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Energy efficiency optimization of one-way and two-way DF relaying considering circuit power

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Abstract

In this paper, the energy efficiency (EE) of a decode and forward (DF) relay system is studied, where two sources communicate through a half-duplex relay node in one-way and two-way relaying strategies. Both the circuitry power and the transmission power of all nodes are taken into consideration. In addition, three different coding schemes for two-way DF relaying strategy with two phases and two-way DF relaying with three phases are considered. The aim is to maximize the EE of the system for a constant spectral efficiency (SE). For this purpose, the transmission time and the transmission power of each node are optimized. Simulations are used to compare the EE–SE curve of different DF strategies with one-way and two-way amplify and forward (AF) strategies and direct transmission (DT), to find the best energy efficient strategy in different SE conditions. Analytical and simulation results demonstrate that in low SE conditions, DF relaying strategies are more energy efficient compared to that of AF strategies and DT. However, in high SE conditions, the EE of two-way AF relaying and DT strategy outperform some of the DF relaying strategies. In simulations, the impact of different circuitry power and different channel conditions on the EE–SE curves are also investigated.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Mohammad Hossein Chinaei, Mohammad Javad Omidi, Jafar Kazemi & Foroogh Sadat Tabataba

Authors
  1. Mohammad Hossein Chinaei
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  2. Mohammad Javad Omidi
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  3. Jafar Kazemi
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  4. Foroogh Sadat Tabataba
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Corresponding author

Correspondence to Mohammad Hossein Chinaei.

Appendix

Appendix

In this Appendix, it is explained how (30) can be written as (31) in details. We consider two possible states to clear the proof:

  1. 1.

    If \((2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)/\left| {h_{2} } \right|^{2} \ge (2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)/\left| {h_{1} } \right|^{2}\):

With this assumption (30) is written as:

$$P_{s1\hbox{min} }^{T} + P_{r\hbox{min} }^{T} + P_{s2\hbox{min} }^{T} \ge \frac{{(2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)N_{0} }}{{\left| {h_{1} } \right|^{2} }} + \frac{{(2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)N_{0} }}{{\left| {h_{2} } \right|^{2} }} + \frac{{\left| {h_{1} } \right|^{2} (2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)N_{0} }}{{\left| {h_{2} } \right|^{4} }}.$$
(68)

If we substitute the assumption \(\left| {h_{1} } \right|^{2} /\left| {h_{2} } \right|^{2} \ge (2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)/(2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)\) in (68), the minimum summation of the transmission powers is derived as (31).

  1. 2.

    if \((2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)/\left| {h_{2} } \right|^{2} \le (2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)/\left| {h_{1} } \right|^{2}\):

With this assumption (30) is written as:

$$P_{s1\hbox{min} }^{t} + P_{r\hbox{min} }^{t} + P_{s2\hbox{min} }^{t} \ge \frac{{\left| {h_{2} } \right|^{2} (2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)N_{0} }}{{\left| {h_{1} } \right|^{4} }} + \frac{{(2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)N_{0} }}{{\left| {h_{1} } \right|^{2} }} + \frac{{(2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)N_{0} }}{{\left| {h_{2} } \right|^{2} }}.$$
(69)

If we substitute the assumption \(\left| {h_{2} } \right|^{2} /\left| {h_{1} } \right|^{2} \ge (2^{{\frac{{2B_{1} }}{{WT_{TWUB} }}}} - 1)/(2^{{\frac{{2B_{2} }}{{WT_{TWUB} }}}} - 1)\) in (69), the minimum summation of the transmission powers is obtained as (31).

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Chinaei, M.H., Omidi, M.J., Kazemi, J. et al. Energy efficiency optimization of one-way and two-way DF relaying considering circuit power. Wireless Netw 22, 367–381 (2016). https://doi.org/10.1007/s11276-015-0972-6

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