In this study, the sum throughput maximisation problem for cognitive radio networks (CRNs) based on the multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) structure has been investigated. Hence, the intention is to maximise the downlink sum throughput of the CRN in a way that the sum power of the cognitive base station (CBS) remains below the given power limit and the induced interference on each subcarrier guarantees the interference threshold level predefined by primary users. Here, due to combinatorial constraints, the complex problem should be resolved. Hence, the core purpose of this study is to prepare a novel resource assignment algorithm that tries to fulfil these combinatorial constraints simultaneously. Therefore, this study makes progress towards solving the problem theoretically based on convex optimisation framework. An optimal solution has been implemented by proposing the iterative algorithm in which an optimal level of Lagrangian coefficients is obtained. Then, because of the optimal algorithm intricacy, the two low complicated algorithms are further suggested based on the solutions of two simplified versions of the original problem. Numerical results demonstrate that the suggested algorithms improve sum throughput considerably in comparison with classical algorithm. The proposed simplified algorithms converge to the optimal solutions' performance while their complexities are desirable for practical implementation.