Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems
IEEE Transactions on Signal Processing
Performance limits of coded diversity methods for transmitter antenna arrays
IEEE Transactions on Information Theory
Space-time transmit precoding with imperfect feedback
IEEE Transactions on Information Theory
On beamforming with finite rate feedback in multiple-antenna systems
IEEE Transactions on Information Theory
Grassmannian beamforming for multiple-input multiple-output wireless systems
IEEE Transactions on Information Theory
Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels
IEEE Journal on Selected Areas in Communications
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We design precoding codebooks for the situation when the spatial correlation is not known at the transmitter, but its distribution is. The optimum codebooks combine features of Grassmannian precoding, optimum in the limit of spatially i.i.d. channels, and equatorial precoding, where all antennas transmit the same power. Parametrizable families of codebooks interpolating between these two are considered. The optimum choice of parameter depends on the distribution of spatial correlations. In the case of two transmit antennas, the interpolation is between sphere packings in 2D and sphere packings in 1D, and the codebooks can be understood as the vertices of deformed Platonic solids.