Time Reversal (TR) has been proposed as a competitive precoding strategy for low-complexity devices, relying on ultra-wideband waveforms. This transmit processing paradigm can address the need for low power and low complexity receivers, which is particularly important for the Internet of Things, since it shifts most of the communications signal processing complexity to the transmitter side. Due to its spatio-temporal focusing property, TR has also been used to design multiple access schemes for multi-user communications scenarios. However, in wideband time-division multiple access schemes, the signals received by users suffer from significant levels of inter-symbol interference as well as interference from uncoordinated users, which often require additional processing at the receiver side. This paper proposes an iterative TR scheme that aims to reduce the level of interference in wideband multi-user settings, while keeping the processing complexity only at the transmitter side. The performance of the proposed TR-based protocol is evaluated using analytical derivations. In addition, its superiority over the conventional Time Reversal Division Multiple Access (TRDMA) scheme is demonstrated through simulations as well as experimental measurements at $2.5$ GHz carrier frequency with variable bandwidth values.