Specific emitter identification （SEI） leverages the inherent hardware imperfections of wireless device RF front-ends to achieve device identification， serving as a crucial technology for ensuring wireless communication security. However， in complex electromagnetic environments， various perturbations such as carrier frequency offset， sampling clock deviation， gain fluctuation， time shift， and chirp modulation collectively cause distribution shifts in signal features， thereby weakening the stability of RF fingerprint representation and degrading identification performance. To address these issues， this paper proposes a perturbation-aware modulated convolutional neural network （PAM-CNN）. This method first utilizes a perturbation-aware branch to jointly estimate the perturbation state and its parameters in the input signal， and then performs sample-adaptive modulation of the convolution kernels based on the estimation results. This enables the network to structurally suppress the impact of perturbations during the feature extraction process. Simultaneously， a multi-task joint training framework is constructed， incorporating device identification， perturbation detection， and parameter regression， to enhance the model’s robust representation capability under complex perturbation conditions. Experimental results on a real over-the-air ADS-B baseband dataset and its offline perturbation-augmented data demonstrate that， under various superimposed perturbation conditions， the proposed method achieves an identification accuracy of 95.39% at a signal-to-noise ratio （SNR） of 15 dB and outperforms comparison methods across the full SNR range. The results indicate that this method can effectively enhance the robustness of SEI in complex electromagnetic environments.Highlights: 1.This paper proposes a perturbation-aware modulated convolutional neural network for robust specific emitter identification, where five typical perturbations, including carrier frequency offset, sampling clock deviation, gain fluctuation, time shift, and chirp modulation, are explicitly modeled and used to guide sample-adaptive convolution kernel modulation.2.This paper builds a multi-task learning framework that jointly optimizes emitter classification, perturbation detection, and parameter regression. Experiments on real over-the-air ADS-B baseband data and perturbation-augmented data demonstrate that the proposed method improves recognition robustness under multiple perturbations and different SNR conditions.