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One objective of the 5G communication system and beyond is to support massive machine type of communication (mMTC) to propel the fast growth of diverse Internet of Things use cases. The mMTC aims to provide connectivity to tens of billions sensor nodes. The dramatic increase of sensor devices and massive connectivity impose critical challenges for the network to handle the enormous control signaling overhead with limited radio resource. Non-Orthogonal Multiple Access (NOMA) is a new paradigm shift in the design of multiple user detection and multiple access. NOMA with compressive sensing based multiuser detection is one of the promising candidates to address the challenges of mMTC. The survey article aims at providing an overview of the current state-of-art research work in various compressive sensing based techniques that enable NOMA. We present characteristics of different algorithms and compare their pros and cons, thereby provide useful insights for researchers to make further contributions in NOMA using compressive sensing techniques.Keywords Non-orthogonal CDMA · massive connectivity · grant free medium access · compressive sensing multiuser detection IntroductionThe fifth generation (5G) wireless communication system envisions three major use cases: (i) enhanced mobile broadband (eMBB), (ii) ultra-reliable and

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