The Amplify-and-Forward Half-Duplex Cooperative System: Pairwise Error Probability and Precoder Design

In this paper, an exact asymptotic pairwise error probability (PEP) is derived for a half-duplex cooperative system employing an amplify-and-forward (AF) protocol. When compared with the PEP of a traditional multiple-input multiple-output (MIMO) system, the "diversity gain" for the coopera...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 55; no. 2; pp. 605 - 617
Main Authors: Yanwu Ding, Jian-Kang Zhang, Wong, K.M.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.02.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Amplification
Amplify-and-forward (AF)
Applied sciences
Asymptotic properties
Codes
Coding
Coding, codes
cooperative system
Cooperative systems
Design engineering
diversity gain function
Diversity methods
Errors
Exact sciences and technology
Gain
half-duplex
Information, signal and communications theory
Mathematical analysis
MIMO
Mobile antennas
Multiplexing
Optimization
Pairwise error probability
precoder
Protocols
Receiving antennas
Relays
Signal and communications theory
Signal to noise ratio
Telecommunications and information theory
Transmitting antennas
Performance evaluation
Multiplexing
MIMO system
Error probability
Logarithmic function
Amplify-and-forward (AF)
Cooperative systems
precoder
Exponential function
half-duplex
Simulation
Coding
cooperative system
Autocorrelation
diversity gain function
Signal to noise ratio
pairwise error probability
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Description
Summary:In this paper, an exact asymptotic pairwise error probability (PEP) is derived for a half-duplex cooperative system employing an amplify-and-forward (AF) protocol. When compared with the PEP of a traditional multiple-input multiple-output (MIMO) system, the "diversity gain" for the cooperative system is no longer just a simple exponential function of the signal-to-noise ratio (SNR), rather, it involves the logarithm of the SNR. The term diversity gain function is used to designate this characteristic of the PEP. The coding gain, on the other hand, is found similar to that for the MIMO system and is proportional to the determinant of the autocorrelation of the error matrix. Based on our analysis and observations, we propose a design of unitary precoder for the cooperative system to achieve the full diversity gain function. For the case of a 4-QAM signal being transmitted, we further optimize the coding gain and arrive at a closed-form optimum precoder. Simulations indicate that our proposed precoder designs greatly improve the performance of the cooperative system
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2006.885761