Time Reversal (TR) has been proposed as a competitive precoding strategy for low-complexity wireless devices relying on Ultra-WideBand (UWB) signal waveforms. However, when TR is applied for multiple access, the signals received by the multiple users suffer from significant levels of inter-symbol and inter-user interference, which requires additional processing for mitigation by each receiving user. In this paper, we present an iterative Time-Reversal Division Multiple Access (TRDMA) approach that aims to dim the latter interference levels. The performance of iterative TRDMA is evaluated experimentally in a reverberation chamber that mimics a rich scattering indoor wireless propagation environment. The improved efficiency, in terms of the number of algorithmic iterations, of the proposed approach compared to conventional TRDMA, is demonstrated. We also consider a mobile user configuration, where the position of the receiver changes between the channel estimation and data transmission steps. It is showcased, even for this experimental setup, that the proposed iterative TRDMA approach is more efficient than conventional precoding schemes.