Cooperative communications with optimal wireless energy harvesting

In this paper, we analyze the performance of cooperative communications with radio frequency energy harvesting (EH). Different relay selection techniques are studied with optimal harvesting duration. The frame with duration T is decomposed in 3 slots. The duration of first slot is αT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha }T$$\end{document}, and it is dedicated for energy harvesting (0<α<1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0<\alpha <1)$$\end{document}. The duration of second and third slots is (1-α)T/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1-\alpha )T/2$$\end{document}. The second and third slots are dedicated to source and relay transmission. When harvesting duration, α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}T, increases, the packet error probability (PEP) decreases since the harvested energy is large. However, the available time for transmission, (1-α)T/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1-\alpha )T/2$$\end{document}, decreases. If harvesting duration is small, the PEP is high due to a low harvested energy. In this paper, we choose the value of harvesting duration to enhance the throughput. The proposed optimal harvesting duration allows up to 4 dB gain with respect to α=1/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =1/3$$\end{document}, i.e., same duration used for EH and source transmission.