Abstract: Cognitive radio ad hoc networks(CRAHNs) have several advantages over traditional ad hoc networks, like distributed multi-hop architecture, variant network topology and so on. Spectrum sensing is a foundation in the cognitive radio technology. We adopt the compressed sensing approach to attain high-resolution signal recovery at lower than Nyquist sampling rate. In this paper, we use the multi-hop architecture. Each CR sense its individual spectral map that consists of both common spectral components from primary users and individualized spectral innovations arising from interference of other CRs. CRAHNs are dynamic and have no central entity for data fusion. Therefore in this paper, we adopt a gradient-based distributed cooperative scheme. The proposed scheme is based on energy detection. These distributed algorithms converge fast to the globally optimal solutions and have little energy consumption. Simulation results show the effectiveness of the proposed scheme.