  Relay-enabled backscatter communication (BC) is an intriguing paradigm to
alleviate energy shortage and improve throughput of Internet-of-Things (IoT)
devices. Most of the existing works focus on the resource allocation that
considered the unequal and continuous time allocation for both source-relay and
relay-destination links. However, the continuous time allocation may be
infeasible since in practice, the time allocation shall be carried out in
integral multiple of the subframe duration unit. In this article, we study a
discrete time scheme from the perspective of frame structure, where one
transmission block is divided into two phases and the linear mapping is
employed as a re-encoding method to determine the number of subframes for both
phases and the power allocation for each subframe in a relay-enabled BC system.
Based on this, we derive an accurate system-throughput expression and formulate
a mixed-integral non-convex optimization problem to maximize the system
throughput by jointly optimizing the power reflection coefficient (PRC) of the
IoT node, the power allocation of the hybrid access point (HAP) and the linear
mapping matrix, and solve it via a three-step approach. Accordingly, we propose
a low complexity iterative algorithm to obtain the throughput
maximization-based resource allocation solution. Numerical results analyze the
performance of our proposed algorithm, verify the superiority of our proposed
scheme, and evaluate the impacts of network parameters on the system
throughput.
