Wavelet Packet Modulation (WPM) is a multicarrier modulation. The subcarrier allocation and the corresponding power allocation are capable of leveraging the merits of WPM-based multi-user systems to improve system channel capacity. However, the resource allocation in WPM-based systems has never been investigated. Hence we propose in this paper the first resource allocation scheme for WPM-based Cognitive Radio (CR) systems. In our WPM-based CR systems, a Base Station (BS) serves several Secondary Users (SU) in idle or busy bands. The interference imposed on PUs by SUs in busy bands is restricted to a threshold. In fast fading multipath channels, the rapid fading variation may cause inaccurate Channel State Information (CSI) estimation which will lead to the improper resource allocation. To deal with this, our scheme involves two steps - real-time Channel State Information (CSI) estimation and CSI prediction for the next time slot. To timely capture CSI information, the former step exploits the Least Square Means (LSM) estimator. To accurately predict CSI, the latter step employs Kalman filters. Extensive experimental results show that the proposed resource allocation scheme is efficient regarding frequency selective fast fading