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Optimal packet length for wireless communications using reconfigurable intelligent surfaces

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Abstract

Reconfigurable intelligent surfaces (RIS) allow significant throughput enhancement as all reflections have the same phase at the receiver. In this paper, we suggest to optimize packet length for wireless communications using RIS. Two techniques are suggested in order to maximize average or instantaneous throughput. Average throughput maximization requires only the average signal to noise ratio to determine the optimal packet length. The Gradient algorithm is used to maximize the average throughput. Instantaneous throughput maximization requires the instantaneous SNR in order to adapt packet length to channel conditions. We derive in closed form the expression of optimal packet length, maximizing the instantaneous throughput. Our results are valid for any number of reflecting meta-surfaces N of the RIS.

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Authors and Affiliations

  1. King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

    Ghassan Alnwaimi

  2. SUP’COM, Ariana, Tunisia

    Hatem Boujemaa

Authors
  1. Ghassan Alnwaimi
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  2. Hatem Boujemaa
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Correspondence to Ghassan Alnwaimi.

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Appendix A: Second order derivative of throughput with respect to packet length

Appendix A: Second order derivative of throughput with respect to packet length

When RIS is used as a reflector, the second order derivative of throughput with respect to packet length is equal to

$$\begin{aligned} \frac{\partial ^2 ATHR_R^{low}(L)}{\partial L^2}= & {} \frac{-2n_dlog_2(K)}{(L+n_d)^3(1+\alpha )}[1-P_{\Gamma _R}(w_0)]\nonumber \\&+\frac{(L-2n_d)log_2(K)k_1}{(1+\alpha )(L+n_d)^3}p_{\Gamma _R}(w_0)\nonumber \\&-\frac{log_2(K)k_1^2L}{(1+\alpha )(L+n_d)^3}p'_{\Gamma _R}(w_0) \end{aligned}$$
(43)

where \(p'_{\Gamma _R}(x)\) is the derivative of PDF of SNR written as

$$\begin{aligned} p'_{\Gamma _R}(x)\simeq & {} -0.5\sqrt{\frac{N_0}{8\pi E_s\lambda _1\lambda _2\sigma _A^2}}e^{-\frac{\left[ \sqrt{\frac{N_0x}{E_s\lambda _1\lambda _2}} +m_A\right] ^2}{2\sigma _A^2}}\nonumber \\&\left( x^{-1.5} +\frac{N_0}{4E_s\lambda _1\lambda _2\sigma _A^4\sqrt{x}} +\frac{m_A\sqrt{N_0}}{4\sigma _A^4x\sqrt{E_s\lambda _1\lambda _2}}\right) \nonumber \\&-0.5\sqrt{\frac{N_0}{8\pi E_s\lambda _1\lambda _2\sigma _A^2}}e^{-\frac{\left[ \sqrt{\frac{N_0x}{E_s\lambda _1\lambda _2}}-m_A\right] ^2}{2\sigma _A^2}}\nonumber \\&\left( x^{-1.5}+\frac{N_0}{4E_s\lambda _1\lambda _2\sigma _A^4\sqrt{x}}-\frac{m_A\sqrt{N_0}}{4\sigma _A^4x\sqrt{E_s\lambda _1\lambda _2}}\right) \nonumber \\ \end{aligned}$$
(44)

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Alnwaimi, G., Boujemaa, H. Optimal packet length for wireless communications using reconfigurable intelligent surfaces. Telecommun Syst 77, 683–696 (2021). https://doi.org/10.1007/s11235-021-00783-0

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  • DOI: https://doi.org/10.1007/s11235-021-00783-0

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