An attractive research direction for future communication systems is the design of new waveforms that can both support high throughputs and present advantageous signal characteristics. Although most modern systems use orthogonal frequency-division multiplexing (OFDM) for its efficient equalization, this waveform suffers from multiple limitations such as a high adjacent channel leakage ratio (ACLR) and high peak-to-average power ratio (PAPR). In this paper, we propose a learning-based method to design OFDM-based waveforms that satisfy selected constraints while maximizing an achievable information rate. To that aim, we model the transmitter and the receiver as convolutional neural networks (CNNs) that respectively implement a high-dimensional modulation scheme and perform the detection of the transmitted bits. This leads to an optimization problem that is solved using the augmented Lagrangian method. Evaluation results show that the end-to-end system is able to satisfy target PAPR and ACLR constraints and allows significant throughput gains compared to a tone reservation (TR) baseline. An additional advantage is that no dedicated pilots are needed.