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The year 2019 witnessed the rollout of the 5G standard, which promises to offer significant data rate improvement over 4G. While 5G is still in its infancy, there has been an increased shift in the research community for communication technologies beyond 5G. The recent emergence of machine learning approaches for enhancing wireless communications and empowering them with much-desired intelligence holds immense potential for redefining wireless communication for 6G. The evolving communication systems will be bottlenecked in terms of latency, throughput, and reliability by the underlying signal processing at the physical layer. In this position paper, we motivate the need to redesign iterative signal processing algorithms by leveraging deep unfolding techniques to fulfill the physical layer requirements for 6G networks. To this end, we begin by presenting the service requirements and the key challenges posed by the envisioned 6G communication architecture. We outline the deficiencies of the traditional algorithmic principles and data-hungry deep learning (DL) approaches in the context of 6G networks. Specifically, deep unfolded signal processing is presented by sketching the interplay between domain knowledge and DL. The deep unfolded approaches reviewed in this article are positioned explicitly in the context of the requirements imposed by the next generation of cellular networks. Finally, this article motivates open research challenges to truly realize hardware-efficient edge intelligence for future 6G networks.