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Resource optimization for dual-hop device to device networks

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Abstract

In this paper, we consider an orthogonal frequency division multiplexing based device to device network. The communication between source and destination is facilitated by a dual-hop transmission under amplify and forward relaying protocol. The sum throughput of the system is maximized with joint optimization over power allocation at each transmitting node and sub-carrier pairing over two hops. A dual decomposition based solution is proposed subject to separate transmit power constraint at each node. Simulation results are presented to validate the performance of the proposed algorithm where the results are compared with the existing works in literature as well as with a sub-optimal power optimization solution.

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Notes

  1. The data received at relay over a particular carrier can be forwarded over the same or a different sub-carrier.

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Author information

Authors and Affiliations

  1. Transmission Department, Pakistan Telecommunication Company Limited, Islamabad, 44000, Pakistan

    Muhammad Afaq Ahmad

  2. Department of Electrical Engineering, Bahria University, Islamabad, Pakistan

    Muhammad Waqas

  3. KCC Engineering And Contracting Company, North Subhan, Kuwait

    Waleed Ahmad Khan

  4. Department of Electrical Engineering, COMSATS Institute of Information Technology, Islamabad, Pakistan

    Zain Ali & Guftaar Ahmad Sardar Sidhu

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  1. Muhammad Afaq Ahmad
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  2. Muhammad Waqas
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  3. Waleed Ahmad Khan
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  4. Zain Ali
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  5. Guftaar Ahmad Sardar Sidhu
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Correspondence to Guftaar Ahmad Sardar Sidhu.

Appendix

Appendix

$$\begin{aligned}&p_k^4\Psi _{1}-p_k^3\Omega _{1}\!+p_k^2(\Phi _{1,1}\!+\Phi _{1,2})\!+p_k(\Gamma _{1,1}\!+\Gamma _{1,2})\!+\Theta _{1}\!=0. \nonumber \\&\text {where:}\nonumber \\&\Psi _{1}=-\lambda (a_kq_kb_k^2+b_k^2)(y_k^2+2q_ku_ky_k+q_k^2u_k^2).\nonumber \\&\Omega _{1}=\lambda (y_k^2+2q_ku_ky_k+q_k^2u_k^2)(a_k^2q_k^2b_k+2a_kq_kb_k)+\lambda (a_kq_kb_k^2\nonumber \\&\quad +\!b_k^2)(2y_kq_kz_k+2q_k^2z_ku_k+y_kx_k+2y_kv_k+2q_ku_kv_k+q_ku_kx_k).\nonumber \\&\Phi _{1,1}=(A_kq_k^2y_k^2+2A_kq_k^3u_ky_k+q_k^4u_k^2A_k)\!-\!(B_ka_kq_kb_k^2 +B_k\nonumber \\&b_k^2+a_kq_k^2u_kb_k^2x_k+q_ku_kb_k^2x_k).\nonumber \\ {}&\Phi _{1,2}=-\lambda (y_k^2+2q_ku_ky_k+q_k^2u_k^2)(a_k^2q_k^2)-\lambda (2y_kq_kz_k+2q_k^2\nonumber \\ {}&u_kz_k+y_kx_k+2y_kv_k+2q_ku_kv_k+q_ku_kx_k)(a_k^2q_k^2b_k+2a_kq_kb_k)\nonumber \\&\quad -\lambda (q_k^2z_k^2+x_kq_kz_k+2v_kq_kz_k+v_k^2+v_kx_k)(a_kq_kb_k^2+b_k^2).\nonumber \\&\Gamma _{1,1}=(2A_kq_k^3y_kz_k +2A_kq_k^4u_kz_k+A_kq_k^2y_kx_k+2A_kq_k^2y_kv_k\nonumber \\&\quad +2A_kq_k^3u_kv_k+A_kq_k^3u_kx_k)+(B_ka_k^2q_k^2b_k+2a_kq_kb_kB_k+\nonumber \\ {}&a_k^2u_kq_k^3b_kx_k+ 2a_ku_kq_k^2b_kx_k).\nonumber \\&\Gamma _{1,2}=-(a_k^2q_k^2\lambda )(2y_kq_kz_k+2q_k^2u_kz_k+y_kx_k+2y_kv_k+2q_k\nonumber \\&u_kv_k+q_ku_kx_k)-\lambda (a_k^2q_k^2b_k+2a_kq_kb_k)(q_k^2z_k^2+x_kq_kz_k+\nonumber \\&2v_kq_kz_k+v_k^2+v_kx_k).\nonumber \\&\Theta _{1}=(A_kq_k^3z_k^2+A_kq_k^3x_kz_k+2A_kq_k^3b_kz_k+A_kq_k^2b_k^2+A_kq_k^2\nonumber \\&v_kx_k(B_ka_k^2q_k^2+a_k^2u_kq_k^3x_k) -(\lambda a_k^2q_k^2)(q_k^2z_k^2+x_kq_kz_k+2v_k\nonumber \\&q_kz_k+v_k^2+v_kx_k). \end{aligned}$$
(25)

