Accepted to IEEE Trans. on Info Theory, June 2003.
Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input and multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector which often not realizable in practice. In this correspondence, a quantized maximum signal-to-noise ratio (SNR) beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter. Using the distribution of the optimal beamforming vector in independent identically distributed Rayleigh fading matrix channels, the codebook design problem is solved and related to the problem of Grassmannian line packing. The proposed design criterion is flexible enough to allow for side constraints on the codebook vectors. Bounds on the codebook size are derived to guarantee full diversity order. Results on the density of Grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or SNR loss. Monte Carlo simulations are presented that compare the probability of error for different quantization strategies.
Diversity methods, MIMO systems, Rayleigh channels, Grassmannian line packing, limited feedback
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