Joint optimization for throughput maximization in underwater acoustic networks with energy harvesting

Abstract

Since autonomous underwater vehicles (AUVs) are increasing popular in maritime applications, underwater wireless communication with multiple users is becoming more important and practical. In this paper, we investigate the resource allocation in underwater acoustic networks (UAN) with time division multiple access (TDMA) technique. When the uncertain channel state information (CSI) derived from the movement of AUVs in underwater environment is considered, probability constraints are introduced to guarantee the quality of service (QoS). A joint optimization algorithm is proposed, in order to schedule time for energy harvesting (EH) and wireless information transfer (WIT); the proposed algorithm also allocates transmit power to multiple AUVs to maximize the sum-throughput over a time period. The constraints of outage probability and available energy are both considered. The probability constraint is first transformed into an equivalent formulation. Furthermore, an approach with low computational complexity is proposed for power allocation and time assignment based on the residual energy of the buoy. In extensive simulation experiments, the proposed algorithm shows significant throughput increases in long term compared to baseline schemes, and better performance in terms of convergence and energy efficiency (EE) can be achieved.

Appendix

Proof of Theorem 1

We first assume that (x₁, x₂,...,x_n) is the maximum of $\sum \limits _{i=1}^{n}f_{i}(x_{i})$ while (19) is not satisfied, i.e. (29) holds.

$$ \begin{array}{@{}rcl@{}} \frac{1}{x_{j}+F_{j}}\neq\frac{1}{x_{k}+F_{k}}. \end{array} $$

(29)

When the constraint $\sum\limits _{i=1}^{n}x_{i}=C$ is considered, $x_{j}^{\prime }=x_{j}+\theta$ and $x_{k}^{\prime }=x_{k}-\theta$ are assumed, where 𝜃 is a constant with tiny value and i≠j. We can obtain the following,

$$ \begin{array}{@{}rcl@{}} &&\ln(1+x_{j}^{\prime}/F_{j})+\ln(1+x_{k}^{\prime}/F_{k})\\&&=\ln(1+x_{j}/F_{j})+\ln(1+x_{k}/F_{k})\\&&\quad-\theta(\frac{1}{x_{j}+F_{j}}-\frac{1}{x_{k}+F_{k}}). \end{array} $$

(30)

According to Eq. 30, it can be found that $\ln (1+x_{j}^{\prime }/F_{j})+\ln (1+x_{k}^{\prime }/F_{k})\neq \ln (1+x_{j}/F_{j})+\ln (1+x_{k}/F_{k})$; hence the value of $\sum\limits _{i=1}^{n}f_{i}(x_{i})$ can be changed by adding 𝜃 to x_j. In other words, (x₁, x₂,⋯ ,x_n) is not the optimum of $\sum\limits _{i=1}^{n}f_{i}(x_{i})$ if Eq. 29 is true. Therefore, Theorem 1 is proved. □