On beamforming with finite rate feedback in multiple-antenna systems

We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of be...

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Bibliographic Details
Published in:IEEE transactions on information theory 2003-10, Vol.49 (10), p.2562-2579
Main Authors: Mukkavilli, K.K., Sabharwal, A., Erkip, E., Aazhang, B.
Format: Article
Language:English
Subjects:
Antenna feeds
Antennas
Array signal processing
Base stations
Beamforming
Channels
Criteria
Design engineering
Feedback
Finite element analysis
Information systems
Lower bounds
Mathematical analysis
Outages
Performance gain
Power control
Telephone sets
Transmitters
Transmitting antennas
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Summary:We study a multiple-antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations. Assuming that the transmitter uses the quantized information for beamforming, we derive a universal lower bound on the outage probability for any finite set of beamformers. The universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel. Using the bound, it is shown that finite information systems approach the perfect information case as (t-1)2/sup -B/t-1/, where B is the number of feedback bits and t is the number of transmit antennas. The geometrical bounding technique, used in the proof of the lower bound, also leads to a design criterion for good beamformers, whose outage performance approaches the lower bound. The design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook, and is equivalent to the problem of designing unitary space-time codes under certain conditions. Finally, we show that good beamformers are good packings of two-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2003.817433