Error Probability Minimization for Short-Packet Backscatter Communications

Most of Internet of Things (IoT) applications are relying on short packet communications (SPC), while the error probability (EP) of SPC in backscatter communications (Back-Com) has not been sufficiently investigated. Motivated by this, in this work, we minimize the overall EP for a short-packet BackCom network, where multiple sensors sequentially modulate their short-packet information on the energy signal transmitted by the energy source and then backscatter the modulated signal to the receiver. Specifically, we formulate a non-convex mixed integer nonlinear programming problem that minimizes the overall EP by jointly optimizing the short-packet blocklength and power reflection coefficient (PRC) of each sensor. To address it, we derive the expression of the optimal PRC at each sensor in a closed form. Substituting the optimal PRC into the formulated problem, the problem can be transformed into two subproblems that are proved to be convex. Then the optimal blocklength is determined by that of the subproblem that achieves a lower EP. Simulation results show that our proposed scheme outperforms the benchmark schemes in terms of the overall EP.