Optimal Transmission of Short-Packet Communications in Multiple-Input Single-Output Systems

We design the optimal transmission strategy, which maximizes the average achievable data rate of the multiple-input single-output system that adopts short-packet communications. In this system, the <inline-formula><tex-math notation="LaTeX">$N_{A}$</tex-math></inline-formula>-antenna access point (AP) transmits to the single-antenna user with finite blocklength <inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula> after estimating the AP-user channel via downlink training and uplink feedback. For this system, we determine the optimal allocation of the finite resource (e.g., the total transmit power and a finite number of symbol periods) for downlink training, uplink feedback, and data transmission to maximize the average data rate. Specifically, we derive an approximate closed-form lower bound on the average data rate, an explicit result for the optimal number of symbol periods for downlink training, an easy-to-implement method to find the optimal number of symbol periods for uplink feedback, and a simple expression for the optimal power allocation between data transmission and downlink training. By using numerical results, we demonstrate the effectiveness of our analytical solutions and examine the impact of system parameters, e.g., <inline-formula><tex-math notation="LaTeX">$N_{A}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$T$</tex-math></inline-formula>, on the optimal strategy.