Compact feedback for MIMO-OFDM systems over frequency selective channels

Transmit beamforming can improve the performance of multiple-input multiple-output (MIMO) antenna systems. However, the feedback overhead of beamforming matrixes may significantly reduce the FDD system throughput. Efficient feedback techniques were reported recently. However, their complexities can be prohibitively high for systems with large numbers of transmit antennas (M_t) and spatial streams (M_s) since numerous large matrix codebooks of Grassman manifold packing G(M_f,M_s) are required. In Roh et al. (2004), it is shown that the beamforming matrix can be parameterized by independent unit vectors. This implies that quantizing the matrix jointly is equivalent to quantizing the vectors separately. Firsts we show that the distributions of the unit vectors are isotropic on unit spheres. Secondly, a low-complexity, scalable quantization scheme is derived. The key innovation lies in the quantization of the large dimension unit vectors. Each large dimension unit vector is partitioned into smaller dimension vectors and quantized by small size codebooks designed for low dimension unit vectors, and the partition itself is quantized by a 3-bit codebook. Finally, an interpolation scheme is proposed for beamforming matrixes downsampled in frequency domain, which significantly reduces overhead for MIMO-OFDM systems. The missing beamforming vectors are interpolated along the geodesic connecting two fed back vectors on a unit sphere. Simulations demonstrate that the overhead in IEEE 802.16d/e draft can be reduced by a factor of three using the proposed scheme.