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On Beamforming with Finite Rate Feedback in Multiple Antenna Systems (2003)
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BibTeX
@MISC{Mukkavilli03onbeamforming,
author = {Krishna Kiran Mukkavilli and Ashutosh Sabharwal and Elza Erkip and Behnaam Aazhang},
title = {On Beamforming with Finite Rate Feedback in Multiple Antenna Systems},
year = {2003}
}
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Abstract
In this paper, 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 , 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 2-dimensional subspaces in a 2t-dimensional real Grassmannian manifold with chordal distance as the metric.
Keyphrases
multiple antenna system finite rate feedback good beamformers design criterion quantized information unitary space time code good packing outage performance certain condition feedback bit 2-dimensional subspace maximum inner product beamforming vector instantaneous channel realization concise characterization outage probability beamformer codebook transmit antenna perfect information case feedback information chordal distance 2t-dimensional real grassmannian manifold additional bit finite set finite information system geometrical bounding technique
