Constellation Design for Integrated Sensing and Communication with Random Waveforms

Integrated sensing and communication (ISAC) is considered one of the key technologies for next-generation wireless communication. To achieve satisfactory communication and sensing performance simultaneously, it is necessary to maximize compatibility with the existing communication waveform. In this paper, we mainly investigate the ISAC constellation design based on communication waveforms (random waveforms). Firstly, we derive the modulated waveform with constant modulus has a smaller side lobe of periodic auto-correlation function (PACF), i.e., the modulated waveform with constant modulus is more suitable for sensing. To improve the sensing performance of the modulated waveform with non-constant modulus, we propose a ISAC constellation design method based on probabilistic constellation shaping (PCS), which designs the power spectrum of the modulated waveform by adjusting the probabilities of constellation points, thereby reducing the side lobe of PACF. In addition, we design a joint optimization problem between the weighted variance of normalized energy and the communication information entropy (CIE) to obtain the tradeoff between communication and sensing. Finally, we simulate the communication performance and sensing performance of the reshaped waveform, and obtain some interesting conclusions. The simulation results show that, for the modulated waveform with non-constant modulus, the proposed method can reduce the side lobe of PACF, and increase the probability of detection (Pd), along with a minimal loss for CIE and a tiny growth for bit error rate (BER). This work is helpful for the theoretical exploration and system design for ISAC.