Cognitive radio (CR) has dynamic spectrum resource management capability and is an effective way to solve the overcrowding of the Internet of Things (IoT) network spectrum. Broadband spectrum sensing plays an increasingly important role because it can simultaneously tap a large number of dynamic spectrum access opportunities. However, sensing methods based on Nyquist or sub-Nyquist sampling still have many challenges in practical applications. Aiming at the low performance of the traditional sampling scheme in the wide-band domain, and the unsatisfactory detection accuracy of the compressed spectrum sensing in the case of high sparse level, we leveraged the compressed spectrum sensing scheme based on modulated wideband converter (MWC) to reconstruct the signal support, and analyze the reasons why some missing elements always exist in the recovering procedure of support. Furthermore, a binary decision model suitable for wideband detection is established, and a distributed broadband cooperative spectrum sensing algorithm based on hard fusion is proposed to improve the overall support recovery accuracy. The simulation results show that the proposed algorithm improves the recovery probability significantly in restructuring support and shows strong robustness, which can provide reliable support for IoT network communications.