Non-cooperative communications, where a receiver can automatically distinguish and classify transmitted signal formats prior to detection, are desirable for low-cost and low-latency systems. This work focuses on the deep learning enabled blind classification of multi-carrier signals covering their orthogonal and non-orthogonal varieties. We define two signal groups, in which Type-I includes signals with large feature diversity while Type-II has strong feature similarity. We evaluate time-domain and frequency-domain convolutional neural network (CNN) models in simulation with wireless channel/hardware impairments. Simulation results reveal that the time-domain neural network training is more efficient than its frequency-domain counterpart in terms of classification accuracy and computational complexity. In addition, the time-domain CNN models can classify Type-I signals with high accuracy but reduced performance in Type-II signals because of their high signal feature similarity. Experimental systems are designed and tested, using software defined radio (SDR) devices, operated for different signal formats to form full wireless communication links with line-of-sight and non-line-of-sight scenarios. Testing, using four different time-domain CNN models, showed the pre-trained CNN models to have limited efficiency and utility due to the mismatch between the analytical/simulation and practical/real-world environments. Transfer learning, which is an approach to fine-tune learnt signal features, is applied based on measured over-the-air time-domain signal samples. Experimental results indicate that transfer learning based CNN can efficiently distinguish different signal formats in both line-of-sight and non-line-of-sight scenarios with great accuracy improvement relative to the non-transfer-learning approaches.