In this paper, we consider a cognitive radio network where secondary users may have different sets of available channels. We propose a partial cooperation scheme that captures the feature of incomplete channel availability information under spatial heterogeneity. It encourages cooperation among users in a group with the same priority channel, while allows contentions among users from different groups. We show that our proposed scheme achieves a good balance between the channel utilization and additional signaling overhead by comparing with no cooperation and full cooperation schemes. We further derive the lower bound of channel utilization of the proposed scheme by comparing it with a full cooperation scheme. Numerical results show that the average performance of the scheme can be more than two times better than the lower bound derived. In our simulations, the scheme is up to 15% better in channel utilization than the no cooperation scheme.