Today, the radio spectrum is rarely fully utilized. This problem is valid in more domains, e.g., time, frequency and geographical location. To provide an efficient utilization of the radio spectrum, the Cognitive Radio Networks (CRNs) have been advanced. The key idea is to open up the licensed spectrum to unlicensed users, thus allowing them to use the so-called spectrum opportunities as long as they do not harmfully interfere with licensed users. An important focus is laid on the limitation of previously reported research efforts, which is due to the limited consideration of the problem of competition among unlicensed users for spectrum access in heterogeneous CRNs. A software framework is introduced, which is called PRioritized Opportunistic spectrum Access System (PROAS). In PROAS, the heterogeneity aspects of CRNs are specifically expressed in terms of cross-layer design and various wireless technologies. By considering factors like ease of implementation and efficiency of control, PROAS provides priority scheduling based solutions to alleviate the competition problem of unlicensed users in heterogenous CRNs. The advanced solutions include theoretical models, numerical analysis and experimental simulations for performance evaluation. By using PROAS, three particular CRN models are studied, which are based on ad-hoc, mesh-network and cellular-network technologies. The reported results show that PROAS has the ability to bridge the gap between research results and the practical implementation of CRNs.