In this paper, we optimize the performance of a cloud platform to effectively support cooperative spectrum sensing in a cognitive radio (CR) cloud network. This cloud uses the Apache Hadoop platform to run a cooperative spectrum sensing algorithm in parallel over multiple servers in the cloud. A cooperative spectrum sensing algorithm needs to process a very large number of spectrum sensing reports per second to quickly update its database that stores the current activities of all primary users of the CR network. Because the updates of the database must be finished as soon as possible to make the CR approach effective, the cloud platform must be able to run the algorithm in real time with as little overhead as possible. In this work, we first measured the execution time of such an algorithm over our own cloud and the Amazon EC2 public cloud, using the original Hadoop platform design and implementation. We found that the original Hadoop platform has too much fixed overhead and incurs too much delay to the cooperative spectrum sensing algorithm, which makes it unable to update the primary user database in just a few seconds. Therefore, we studied the source code and the design and implementation of the Hadoop platform to improve its performance. Our experimental results show that our improvement of the Hadoop platform can significantly reduce the required time of the cooperative spectrum sensing algorithm and make it more suitable for large-scale CR networks.