This paper presents two random neural network (RNN) based context-aware decision making frameworks to improve adaptive modulation and coding (AMC) in long-term evolution (LTE) downlink systems. In the first framework, AMC is modelled as a traditional classification problem with the aim to maximize the probability of correct classification. The second framework seeks to optimize the throughput as opposed to simply maximizing the probability of the correct classification. To model the second framework, we developed a hybrid cognitive engine (CE) architecture by integrating an RNN based learning algorithm with genetic algorithm (GA) based reasoning. RNN features help CE to concurrently acquire long-term-learning, fast decision making, and less computational complexity, which are essential for the development of any real-time cognitive communication system. The performance of RNN is compared with artificial neural networks (ANN) and state-of-the-art effective exponential SINR mapping (EESM) algorithm. A comprehensive analysis of the proposed RNN based AMC scheme is presented by jointly incorporating the effect of different schedulers, feedback delays, and multi-antenna diversity on the throughput of an orthogonal frequencydivision multiple access (OFDMA) system. The critical analysis of the first framework revealed that RNN based CE can achieve comparable results with faster adaptation, even in severe environment changes without the need of retraining compared to ANN. The analysis of the second approach demonstrated RNNs faster adaptation as compared to ANN with up-to 100% improvement in both system capacity and fairness as compared to EESM algorithm.