and

$$\begin{aligned}&q^4_k\Psi _{2}+q_k^3\Omega _{2}+q_k^2(\Phi _{2,1}+\Phi _{2,2})+q_k(\Gamma _{2,1}+\Gamma _{2,2})+\Theta _{2}=0. \end{aligned}$$
(26)
$$\begin{aligned}&\text {with:}\nonumber \\&\Psi _{2}=-\beta (z_k^2+2p_ku_kz_k+p_k^2u_k^2)(a_k^2b_kp_k+a_k^2).\nonumber \\&\Omega _{2}\!=\!-\beta (z_k^2+2p_ku_kz_k+p_k^2u_k^2)(a_kb_k^2p_k^2\!+2a_kb_kp_k)\!\!-\!\beta (2p_ky_k\nonumber \\&z_k\!\!+z_kx_k\!+ 2z_kv_k\!+2p_k^2y_ku_k\!+\!2p_ku_kv_k\nonumber \\&\quad +\,p_ku_kx_k)(a_k^2b_kp_k\!+\!a_k^2).\nonumber \\&\Phi _{2,1}\!\!=\!(X_kp_k^2z_k^2\!+2X_kp_k^3u_kz_k\!+X_kp_k^4u_k^2)\!-\!(a_k^2b_kp_kY_k+Y_ka_k^2\nonumber \\&\quad +\!a_k^2b_ku_kx_kp_k^2+p_ku_kx_ka_k^2)\!-\!(\beta b_k^2p_k^2)(z_k^2+2p_ku_kz_k+p_k^2u_k^2).\nonumber \\&\Phi _{2,2}\!=\!-\beta (2p_ky_kz_k+z_kx_k+2z_kv_k+2p_k^2y_ku_k+2p_ku_kv_k+\nonumber \\&p_ku_kx_k)(a_kb_k^2p_k^2+2a_kb_kp_k)\!- \!\beta (a_k^2b_kp_k+a_k^2)(p_k^2y_k^2\nonumber \\&\quad +p_ky_kx_k +2p_ky_kv_k+v_kx_k+v_k^2).\nonumber \\&\Gamma _{2,1}=(2X_kp_k^3y_kz_k+Xp_k^2z_kx_k+2X_k p_k^2z_kv_k+2X_kp_k^3\nonumber \\&y_ku_k+2X_kp_k^3u_kv_k+X_kp_k^3u_kx_k)-(a_kb_k^2p_k^2Y_k+2a_kb_kp_k\nonumber \\&Y_k+a_kb_k^2u_kx_kp_k^3+2a_kb_ku_kx_kp_k^2).\nonumber \\&\Gamma _{2,2}=-\beta (b_k^2p_k^2)(2p_ky_kz_k+z_kx_k+2z_kv_k+2p_k^2y_ku_k+2p_k\nonumber \\&u_kv_k+p_ku_kx_k)-\beta (a_kb_k^2p_k^2+2a_kb_kp_k) (p_k^2y_k^2+p_ky_kx_k+\nonumber \\&2p_ky_kv_k+v_kx_k+v_k^2).\nonumber \\&\Theta _{2}=(X_kp_k^4y_k^2+X_kp_k^3y_kx_k+2X_kp_k^3y_kv_k+X_kp_k^2v_kx_k+\nonumber \\&X_kp_k^2v_k^2)-(Y_kb_k^2p_k^2+p_k^3u_kx_kb_k^2)\!-\!\beta (b_k^2p_k^2)(p_k^2y_k^2+p_ky_k x_k\nonumber \\&\quad +2p_ky_kv_k+v_kx_k+v_k^2). \end{aligned}$$
(27)

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Ahmad, M.A., Waqas, M., Khan, W.A. et al. Resource optimization for dual-hop device to device networks. Telecommun Syst 69, 273–283 (2018). https://doi.org/10.1007/s11235-018-0439-z

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