Speech emotion sensing in communication networks has a wide range of applications in real life. In these applications, voice data are transmitted from the user to the central server for storage, processing, and decision making. However, speech data contain vulnerable information that can be used maliciously without the user's consent by an eavesdropping adversary. In this work, we present a privacy-enhanced emotion communication system for preserving the user personal information in emotion-sensing applications. We propose the use of an adversarial learning framework that can be deployed at the edge to unlearn the users' private information in the speech representations. These privacy-enhanced representations can be transmitted to the central server for decision making. We evaluate the proposed model on multiple speech emotion datasets and show that the proposed model can hide users' specific demographic information and improve the robustness of emotion identification without significantly impacting performance. To the best of our knowledge, this is the first work on a privacy-preserving framework for emotion sensing in the communication network.