Joint Sensing and Communications in Finite Block-Length Regime

Systems that combine sensing and communication functionalities are gaining interest for several possible applica- tions related to the internet of things (IoT) and the upcoming 6G mobile radio networks. Studies have recently been proposed to find the optimal tradeoff between sensing and communi- cation performance. However, these studies assume continuous transmission and thus consider that the time available for estimation can always be large enough to achieve some desired accuracy. Moreover, in line with this assumption, communication performance is measured via the well-known Shannon capacity, which implicitly assumes indefinitely long error correction codes. However, in the case of short packet transmissions, such as the case in several IoT applications, the above assumption is unrealistic, as the length of the transmitted packet limits that of the error correction code and the observation time for parameter estimation. Therefore, this paper aims at investigating the optimal tradeoff between the data transmission and the target localization capabilities in a finite block-length regime, by making use of some typical metrics of the finite length information theory. In particular, the optimal beamforming, which minimizes the Cram´er Rao bound of target localization, is derived under a constraint over the block error probability for given packet length values.