Joint Optimization of the Transmit Covariance and Relay Precoder in General Gaussian Amplify-and-Forward Relay Channels

The maximum data rate that can be achieved by the strictly causal full-duplex amplify-and-forward (AF) scheme in general Gaussian relay channels is achieved by Gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder. This prob...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 59; no. 9; pp. 5331 - 5351
Main Authors: Gohary, Ramy H., Yanikomeroglu, Halim
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Access methods and protocols, osi model
Applied sciences
Asymptotic methods
Codes
Complexity theory
Covariance matrices
Exact sciences and technology
Full-duplex AF relaying
Information theory
Information, signal and communications theory
Joints
KKT conditions
MIMO
Normal distribution
Optimization
Relays
Schur basis
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Teleprocessing networks. Isdn
Transmission and modulation (techniques and equipments)
tridiagonal matrices
Vectors
Performance evaluation
Relaying
Relay
Schur basis
Interlacing
KKT conditions
Gaussian channel
Coding circuit
Transmission protocol
Information rate
Information transmission
Optimization
tridiagonal matrices
Duplex process
Full-duplex AF relaying
Codebook
Relay channel
High power
Covariance
Routing protocols
Causality
Low-power electronics
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:The maximum data rate that can be achieved by the strictly causal full-duplex amplify-and-forward (AF) scheme in general Gaussian relay channels is achieved by Gaussian codebooks and can be cast as the solution of an optimization problem of the input transmit covariance and relay precoder. This problem possesses an intricate nonconvex structure and is hence difficult to solve. To circumvent this difficulty, the relay precoder is assumed to be given and then the Karush-Kuhn-Tucker conditions are used to obtain closed form expressions for the optimal input covariance corresponding to that precoder. These expressions are used to show that subdiagonal precoders suffice to attain the maximum achievable rate of the AF scheme at any source transmit power. In addition to significantly reducing the effort expended in searching for the optimal relay precoder, this observation enables us to find the optimal precoders at low and high source transmit powers. For asymptotically low transmit powers, the optimal relaying mechanism is shown to possess an interlacing structure, thereby resembling half-duplex operation. In contrast, for asymptotically high transmit powers, it is optimal for the relay to be silent. The asymptotic analysis enables us to develop an explicit formulation for a suboptimal precoder that, at intermediate source transmit powers, are shown numerically to outperform asymptotically optimal precoders.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2266656