Constellation Shaping for OFDM-ISAC Systems: From Theoretical Bounds to Practical Implementation

TL;DR

This paper investigates constellation shaping as a means to simultaneously improve S&C performance in orthogonal frequency division multiplexing (OFDM)-based ISAC systems and demonstrates that constellation shaping enables a flexible trade-off between S&C, can approach the derived upper bound, and significantly outperforms conventional modulation formats.

Abstract

Integrated sensing and communications (ISAC) promises new use cases for mobile communication systems by reusing the communication signal for radar-like sensing. However, sensing and communications (S&C) impose conflicting requirements on the modulation format, resulting in a tradeoff between their corresponding performance. This paper investigates constellation shaping as a means to simultaneously improve S&C performance in orthogonal frequency division multiplexing (OFDM)-based ISAC systems. We begin by deriving how the transmit symbols affect detection performance and derive theoretical lower and upper bounds on the maximum achievable information rate under a given sensing constraint. Using an autoencoder-based optimization, we investigate geometric, probabilistic, and joint constellation shaping, where joint shaping combines both approaches, employing both optimal maximum a-posteriori decoding and practical bit-metric decoding. Our results show that constellation shaping enables a flexible trade-off between S&C, can approach the derived upper bound, and significantly outperforms conventional modulation formats. Motivated by its practical implementation feasibility, we review probabilistic amplitude shaping (PAS) and propose a generalization tailored to ISAC. For this generalization, we propose a low-complexity log-likelihood ratio computation with negligible rate loss. We demonstrate that combining conventional and generalized PAS enables a flexible and low-complexity tradeoff between S&C, closely approaching the performance of joint constellation shaping.

Figures (15)

• Figure 1: Considered ISAC scenario. A base station employs a unified transmit signal with an optimized constellation to communicate with an UE and to sense the environment in a radar-like manner. The objective of the ISAC base station is to transmit data to the UE and to detect a TOI, such as a drone, in the presence of an interfering object like a building. Constellation shaping enables a flexible trade-off between communication throughput and detection probability of potential targets, and it improves both simultaneously compared with legacy modulation formats.
• Figure 2: Block diagram of the considered monostatic OFDM-ISAC system. The unified ISAC signal is employed for achieving both SC tasks.
• Figure 3: PDF of the noise at the input of the target detector, i.e., at the output of the IFFT assuming a 16.0-QAM and a sensing SNR of 20dB in a single target scenario for various numbers of sub-carriers.
• Figure 4: Proposed AE framework to shape constellations for ISAC. The trainable parameters are marked in orange and their normalization in gray.
• Figure 5: Encoding structure of conventional PAS, based on bocherer_bandwidth_2015buchali_rate_2016, and the proposed generalized PAS. In both schemes, a distribution matcher (DM) generates shaped amplitudes, while sign or phase bits are derived from a combination of uniformly distributed parity bits $\boldsymbol{P}_{\text{FEC}}$ and information bits. In conventional PAS, a single sign bit modulates the sign of real-valued ASK symbols, requiring two parallel encoders for the real and imaginary parts. In generalized PAS, multiple phase bits are mapped to discrete phases, directly generating complex-valued, circularly symmetric constellations. The generalization preserves the advantages of the original scheme while enhancing sensing performance.