Compressive spectrum sensing using chaotic matrices for cognitive radio networks

Compressive sensing is an emerging technique in cognitive radio systems, through which sub-Nyquist sampling rates can be achieved without loss of significant information. In collaborative spectrum sensing networks with multiple secondary users, the problem is to find a reliable and fast sensing method and to secure communication between members of the same network. The method proposed in this paper provides both quick and reliable detection through compressive sensing and security through the use of deterministic chaotic sensing matrices. Deterministic matrices have an advantage over random ones since they are easier to generate and store. Moreover, it is much easier to verify whether a deterministic matrix satisfies the conditions for compressive sensing compared with random matrices, which is what makes them an interesting area of research in compressive sensing. Also, it would be a great advantage if the sensing matrices also provide inherent security, which is the motivation for using chaotic matrices in this paper, since any slight changes in the chaotic parameters result in highly uncorrelated chaotic sequences, hence entirely different sensing matrices. This makes it impossible to reconstruct the signal without proper knowledge of the parameters used to generate the sensing matrix. They can also be easily regenerated by knowing the correct initial values and parameters. Additionally, new modifications are proposed to the existing structures of chaotic matrices. The performance of chaotic sensing matrices for both existing and modified structures is compared with that of random sensing matrices.