Optimizing DFT-s-OFDM Waveform for ISAC: A Probabilistic Constellation Shaping Approach

Integrated sensing and communications (ISAC) has emerged as a promising paradigm for future wireless networks. Against this background, this paper proposes a probabilistic constellation shaping (PCS) framework for discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM)-based ISAC systems. We first derive a closed-form ambiguity function (AF) of DFT-s-OFDM waveforms, which reveals a direct relationship between velocity estimation accuracy and the constellation's kurtosis. We formulate the PCS design as an optimization problem that maximizes communication throughput while constraining the kurtosis to explicitly control sensing performance. For nonlinear channels with power amplifier distortion, a surrogate-assisted evolutionary algorithm is proposed, which efficiently identifies the Pareto-optimal front with low computational complexity. Simulations demonstrate that our framework achieves a superior and highly tunable performance trade-off compared to conventional uniform constellations.