Improved-SOMP Algorithm Based on Principal Component Estimation for Wideband Spectrum Sensing

Wideband spectrum sensing (WBSS) based on sub-Nyquist sampling (SNS) effectively alleviates sampling pressure, improves spectrum utilization, and has significant applications in modulation recognition and localization. Recovery algorithms widely used in WBSS are the classical simultaneous orthogonal matching pursuit (SOMP) algorithm and its variants. For the optimization function, the sensing matrix in the SNS model based on multirate or multicoset sampling in earlier research is typically a unitary matrix, allowing the optimization to be achieved by transposing the sensing matrix. However, current research is increasingly shifting towards models that use the Modulated Wideband Converter (MWC) structure as the basis for SNS, where the sensing matrix is generally non-unitary. In this context, the traditional transpose operation no longer provides accurate results, leading to a significant decline in optimization performance. Additionally, for the estimation method, SOMP typically employs the least squares (LS) method, which suffers from large variance and sensitivity to noise, significantly reducing estimation accuracy, especially when the signal is sparse or noise levels are high. It is due to the fact that LS assumes that all signal components contribute equally to the estimation, which prevents it from fully exploiting the sparsity of the wideband signal in WBSS, thereby affecting estimation accuracy. To address these issues, this paper proposes an improved SOMP algorithm based on principal component (PC) estimation. First, in the optimization function, we replace the transpose operation with a pseudo-inverse for a non-unitary sensing matrix to more closely fit the communication system model. Second, in the estimation method, we replace LS method with PC estimation, which focuses on the main components of the signal while ignoring secondary ones, making full use of the signal's sparsity. And we prove that PC estimation has a lower variance. Finally, for the SOMP and its variants, the proposed methods are effective in both aspects. And simulations illustrate the correctness of the proposed methods.