###### Abstract  
Orthogonal frequency division multiplexing (OFDM) has been regarded as an attractive waveform for integrated sensing and communication (ISAC). However, suffering from its high peak-to-average power ratio (PAPR), sensitivity to phase noise (PN), and spectral efficiency saturation, the performance of OFDM in ISAC is limited. Against this background, this paper proposes a constellation-optimized index-modulated OFDM (CO-IM-OFDM) framework that leverages neural networks to design a constellation suitable for subcarrier activation patterns. A correlation model between index modulation and constellation is established, enabling adaptive constellation mapping in IM-OFDM. Then, Adam optimizer is employed to train the constellation tailored for ISAC, enhancing spectral efficiency under PN and PAPR constraints. Furthermore, a weighting factor is defined to characterize the joint communication-sensing performance, thus optimizing the overall system performance. Simulation results demonstrate that the proposed method can achieve improvements in bit error rate (BER) by over 4 dB and in Cramer-Rao bound (CRB) by 2% to 8% compared to traditional IM-OFDM constellation mapping. It overcomes fixed constellation constraints of conventional IM-OFDM systems, offering theoretical innovation waveform design for low-power communication-sensing systems in highly dynamic environments. IM-OFDM; constellation; deep learning; ISAC  
Li Li  
division multiplexing (IM-OFDM), which represents a dual-functional waveform technology, has shown emerging potential for ISAC applications [9; 10]. In particular, benefiting from its dynamic activation of the subcarrier, IM-OFDM enables low-power transmission [11]. IM-OFDM encodes information not only through conventional quadrature amplitude modulation (QAM) symbols, but also through the indices of activated subcarriers in the frequency domain [12; 13]. While index modulation grants IM-OFDM advantages, including superior energy efficiency, reduced PAPR, and robustness against inter-carrier interference (ICI), the selective subcarrier activation procedure introduces inherent spectral efficiency compromises compared to traditional OFDM [14]. Adaptive constellation design for IM-OFDM can effectively enhance spectral efficiency. For example, the authors in [15] proposed dual-mode OFDM-IM (DM-OFDM-IM), which partitions subcarriers within subblocks into two groups and employs different constellation mappings for each group to improve transmission rates. However, conventional constellations exemplified by phase shift keying (PSK) and QAM induce significant power penalty due to the increased PAPR. To tackle this problem, the authors in [16; 17] proposed distinct constellation pairs to reduce pairwise error probability (PEP) and bit error rate (BER) in DM-OFDM-IM systems. The authors in [18] introduced transmit diversity in IM-OFDM through silent subcarriers and multi-signal constellations, which further improved power efficiency. Nevertheless, existing IM-OFDM constellation designs predominantly employ conventional constellation combinations, which achieve a mild throughput improvement while fundamentally suffering critical limitations of PAPR and PN [19; 20]. Recently, artificial intelligence (AI) has shown significant potential in adaptive constellation generation tailored to IM-OFDM under stringent constraints [21; 22; 23; 24]. In contrast to conventional constellation designs, which are based on the assumptions of ideal Gaussian channels while ignoring the effect of hardware impairments such as nonlinearities of the power amplifier (PA) [25], the AI-enabled constellation design shows the ability to adapt to such impairments. More specifically, with the help of neural networks, the transceiver of wireless communication systems is represented as a specialized neural network capable of learning symbol mapping processes and channel characteristics, thus reconstructing signals with minimal distortion at the receiver [26; 27; 28]. Ref.