Image processing can exploit a sparsity property in the discrete cosine domain, i.e., many images’ discrete cosine transform (DCT) coefficients are zero or small enough to be regarded as zero. For example, audio signals are sparse in the frequency domain, especially for the sounds representing tones. This form of sparse (or compressible) structure arises naturally in many applications. Sparse representation expresses some signals as a linear combination of a few atoms from a prespecified and overcomplete dictionary. This article will provide readers a clear picture of how to exploit sparsity properties to process wireless signals in different applications. Moreover, we identify other potential applications and research challenges for sparse representation for 5G and IoT networks. Then we introduce recent research progress in applying CS to address the major opportunities and challenges in these networks, including wide-band spectrum sensing in cognitive radio networks (CRNs), data collection in IoT networks, and channel estimation and feedback in massive multiple-input, multiple-output (MIMO) systems. This article starts from a comprehensive overview of CS principles and different sparse domains potentially used in 5G and IoT networks. With the help of the sparsity property, CS is able to enhance the spectrum efficiency (SE) and energy efficiency (EE) of fifth-generation (5G) and Internet of Things (IoT) networks. In this article, we will discuss various applications of sparse representation in wireless communications, with a focus on the most recent compressive sensing (CS)-enabled approaches. Sparse representation can efficiently model signals in different applications to facilitate processing.

Cs evolution condition zero