Abstract
In this paper, we focus on studying the optimal joint relay positioning and power allocation for two serial relays’ transmission. We consider that information exchanges in Rayleigh flat-fading channels between two end-users which have symmetric traffic requirements in terms of the data rate. Multiple serial half-duplex relay nodes are employed to extend the communication coverage and assist the bidirectional communication between two end-users using the analog network coding protocol. With the objective of minimizing the total transmitting energy at the required data rate c, we investigate the optimal relay positioning and power allocation and then propose sub-optimal solutions for a two-serial-relay one-way channel and a two-serial-relay two-way channel due to no close-form optimal solution. Simulation results demonstrate a consistency with our proposed schemes.
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Acknowledgments
This work is financially supported by NSFC No. 61071214.
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Appendices
Optimal Relay Positioning and Power Allocation in One-Way One-Relay Transmission
In one-way transmission between \(R_1\) and \(S_2\) via \(R_2\), the optimization problem on relay positioning and power allocation can be expressed as
Applying KKT conditions into (40), its solution can be obtained as
Therefore,
Let \(\frac{\partial \xi 1_{min}}{\partial d_2}=0\), it is concluded that
By substituting (43) into (41), the transmit power becomes
And the corresponding transmit power at \(R_1, R_2\) and \(S_2\) is respectively obtained as
and
Optimal Relay Positioning and Power Allocation in Two-Way One-Relay Transmission
In two-way data transmission between \(R_1\) and \(S_2\) via \(R_2\), the optimization problem on relay positioning and power allocation can be expressed as
Applying KKT conditions into (46), its solution can be obtained as
Therefore,
Let \(\frac{\partial \xi 3_{min}}{\partial d_2}=0\), it is concluded that
By substituting (49) into (47), the transmit power becomes
And the corresponding transmit power at \(R_1, R_2\) and \(S_2\) is respectively obtained as
and
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Zhou, J., Zhu, C., Wang, D. et al. Energy Efficient Relay Positioning and Power Allocation for Multi-Relay Symmetric Channel with Analog Network Coding. Wireless Pers Commun 84, 2735–2755 (2015). https://doi.org/10.1007/s11277-015-2764-9
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DOI: https://doi.org/10.1007/s11277-015-2764-9