Capacity Approximations for a Deterministic MIMO Channel

In this paper, we derive closed form approximations for the capacity of a point-to-point, deterministic Gaussian MIMO communication channel. We focus on the behavior of the inverse eigenvalues of the Gram matrix associated with the gain matrix of the MIMO channel, by considering small variance and l...

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Bibliographic Details
Published in:Advances in electrical and computer engineering 2011-08, Vol.11 (3), p.3-10
Main Authors: MOSKOWITZ, I. S., COTAE, P., KANG, M. H., SAFIER, P. N.
Format: Article
Language:English
Subjects:
channel capacity
MIMO
Telatar conjecture
transmitter optimization
water filling
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Summary:In this paper, we derive closed form approximations for the capacity of a point-to-point, deterministic Gaussian MIMO communication channel. We focus on the behavior of the inverse eigenvalues of the Gram matrix associated with the gain matrix of the MIMO channel, by considering small variance and large power assumptions. We revisit the concept of deterministic MIMO capacity by pointing out that, under transmitter power constraint, the optimal transmit covariance matrix is not necessarily diagonal. We discuss the water filling algorithm for obtaining the optimal eigenvalues of the transmitter covariance matrix, and the water fill level in conjunction with the Karush-Kuhn-Tucker optimality conditions. We revise the Telatar conjecture for the capacity of a non-ergodic channel. We also provide deterministic examples and numerical simulations of the capacity, which are discussed in terms of our mathematical framework.
ISSN:1582-7445
1844-7600
DOI:10.4316/aece.2011.03001