On the Sensing Capacity of Gaussian "Beam-Pointing" Channels with Block Memory and Feedback

Abstract

Driven by the demands of high-frequency wireless communications in 5G and 6G systems (e.g., mmWave, sub-THz), we explore a state-dependent {\em Gaussian beam-pointing} (GBP) channel. In this model, the channel state defines an unknown angle of departure (AoD), which remains constant within each coherence block of $Q$ time slots but changes independently across blocks. The transmitter receives strictly causal feedback which may originate from a radar detection system or explicit feedback from the receiver at the end of each slot and estimates the AoD at the end of each block. To enhance transmission efficiency, we propose a joint communication and sensing scheme. While the communication capacity of the GBP channel has been previously analyzed by the authors, this work focuses on sensing capacity, characterized by the mutual information between the channel state and the feedback conditioned on the transmitted signal. We derive an upper bound using dynamic programming and propose an achievable inner bound on the sensing capacity, both formulated as optimization problems. For the special case of $Q=1$, the proposed transmission scheme achieves the optimal sensing rate and highlights the inherent trade-off between sensing and communication performance.