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Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form

Hassibi, Babak and Marzetta, Thomas L. (2002) Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form. IEEE Transactions on Information Theory, 48 (6). pp. 1473-1484. ISSN 0018-9448. doi:10.1109/TIT.2002.1003835.

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An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix-having orthonormal columns, and a probability density that is invariant to premultiplication by an independent unitary matrix-plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. We take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for M=min(N, T/2) transmit antennas, where N is the number of receive antennas and T is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna.

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Additional Information:© Copyright 2002 IEEE. Reprinted with permission. Manuscript received March 7, 2001; revised November 2, 2001. [Posted online: 2002-08-07] The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Washington DC, June 2001. The authors would like to thank the editor and reviewers for useful comments that led to the improvement of this paper.
Subject Keywords:Isotropically random (i.r.) unitary matrix, multiple antennas, unitary space–time modulation (USTM), wireless communications
Issue or Number:6
Record Number:CaltechAUTHORS:HASieeetit02b
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6793
Deposited By: Archive Administrator
Deposited On:21 Dec 2006
Last Modified:08 Nov 2021 20:37

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