- Andrew Resnick, Ph.D. Department of Physiology and Biophysics Case Western Reserve University
From: Clay on 28 Dec 2006 20:11 Madhu wrote: > > Hello Madhu, > > > > You may find some of your answers by looking up Stokes Parameters and > > the Mueller Calculus. While these were developed for dealing with > > light, they are useful for working with any E-M radiation. > > > > Clay > > Thanks Clay. On your suggestion, I read up on Stokes and Mueller > Calculus. I find them too entrenched in Physics and a bit too rigorous. > I'm looking for something a little more high level, that can help me > understand what the elements in the polarization covariance matrix > mean. > > Madhu Hello Madhu, I referred you to the Stokes/Mueller method since I assumed you may be dealing with partialy polarized waves (or made to appear that way after time averaging). Jones matrices are much simpler, but then complete polarization is assumed. Clay
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