Number of FLOPs of Training DNNs for Learning Precoding

Deep neural networks (DNNs) have been widely used for learning precoding policy to achieve good system performance with low computational complexity. However, existing DNNs for learning precoding cannot be generalized to the number of users. Consequently, the DNNs have to be retrained frequently, which incurs unaffordable computational cost for training, especially when the number of antennas is large. As a metric of time complexity, the number of floating-point operations (FLOPs) has been analyzed for inference in literature. Yet the time complexity of training DNNs for learning wireless policies has only been evaluated in terms of running time. To gain useful insight into developing deep learning methods with low-cost training, in this paper we derive the numbers of FLOPs of training three DNNs used for learning precoding, which are circular convolution neural network (CCNN), linear convolution neural network with fully-connected layers (F-LCNN), and fully-connected neural network (FNN). We then compare them with those of inference. Analytical results show that the ratio of the approximate numbers of FLOPs for training to those for inference depends on the numbers of epochs and training samples. Simulation results show that the time complexity of training scales with the number of antennas faster than that of inference, and the complexity of training the F-LCNN and FNN scales faster than that of training the CCNN.