Cognitive radio networks (CRN) have been tipped as one of the most promising paradigms for next generation wireless communication, due primarily to its huge promise of mitigating the spectrum scarcity challenge. To help achieve this promise, CRN develop mechanisms that permit spectrum spaces to be allocated to, and used by more than one user, either simultaneously or opportunistically, under certain preconditions. However, because of various limitations associated with CRN, spectrum and other resources available for use in CRN are usually very scarce. Developing appropriate models that can efficiently utilise the scarce resources in a manner that is fair, among its numerous and diverse users, is required in order to achieve the utmost for CRN. 'Resource allocation (RA) in CRN' describes how such models can be developed and analysed. In developing appropriate RA models for CRN, factors that can limit the realisation of optimal solutions have to be identified and addressed; otherwise, the promised improvement in spectrum/resource utilisation would be seriously undermined. In this thesis, by a careful examination of relevant literature, the most critical limitations to RA optimisation in CRN are identified and studied, and appropriate solution models that address such limitations are investigated and proffered. One such problem, identified as a potential limitation to achieving optimality in its RA solutions, is the problem of heterogeneity in CRN. Although it is indeed the more realistic consideration, introducing heterogeneity into RA in CRN exacerbates the complex nature of RA problems. In the study, three broad classifications of heterogeneity, applicable to CRN, are identified; heterogeneous networks, channels and users. RA models that incorporate these heterogeneous considerations are then developed and analysed. By studying their structures, the complex RA problems are smartly reformulated as integer linear programming problems and solved using classical optimisation. This smart move makes it possible to achieve optimality in the RA solutions for heterogeneous CRN. Another serious limitation to achieving optimality in RA for CRN is the strictness in the level of permissible interference to the primary users (PUs) due to the activities of the secondary users (SUs). To mitigate this problem, the concept of cooperative diversity is investigated and employed. In the cooperative model, the SUs, by assisting each other in relaying their data, reduce their level of interference to PUs significantly, thus achieving greater results in the RA solutions. Furthermore, an iterative-based heuristic is developed that solves the RA optimisation problem timeously and efficiently, thereby minimising network complexity. Although results obtained from the heuristic are only suboptimal, the gains in terms of reduction in computations and time make the idea worthwhile, especially when considering large networks. The final problem identified and addressed is the limiting effect of long waiting time (delay) on the RA and overall productivity of CRN. To address this problem, queueing theory is investigated and employed. The queueing model developed and analysed helps to improve both the blocking probability as well as the system throughput, thus achieving significant improvement in the RA solutions for CRN. Since RA is an essential pivot on which the CRN's productivity revolves, this thesis, by providing viable solutions to the most debilitating problems in RA for CRN, stands out as an indispensable contribution to helping CRN realise its much-proclaimed promises. / Thesis (PhD)--University of Pretoria, 2017. / Electrical, Electronic and Computer Engineering / PhD / Unrestricted