OFDM-ISAC over Data Payloads: MSE Analysis, Constellation Design, and Experimentation
Orthogonal frequency division multiplexing (OFDM) is a key waveform for integrated sensing and communication (ISAC) systems due to its high spectral efficiency and inherent compatibility with modern wireless standards. However, its fundamental estimation-theoretic sensing performance under random data modulation remains largely unexplored. This paper presents a unified and explicit performance analysis of OFDM-based ISAC systems for multi-target range estimation, focusing on the distinct impacts of the modulation constellation on the sensing performance. We develop a comprehensive estimation-theoretic framework to characterize the range estimation mean-square error (MSE) for both matched filtering (MF) and reciprocal filtering (RF) sensing receiver architectures. Our theoretical analysis reveals that in multi-target and clutter-rich environments, the sensing performance of the MF receiver is fundamentally limited by the fourth-order moment (kurtosis) of the constellation, which determines the data-dependent sidelobe interference level. In contrast, the RF receiver eliminates such interference at the cost of noise enhancement, with its performance governed by the inverse second-order moment of the constellation. Building on these closed-form MSE derivations, we propose a sensing-receiver specific geometric constellation shaping (GCS) framework. By jointly optimizing the constellation geometry based on the minimum Euclidean distance (MED) and receiver-dependent sensing metrics, we enable a flexible trade-off between communication reliability and sensing precision. Our results demonstrate that the proposed constellation shaping provides significant performance gains and facilitates a tailored sensing and communication trade-off across different receiver architectures in practical over-the-air implementations.