  This paper considers an ambient backscatter communication (AmBC) network in
which a full-duplex access point (FAP) simultaneously transmits downlink
orthogonal frequency division multiplexing (OFDM) signals to its legacy user
(LU) and receives uplink signals backscattered from multiple BDs in a
time-division-multiple-access manner. To maximize the system throughput and
ensure fairness, we aim to maximize the minimum throughput among all BDs by
jointly optimizing the backscatter time and reflection coefficients of the BDs,
and the FAP's subcarrier power allocation, subject to the LU's throughput
constraint, the BDs' harvested-energy constraints, and other practical
constraints. For the case with a single BD, we obtain closed-form solutions and
propose an efficient algorithm by using the Lagrange duality method. For the
general case with multiple BDs, we propose an iterative algorithm by leveraging
the block coordinated decent and successive convex optimization techniques. We
further show the convergence performances of the proposed algorithms and
analyze their complexities. In addition, we study the throughput region which
characterizes the Pareto-optimal throughput trade-offs among all BDs. Finally,
extensive simulation results show that the proposed joint design achieves
significant throughput gain as compared to the benchmark schemes.
