This paper is concerned with a cognitive cloud radio access network (CRAN) with a special attention to efficient and reliable transmission of big data. In particular, the paper focuses on optimizing performance of secondary users (SUs) in the downlink. Existing approaches either try to maximize the number of accepted SUs or the sum data rate of accepted SUs. The first approach unfairly favors users with small data requests, whereas the second approach allocates most resources to users with better channel conditions. In contrast, this paper develops a novel approach that favors big data requests while simultaneously maintaining a certain degree of fairness among SUs. To this end, we first introduce a novel objective function that allows us to jointly optimize deadline-aware time scheduling, spectrum allocation, SU selection, and remote radio head (RRH) allocation for SUs. Second, we demonstrate that finding the global optimum solution for the formulated problem entails the enumeration of all colorful independent sets on a generalized interval graph which is known to be NP-hard. Third, we propose a dynamic programming (DP) approach which yields the global optimum solution at a reduced computational cost. Fourth, we analyze the complexity of the proposed DP approach and numerically compare its performance against existing baseline algorithms. Numerical and simulation results revealed that our solution favors big data users while incurring only a small degradation in the fairness index. Our proposed solution is practical for small-to-medium size networks. Furthermore, it offers a benchmark against which any new sub-optimal low-complexity algorithm can be compared to determine how far from the global optimum its performance is.