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This paper discusses the issue of dynamic resource allocation (DRA) in the context of cognitive radio (CR) networks. We present a general framework adopting generalized transmitter and receiver signal- expansion functions, which allow us to join DRA with waveform adaptation, two procedures that are currently carried out separately. Moreover, the proposed DRA can handle many types of expansion functions or even combinations of different types of functions. An iterative game approach is adopted to perform multi-player DRA, and the best-response strategies of players are derived and characterized using convex optimization. To reduce the implementation costs of having too many active expansion functions after optimization, we also propose to combine DRA with sparsity constraints for dynamic function selection. Generally, it incurs little rate-performance loss since the effective resources required by a CR are in fact sparse.