The effect of finite rate feedback on CDMA signature optimization and MIMO beamforming vector selection

Authors:
Wei Dai;Youjian Liu;Brian Rider
Affiliations:
Department of Electrical and Computer Engineering, University of Illinois, Urbana, IL;Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO;Mathematics Department, University of Colorado, Boulder, CO
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

We analyze the effect of finite rate feedback on code-division multiple-access (CDMA) signature optimization and multiple-input multiple-output (MIMO) beamforming vector selection. In CDMA signature optimization, for a particular user, the receiver selects a signature vector from a codebook to best avoid interference from other users, and then feeds the corresponding index back to the specified user. For MIMO beamforming vector selection, the receiver chooses a beamforming vector from a given codebook to maximize the instantaneous information rate, and feeds back the corresponding index to the transmitter. These two problems are dual: both can be modeled as selecting a unit norm vector from a finite size codebook to "match" a randomly generated Gaussian matrix. Assuming that the feedback link is rate limited, our main result is an exact asymptotic performance formula where the length of the signature/beamforming vector, the dimensions of interference/channel matrix, and the feedback rate approach infinity with constant ratios. The proof rests on the large deviations of the underlying random matrix ensemble. Further, we show that random codebooks generated from the isotropic distribution are asymptotically optimal not only on average, but also in probability.