Grassmannian Design Package for Limited Feedback Systems

In this project, we developped smooth optimzation algorithms on the Grassmannian manifold to tackle the problem of codebook design.

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We were successfully able to design Grassmannian subspace packings that maximize the minimum Chordal distance or Fubini Study distance, line packings, line packings with constant modulus and line packings with defined alphabet. Nested codebooks from defined alphabet have also developped. The Matlab code for some of these packings can be downloaded from here. Also, I have two papers describing the alogirthms that have been used for the generation of such packings. These paper are available in my publications page, in addition to this page, which includes some of our designed codebooks that can be used directly. (For detailed results and downloading packings, click here).

 

Here is a quick summary of the achieved results:

1. For Subspace packings with Fubini Study distance, our packings have larger distances than those found in Love’s website.

2. For Subspace packings with chordal distance, our packings are as good as the packings presented by S. Dhillon, T. Stromher, R. W. Heath Jr., and J. A. Tropp .

3. For Line packings, our packings are as good as the packings presented by S. Dhillon, T. Stromher, R. W. Heath Jr., and J. A. Tropp .

4. For Line packings with constant modulus, we constructed packings of distances that are very close to the corresponding packings without any restrictions.

5. For Line packings with constant modulus and defined alphabet (QPSK), our results are either new or as good as /better than the known results.

6. For Subspace packings with nested structure, our results are novel.

7. For Subspace packings with nested structure and defined alphabet, our results are novel.