Abstract: Abstract：Objectives Underwater bio-inspired integrated sensing and communication (ISAC) systems require shared waveforms that simultaneously achieve bio-inspired covertness and active detection performance. Addressing the detection performance optimization problem for cetacean whistle waveforms, this study establishes a unified analytical framework based on the principle of stationary phase (PSP) to systematically reveal the causal relationship between instantaneous frequency structure and ambiguity function morphology, and on this basis proposes a multi-tone sinusoidal frequency-modulated waveform optimization method using a genetic algorithm with golden-ratio initialization. Methods First, using the wideband ambiguity function (WAF) as the core analytical tool, asymptotic expressions of the WAF are derived via PSP for six typical cetacean whistle waveforms (constant, concave, convex, up-sweep, down-sweep, and sinusoidal), establishing the causal mapping of "number of monotonic intervals of instantaneous frequency → number of effective stationary phase points → WAF morphology." This mapping enables theoretically grounded waveform selection and identifies the sinusoidal whistle as the optimal candidate. Second, to address the two inherent limitations of sinusoidal whistles—near-zone sidelobes and periodic grating lobes—a genetic algorithm optimization framework for multi-tone sinusoidal FM waveforms is proposed, with the golden ratio used as the initial value. Grounded in the stationary phase superposition theorem, the framework optimizes the specific values of multiple modulation frequency components while keeping the total frequency deviation (range resolution) and the minimum modulation frequency (grating lobe constraint) fixed, thereby disrupting the periodic grating lobe structure and further suppressing Doppler sidelobes. Results Both theoretical derivations and simulation results consistently demonstrate that the sinusoidal whistle, owing to its periodic non-monotonic instantaneous frequency structure, possesses the largest number of effective stationary phase points and achieves the best overall performance in terms of autocorrelation sidelobe suppression, ambiguity function concentration, reverberation resistance, and Doppler tolerance. After genetic algorithm optimization, Doppler sidelobe suppression of 4–6 dB is achieved, and the grating lobe structure is significantly weakened due to the incommensurability of golden-ratio modulation frequencies. Conclusions The proposed PSP-based waveform optimization method provides a complete technical pathway—from theoretical waveform selection to waveform optimization—for shared waveform engineering design in bio-inspired underwater ISAC systems.