Improved-SOMP Algorithm Based On Ridge Regression for Wideband Spectrum Sensing

The simultaneous orthogonal matching pursuit (SOMP) algorithm and its variants are the main recovery algorithms based on sub-Nyquist sampling (SNS) in Wideband spectrum sensing (WBSS). In this letter, we propose an improved SOMP algorithm based on the Ridge Regression estimation (RR) and its simplified algorithm. First, in SOMP’s optimization function, since the sensing matrix in the current mainstream Modulated Wideband Converter (MWC) structure is non-unitary, the traditional method of transposing the sensing matrix for optimization is no longer accurate. Thus, we replace the transpose operation with a pseudo-inverse for non-unitary sensing matrix to better fit the MWC structure. Second, in SOMP’s estimation method, we replace the high-variance-suffering least squares (LS) with RR. By leveraging the bias induced by RR, a range of bias values with smaller variance than LS is proven, and a sub-optimal solution of bias is derived to enhance performance. Furthermore, based on the non-singular characteristics of the sensing matrix, we give RR-SOMP’s simplified algorithm with lower complexity by removing orthogonal transformation. Finally, for the SOMP’s variants, the proposed methods are also effective in both aspects. Simulations validate the effectiveness of the proposed methods.