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In this work, we investigate the use of backscattered mm-wave radio signals for the joint tracking and recognition of identities of humans as they move within indoor environments. We build a system that effectively works with multiple persons concurrently sharing and freely moving within the same indoor space. This leads to a complicated setting, which requires one to deal with the randomness and complexity of the resulting (composite) backscattered signal. The proposed system combines several processing steps: at first, the signal is filtered to remove artifacts, reflections and random noise that do not originate from humans. Hence, a density-based classification algorithm is executed to separate the Doppler signatures of different users. The final blocks are trajectory tracking and user identification, respectively based on Kalman filters and deep neural networks. Our results demonstrate that the integration of the last-mentioned processing stages is critical towards achieving robustness and accuracy in multi-user settings. Our technique is tested both on a single-target public dataset, for which it outperforms state-of-the-art methods, and on our own measurements, obtained with a 77 GHz radar on multiple subjects simultaneously moving in two different indoor environments. The system works in an online fashion, permitting the continuous identification of multiple subjects with accuracies up to 98%, e.g., with four subjects sharing the same physical space, and with a small accuracy reduction when tested with unseen data from a challenging real-life scenario that was not part of the model learning phase.