We propose a novel deep energy autoencoder (EA) for noncoherent multicarrier multiuser single-input multipleoutput (MU-SIMO) systems under fading channels. In particular, a single-user noncoherent EA-based (NC-EA) system, based on the multicarrier SIMO framework, is first proposed, where both the transmitter and receiver are represented by deep neural networks (DNNs), known as the encoder and decoder of an EA. Unlike existing systems, the decoder of the NC-EA is fed only with the energy combined from all receive antennas, while its encoder outputs a real-valued vector whose elements stand for the subcarrier power levels. Using the NC-EA, we then develop two novel DNN structures for both uplink and downlink NC-EA multiple access (NC-EAMA) schemes, based on the multicarrier MUSIMO framework. Note that NC-EAMA allows multiple users to share the same sub-carriers, thus enables to achieve higher performance gains than noncoherent orthogonal counterparts. By properly training, the proposed NC-EA and NC-EAMA can efficiently recover the transmitted data without any channel state information estimation. Simulation results clearly show the superiority of our schemes in terms of reliability, flexibility and complexity over baseline schemes.