Reshaping the ISAC Tradeoff Under OFDM Signaling: A Probabilistic Constellation Shaping Approach

• Published in: IEEE transactions on signal processing Vol. 72; pp. 4782 - 4797
• Main Authors: Du, Zhen, Liu, Fan, Xiong, Yifeng, Han, Tony Xiao, Eldar, Yonina C., Jin, Shi
• Format: Journal Article
• Language: English
• Published: New York IEEE 2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; ambiguity function; Communication; Communication symbols; Constellations; Fans; Heuristic methods; Integrated sensing and communication; Integrated sensing and communications; OFDM; Optimization models; Orthogonal Frequency Division Multiplexing; Phase shift keying; probabilistic constellation shaping; Probabilistic logic; Probability theory; Quadrature amplitude modulation; Sidelobes; Statistical analysis; Target detection; Tradeoffs; Waveforms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2024.3465499

Integrated sensing and communications is regarded as a key enabling technology in the sixth generation networks, where a unified waveform, such as orthogonal frequency division multiplexing (OFDM) signal, is adopted to facilitate both sensing and communications (S&C). However, the random communication data embedded in the OFDM signal results in severe variability in the sidelobes of its ambiguity function (AF), which leads to missed detection of weak targets and false detection of ghost targets, thereby impairing the sensing performance. Therefore, balancing between preserving communication capability (i.e., the randomness) while improving sensing performance remains a challenging task. To cope with this issue, we characterize the random AF of OFDM communication signals, and demonstrate that the AF variance is determined by the fourth-moment of the constellation amplitudes. Subsequently, we propose an optimal probabilistic constellation shaping (PCS) approach by maximizing the achievable information rate (AIR) under the fourth-moment, power and probability constraints, where the optimal input distribution may be numerically specified through a modified Blahut-Arimoto algorithm. To reduce the computational overheads, we further propose a heuristic PCS approach by actively controlling the value of the fourth-moment, without involving the communication metric in the optimization model, despite that the AIR is passively scaled with the variation of the input distribution. Numerical results show that both approaches strike a scalable performance tradeoff between S&C, where the superiority of the PCS-enabled constellations over conventional uniform constellations is also verified. Notably, the heuristic approach achieves very close performance to the optimal counterpart, at a much lower computational complexity.