This disclosure provides systems, methods and apparatus, including computer programs encoded on computer storage media, for performing wireless communication using digital post distortion, for example, with a large antenna array where the number of transmit antennas may be greater than a number of spatial streams. A transmitting device and a receiving device determine a perturbed precoding matrix based on a precoding perturbation rule. The transmitting device precodes a signal using the perturbed precoding matrix and transmits via the number of antennas greater than the number of spatial streams. The receiving device receives the signal and subtracts non-linearities from the received signal based on a channel estimation using the perturbed precoding matrix over one or more iterations.