Sphere Packing Analysis for Performance Trade-off in Joint Communications and Sensing-Part I: General Principle

Joint communications and sensing (JCS) provides an effective approach to enhance the spectral efficiency of wireless systems. When integrating these historically independent functions in the same waveform, both communication and sensing may suffer from performance degradation, thus resulting in a trade-off between their performances. A fundamental question is how to obtain bounds for the communication- sensing trade-off in JCS. In this paper, a geometric approach is adopted, namely evaluating the volume of a feasible waveform set given the tolerable performance degradation of sensing and then bounding the number of possible communication codewords using the sphere packing methodology. In particular, mathematical tools in high-dimensional geometry are leveraged for the volume calculation in the first of this paper. Applications for concrete sensing performance metrics will be left to the second part of the paper.