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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| Veröffentlicht in: | IEEE transactions on signal processing Jg. 55; H. 2; S. 605 - 617 |
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| Sprache: | Englisch |
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IEEE
01.02.2007
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | 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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| AbstractList | 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 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. 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. |
| Author | Yanwu Ding Wong, K.M. Jian-Kang Zhang |
| Author_xml | – sequence: 1 surname: Yanwu Ding fullname: Yanwu Ding organization: Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, Ont – sequence: 2 surname: Jian-Kang Zhang fullname: Jian-Kang Zhang organization: Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, Ont – sequence: 3 givenname: K.M. surname: Wong fullname: Wong, K.M. organization: Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, Ont |
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| Keywords | 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 |
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| References | jing (ref14) 0 ref10 ref2 ref1 zhang (ref23) 2004 ref17 ref16 giraud (ref19) 1996; 42 ref18 jing (ref13) 0 ref25 ref20 ref22 ref21 murnaghan (ref26) 1962; iii chang (ref12) 2004; 4 ref28 ref27 ref8 ref7 ref9 ref4 ref3 ref6 yang (ref15) 2005 ref5 marcus (ref24) 1977 zhang (ref11) 2003; 49 lebedev (ref29) 1965 |
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| Snippet | In this paper, an exact asymptotic pairwise error probability (PEP) is derived for a half-duplex cooperative system employing an amplify-and-forward (AF)... 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... |
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| SubjectTerms | 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 |
| Title | The Amplify-and-Forward Half-Duplex Cooperative System: Pairwise Error Probability and Precoder Design |
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