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The successful emergence of deep learning (DL) in wireless system applications has raised concerns about new security-related challenges. One such security challenge is adversarial attacks. Although there has been much work demonstrating the susceptibility of DL-based classification tasks to adversarial attacks, regression-based problems in the context of a wireless system have not been studied so far from an attack perspective. The aim of this paper is twofold: (i) we consider a regression problem in a wireless setting and show that adversarial attacks can break the DL-based approach and (ii) we analyze the effectiveness of adversarial training as a defensive technique in adversarial settings and show that the robustness of DL-based wireless system against attacks improves significantly. Specifically, the wireless application considered in this paper is the DL-based power allocation in the downlink of a multicell massive multi-input-multi-output system, where the goal of the attack is to yield an infeasible solution by the DL model. We extend the gradient-based adversarial attacks: fast gradient sign method (FGSM), momentum iterative FGSM, and projected gradient descent method to analyze the susceptibility of the considered wireless application with and without adversarial training. We analyze the deep neural network (DNN) models performance against these attacks, where the adversarial perturbations are crafted using both the white-box and black-box attacks.