Our goal in this paper is to discuss several issues and challenges involved with dynamic spectrum access in cognitive radio networks (CRNs). In this context, we introduce three optimization problems for spectrum shaping in cognitive radio networks (CRNs) using orthogonal frequency division multiplexing (OFDM). These optimization problems utilize the concept of transmission hyperspace (TH). The first problem involves maximization of sum-rate of the network under primary and secondary quality-of-service (QoS) constraints utilizing frequency and space dimensions of the TH. The second problem relaxes the omnidirectional assumption and incorporates antenna directionality in the first problem. As for the third problem, time dimension of the TH is added to the first two problems and the resulting problem is formulated as a time scheduling problem. We show that all these problems are NP-hard which requires the development of efficient heuristic algorithms.