Title: Revealing the Trade-off in ISAC Systems: The KL Divergence Perspective

Abstract: Integrated sensing and communication (ISAC) is regarded as a promising technique for 6G communication network. In this letter, we investigate the Pareto bound of the ISAC system in terms of a unified Kullback-Leibler (KL) divergence performance metric. We firstly present the relationship between KL divergence and explicit ISAC performance metric, i.e., demodulation error and probability of detection. Thereafter, we investigate the impact of constellation and beamforming design on the Pareto bound via deep learning and semi-definite relaxation (SDR) techniques. Simulation results show the trade-off between sensing and communication performance in terms of bit error rate (BER) and probability of detection under different parameter set-ups.