  Sparse representation can efficiently model signals in different applications
to facilitate processing. In this article, we will discuss various applications
of sparse representation in wireless communications, with focus on the most
recent compressive sensing (CS) enabled approaches. With the help of the
sparsity property, CS is able to enhance the spectrum efficiency and energy
efficiency for the fifth generation (5G) networks and Internet of Things (IoT)
networks. This article starts from a comprehensive overview of CS principles
and different sparse domains potentially used in 5G and IoT networks. Then
recent research progress on applying CS to address the major opportunities and
challenges in 5G and IoT networks is introduced, including wideband spectrum
sensing in cognitive radio networks, data collection in IoT networks, and
channel estimation and feedback in massive MIMO systems. Moreover, other
potential applications and research challenges on sparse representation for 5G
and IoT networks are identified. This article will provide readers a clear
picture of how to exploit the sparsity properties to process wireless signals
in different applications.
