Flexible codebook design for limited feedback systems

Central Publication

• Ahmed Medra and Timothy N. Davidson.
  Flexible codebook design for limited feedback systems via sequential smooth optimization on the Grassmannian manifold
  IEEE Transactions on Signal Processing,
  62(5):1305-1318, March 2014.

Abstract

• Grassmannian quantization codebooks play a central role in a number of limited feedback schemes for single and multi-user multiple-input multiple-output (MIMO) communication systems. In practice, it is often desirable that these codebooks possess additional properties that facilitate their implementation, beyond the provision of good quantization performance. Although some good codebooks exist, their design tends to be a rather intricate task. The goal of this paper is to suggest a flexible approach to the design of Grassmannian codebooks based on sequential smooth optimization on the Grassmannian manifold and the use of smooth penalty functions to obtain additional desirable properties. As one example, the proposed approach is used to design rank-2 codebooks with a large minimum distance that also have a nested structure and elements from a phase-shift keying (PSK) alphabet. In some numerical comparisons, codebooks designed using the proposed approach have better Fubini-Study distance properties than some existing codebooks, and provide tangible performance gains when applied to a simple MIMO downlink scenario with zero-forcing beamforming, per-user unitary beamforming and rate control (PU2RC), and block diagonalization signalling. Furthermore, the proposed approach yields codebooks that attain desirable additional properties without incurring a substantial degradation in performance.

Paper

• The manuscript is available as a pdf file.

Additional References

• A preliminary version of this work appears in
  • A. Medra and T. N. Davidson. Flexible codebook design for limited feedback downlink systems via smooth optimization on the Grassmannian manifold. In Proceedings of the IEEE International Workshop on Signal Processing Advances in Wireless Communications, pages 50-54, Cesme, Turkey, June 2012. (pdf file).

Further information

• To facilitate further evaluation of the codebooks that we have designed, we now provide Matlab *.mat files for the codebooks that were discussed in our SPAWC 2012 paper.

• For a codebook of N matrices of size M_t x M, the elements of the codebook are stored in a matrix denoted "codebook" of size M_t x MN. The first M columns of "codebook" contain the first element of the codebook, the next M columns contain the second element, and so on.

• To assist in the extraction of the elements of the codebooks, and the evaluation of their distance spectra, we have provided a short Matlab *.m file.

• Codebooks designed to have large minimum Fubini-Study distances.
  (Table 1 in the SPAWC 2012 paper)
  • M_t=4, M=2:
    • N=4
    • N=8
    • N=16
    • N=32
    • N=64
  • M_t=6, M=2:
    • N=16
    • N=32
    • N=64
  • M_t=6, M=3:
    • N=16
    • N=32
    • N=64
  • M_t=8, M=2:
    • N=32

• Codebooks for M=1 (beamforming codebooks) with QPSK alphabet
  (Table 2 in SPAWC 2012 paper)
  • M_t=4
    • N=8
    • N=16
    • N=32
  • M_t=6
    • N=8
    • N=16
    • N=32
  • M_t=8
    • N=16
    • N=32
• Nested codebooks (M=1 nested in M=2) with QPSK alphabet
  (Table 3 in SPAWC 2012 paper)
  • M_t=4
    • N=8
    • N=16
  • M_t=6
    • N=8
    • N=16
  • M_t=8
    • N=8
    • N=16

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