With millimeter wave wireless communications, the resulting radiation reflects on most visible objects, creating rich multipath environments, namely in urban scenarios. The radiation captured by a listening device is thus shaped by the obstacles encountered, which carry latent information regarding their relative positions. In this paper, a system to convert the received millimeter wave radiation into the device's position is proposed, making use of the aforementioned hidden information. Using deep learning techniques and a pre-established codebook of beamforming patterns transmitted by a base station, the simulations show that average estimation errors below 10 meters are achievable in realistic outdoors scenarios that contain mostly non-line-of-sight positions, paving the way for new positioning systems.