Two-Timescale Cross-Layer Design for URLLC Over Parallel Fading Channels With Imperfect CSI

This paper investigates the cross-layer design for point-to-point ultra-reliable low latency communication (URLLC) over parallel fading sub-channels by jointly considering channel estimation and adaptive data transmission. The model includes a stochastic traffic arrival process and the transmissions are done in the finite blocklength (FBL) regime with imperfect channel state information (CSI). Specifically, we formulate a two-timescale total average power minimization problem under reliability, latency, and peak power constraints. In the large timescale, the pilot length and pilot power are optimized while in the small timescale, the data transmit power and decoding error probability are optimized according to the estimated channel coefficients and queueing information. As a starting step in our small timescale solution, we train a deep reinforcement learning (DRL) agent employing the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm to allocate the data transmit power on each sub-channel and determine the decoding error probability to satisfy the URLLC constraints in an ideal environment with perfect instantaneous CSI. Then we utilize a water-filling framework to accommodate the trained TD3 network for the environment with imperfect CSI. Based on the small timescale optimization method, we adopt the ternary search algorithm to optimize the pilot length and pilot power through Monte Carlo evaluations in the large timescale. Simulation results are provided to reveal the impact of the reliability, latency and the number of sub-channels. Furthermore, the trained network is demonstrated to be robust towards different traffic arrival models, as well as variations of the average arrival rate.