This paper describes preliminary research on enhancing the Ephemeral Diffie-Hellman Over COSE (EDHOC) protocol with a new pre-shared key (PSK) authentication method. The research focuses on the design and the potential benefits of PSK for improving session key update efficiency, and reducing computational overhead compared to existing authentication methods in EDHOC. We outline the planned implementation and evaluation strategy that will include performance metrics such as latency, computational cost, memory usage, and energy consumption across various hardware and software configurations. This work aims to optimize EDHOC for secure communication in resource-constrained environments.