A Recursion-Based SNR Determination Method for Short Packet Transmission: Analysis and Applications

The short packet transmission (SPT) has gained much attention in recent years. In SPT, the most significant characteristic is that the finite blocklength code (FBC) is adopted. With FBC, the signal-to-noise ratio (SNR) cannot be expressed as an explicit function with respect to the other transmission parameters. This raises the following two problems for the resource allocation in SPTs: (i) The exact value of the SNR is hard to determine, and (ii) The property of SNR w.r.t. the other parameters is hard to analyze, which hinders the efficient optimization of them. To simultaneously tackle these problems, we have developed a recursion method in our prior work. To emphasize the significance of this method, we further analyze the convergence rate of the recursion method and investigate the property of the recursion function in this paper. Specifically, we first analyze the convergence rate of the recursion method, which indicates it can determine the SNR with low complexity. Then, we analyze the property of the recursion function, which facilitates the optimization of the other parameters during the recursion. Finally, we also enumerate some applications for the recursion method. Simulation results indicate that the recursion method converges faster than the other SNR determination methods. Besides, the results also show that the recursion-based methods can almost achieve the optimal solution of the application cases.