Achievable Rate Maximization for Multi-Antenna WPT Enabled Symbiotic Communication Network

In this work, we study a multi-antenna wireless power transfer (WPT) empowered symbiotic Internet of Things (IoT), where a passive user functions as a relay to assist the short packet transmission from the source to the obstructed user, operating under the ‘harvest-then-forward’ regime. Considering the dual demands of high reliability and high data rates, we formulate a problem aimed at maximizing the minimum achievable rate while bounding the transmission error probability in a two-hop scenario. This is achieved by jointly optimizing the multi-antenna sinewave for WPT, power for wireless information transfer (WIT) and determining the blocklength for both WPT and WIT. Nevertheless, the formulated problem is a challenging nonconvex one due to the practical nonlinear energy harvesting (EH) model, finite blocklength performance (FBL) model, and the intricate interdependencies among the variables involved. To address this issue, we establish subproblems for sinewave design and blocklength allocation, with equivalent solutions that align with the original problem. In particular, we derive an optimal closed-form solution to the optimal multi-antenna waveform amplitude design for harvested power maximization while practically taking the nonlinear EH process and the constraint of single antenna power limit into account. For the nonconvex blocklength optimization subproblem, we for the first time prove the joint concavity of the achievable rate with respect to signal-to-noise ratio (SNR) and blocklength. By introducing slack variables and employing successive convex approximation (SCA) method, we convert the original nonconvex problem into a series of local convex problems, which enables an efficient iterative suboptimal solution. Finally, via simulations, we validate our analytical model, evaluate the system performance, and highlight the advantages of our proposed design, including the utilization of multi-antenna for WPT and the corresponding resource allocation design.