Given the rapid changes in telecommunication systems and their higher dependence on artificial intelligence, it is increasingly important to have models that can perform well under different, possibly adverse, conditions. Deep Neural Networks (DNNs) using convolutional layers are state-of-the-art in many tasks in communications. However, in other domains, like image classification, DNNs have been shown to be vulnerable to adversarial perturbations, which consist of imperceptible crafted noise that when added to the data fools the model into misclassification. This puts into question the security of DNNs in communication tasks, and in particular in modulation recognition. We propose a novel framework to test the robustness of current state-of-the-art models where the adversarial perturbation strength is dependent on the signal strength and measured with the "signal to perturbation ratio" (SPR). We show that current state-of-the-art models are susceptible to these perturbations. In contrast to current research on the topic of image classification, modulation recognition allows us to have easily accessible insights on the usefulness of the features learned by DNNs by looking at the constellation space. When analyzing these vulnerable models we found that adversarial perturbations do not shift the symbols towards the nearest classes in constellation space. This shows that DNNs do not base their decisions on signal statistics that are important for the Bayes-optimal modulation recognition model, but spurious correlations in the training data. Our feature analysis and proposed framework can help in the task of finding better models for communication systems.