The demand for wideband wireless spectrum is increasing rapidly due to a rapidly expanding market of satellite communications and multimedia wireless services while the usable spectrum is becoming scarce due to current spectrum segmentation and static frequency allocation policies. Cognitive Radio (CR) can be an efficient technique to increase the spectrum utilization efficiency of heterogeneous wireless networks. Compressive sensing (CS) can overcome the traditional restriction that sampling rate must satisfy the Nyquist sampling theory, and it is also an important technology available for the integrated space-ground network. Aiming at the problem that the measurement processes of orthogonal matching pursuit (OMP) are easy to be disturbed by noise and the sparse information may not be available for practical applications. To overcome these problems, we have extended the idea of OMP to illustrate another recovery scheme called stochastic gradient orthogonal matching pursuit (SGOMP). It’s shown that the proposed algorithm shows robustness against noise. Moreover, with modified the early termination threshold (ETT), the complexity of the proposed algorithm can be reduced.