Spectrum sensing in cognitive radio with robust principal component analysis

Spectrum sensing is a cornerstone in cognitive radio. Covariance matrix based method has been widely used in spectrum sensing. As is well-known that the covariance matrix of white noise is proportional to the identity matrix which is sparse. On the other hand, the covariance matrix of signal is usually low-rank. Robust principal component analysis (PCA) has been proposed recently to recover the low-rank matrix which is corrupted by a sparse matrix with arbitrarily large magnitude non-zero entries. In this paper, robust PCA for spectrum sensing is proposed based on the sample covariance matrix. The received signal will be divided into two segments. Robust PCA will be applied to extract the low-rank matrices from the sample covariance matrices of both segments. The primary user's signal is detected if the discrepancy between the recovered low-rank matrices is smaller than a predefined threshold. The simulations are done both on the simulated and captured DTV signal. Also, the simulations that robust PCA is taken as a de-noising process for sample covariance matrix are also implemented in this paper.