Generalized analysis of MU-MISO time reversal-based systems over correlated multipath channels with estimation error

In this letter, we analyze the performance of multi-user multiple-input single-output time reversal (MU MISO TR)-based systems in a generalized framework. The considered propagation is correlated in both the space and the frequency domains, and channel estimation errors (CEEs) at the transmitter side are also taken into account. We derive a novel average signal-to-interference-plus-noise (SINR) formula in closed-form for TR-based systems. This formula is based on the exact expressions of the expectations of the powers of the desired signal, the inter-symbol interference (ISI) and the inter-user interference (IUI) components. These expressions allow us to reveal, for the first time, properties of time reversal which remained unknown up to now. More precisely, CEE has no influence on the ISI in terms of average power, whereas it degrades the power of the desired message-bearing signal. Moreover, irrespective of the central tap, the other taps of the IUI are independent from the effects of both inter-user correlation and CEE. Our analytical results are validated in both ultra-wideband and conventional broadband channels. Finally, these results are numerically compared to previous works.