Grassmannian beamforming for multiple-input multiple-output wireless systems

Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming ve...

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Bibliographic Details
Published in:IEEE transactions on information theory 2003-10, Vol.49 (10), p.2735-2747
Main Authors: Love, D.J., Heath, R.W., Strohmer, T.
Format: Article
Language:English
Subjects:
Array signal processing
Beamforming
Channel state information
Channels
Computer simulation
Design engineering
Diversity reception
Feedback
Input output
Mathematical analysis
MIMO
Monte Carlo methods
Optimization
Quantization
Rayleigh channels
Resilience
Signal to noise ratio
Transmitters
Vectors (mathematics)
Wireless networks
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Summary:Transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple-input multiple-output (MIMO) wireless systems. Unfortunately, optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector; both are hard to realize. In this article, 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. By using the distribution of the optimal beamforming vector in independent and 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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.817466