Reliability-optimal pilot-assisted transmission for URLLC over non-reciprocal MISO channels: TDD or FDD?

In this paper, we focus on the pilot-assisted transmission design for downlink URLLC over non-reciprocal channels, in which the multi-antenna controller sends mission-critical data signals to a single-antenna actuator. In this system, the prior knowledge of downlink channel state information (CSI) is a prerequisite for reliable data transmission. Generally, the acquisition of downlink CSI is completed either via the uplink pilot measurement exploiting channel reciprocity and time-division duplex (TDD) operation, or via the downlink pilot measurement with quantized feedback and frequency division duplex (FDD) operation. Inspired by this, we aim to investigate how the degree of channel non-reciprocity impacts the transmission reliability of our URLLC system, and the superiority between the TDD mode and FDD mode in terms of transmission reliability maximization. To describe the degree of reliability loss, we derive the closed-form approximations on the transmission error probability of URLLC in TDD and FDD modes, via leveraging the Gauss-Hermite and Gauss-Chebyshev quadrature rules. Following by the theoretical approximations, we demonstrate how to determine the optimal training pilot length and quantized feedback duration that maximize the transmission reliability under given latency constraint. Through numerical results, we validate the accuracy of theoretical approximations derived in this paper, and obtain some meaningful conclusions.