Modulated signal detection has been rapidly advancing in various wireless communication systems as it's a core technology of spectrum sensing. To address the non-Gaussian statistical of noise in radio channels, especially its pulse characteristics in the time/frequency domain, this paper proposes a method based on Information Geometric Difference Mapping (IGDM) to solve the signal detection problem under Alpha-stable distribution (α-stable) noise and improve performance under low Generalized Signal-to-Noise Ratio (GSNR). Scale Mixtures of Gaussians is used to approximate the probability density function (PDF) of signals and model the statistical moments of observed data. Drawing on the principles of information geometry, we map the PDF of different types of data into manifold space. Through the application of statistical moment models, the signal is projected as coordinate points within the manifold structure. We then design a dual-threshold mechanism based on the geometric mean and use Kullback-Leibler divergence (KLD) to measure the information distance between coordinates. Numerical simulations and experiments were conducted to prove the superiority of IGDM for detecting multiple modulated signals in non-Gaussian noise, the results show that IGDM has adaptability and effectiveness under extremely low GSNR.