  In this paper, we study the throughput utility functions in buffer-equipped
monostatic backscatter communication networks with multi-antenna Readers. In
the considered model, the backscatter nodes (BNs) store the data in their
buffers before transmission to the Reader. We investigate three utility
functions, namely, the sum, the proportional and the common throughput. We
design online admission policies, corresponding to each utility function, to
determine how much data can be admitted in the buffers. Moreover, we propose an
online data link control policy for jointly controlling the transmit and
receive beamforming vectors as well as the reflection coefficients of the BNs.
The proposed policies for data admission and data link control jointly optimize
the throughput utility, while stabilizing the buffers. We adopt the
min-drift-plus-penalty (MDPP) method in designing the control policies.
Following the MDPP method, we cast the optimal data link control and the data
admission policies as solutions of two independent optimization problems which
should be solved in each time slot. The optimization problem corresponding to
the data link control is non-convex and does not have a trivial solution. Using
Lagrangian dual and quadratic transforms, we find a closed-form iterative
solution. Finally, we use the results on the achievable rates of finite
blocklength codes to study the system performance in the cases with short
packets. As demonstrated, the proposed policies achieve optimal utility and
stabilize the data buffers in the BNs.
