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Utilizing channel reciprocity, the traditional time-reversal technique boosts the signal-to-noise ratio at the receiver with very low transmitter complexity. However, the large delay spread gives rise to severe inter-symbol interference (ISI) when the data rate is high, and the achievable transmission rate is further degraded in the multiuser downlink due to the inter-user interference (IUI). In this work, we study the weighted sum rate optimization problem by means of waveform design in the time-reversal multiuser downlink where the receiver processing is based on a single sample. Power allocation has a significant impact on the waveform design problem. We propose a new power allocation algorithm named Iterative SINR Waterfilling, which is able to achieve comparable sum rate performance to that of globally optimal power allocation. We further propose another approach called Iterative Power Waterfilling for multiple data streams. Iterative SINR Waterfilling provides better performance than Iterative Power Waterfilling in the scenario of high interference, while Iterative Power Waterfilling can work under multiple data streams. Simulation results show the superior performance of the proposed algorithms in comparison with other waveform designs such as zero-forcing and conventional time-reversal waveform.