Unified Waveform Design in Joint Communications and Sensing with Clutters: Shannon or Cramer-Rao?

In joint communications and sensing (JCS), the performance metrics belong to the areas of information theory and estimation theory, respectively. The lack of unified design criterion prohibits gaining intuitions and unifying the mathematical structure in the analysis and design of JCS. This paper endeavors to unify both performance metrics of communications and sensing in either information-theoretic or estimation-theoretic framework. In the information-theoretic framework, the mutual information between the target and received signal, conditioned on the transmitted signal, is maximized while that of clutter and signal is minimized, which is formulated as an optimization problem. For the estimation-theoretic framework, the differential relationship between mutual information and minimum mean square error (MMSE) is leveraged to unify both communications and radar sensing in terms of MMSE. Both criteria are evaluated and compared using numerical simulations.