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

Benedikt Geiger, Fan Liu, Shihang Lu, Andrej Rode, Daniel Gil Gaviria, Charlotte Muth, and Laurent Schmalen

In OFDM-ISAC systems, the sensing performance (detection probability) depends on the kurtosis (fourth moment) of the transmit constellation. This repository provides a MATLAB implementation for the numerical evaluation of upper and lower bounds on the achievable mutual information of complex-valued signaling under power and kurtosis constraints.

The code computes:

• Lagrange multipliers of the maximum-entropy distribution subject to moment constraints,
• the resulting input and output entropies,
• and corresponding upper and lower mutual-information bounds as a function of the kurtosis constraint. The implemented numerical procedures correspond to (23)–(32) in [1]

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Requirements

• MATLAB R2022b or later (tested with R2023b)
• Optimization Toolbox (for fzero and fsolve)

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Reference

[1] B. Geiger, F. Liu, S. Lu, A. Rode, D. Gil Gaviria, C. Muth, and L. Schmalen, “Constellation shaping for OFDM-ISAC systems: From theoretical bounds to practical implementation”, submitted to IEEE TCOM, 2025. arXiv:2509.04055