This paper considers the problem of pilot contamination (PC) in large-scale multi-cell multiple-input multipleoutput (MIMO) aided orthogonal frequency division multiplexing systems. We propose an efficient scheme relying on an optimal pilot design conceived for time-domain channel estimation, which can either completely eliminate PC or significantly reduce it, depending on the channel's coherence time. This is achieved by designing an optimal pilot set to allowing us to beneficially group the

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... ers in all the cells and to assign a time-shifted pilot transmission to the different groups. Unlike the existing PC elimination schemes which require an excessively long channel coherence time, our proposed scheme is capable of completely eliminating PC under a much shorter coherence time. Moreover, the existing PC elimination schemes can no longer be used if the channel coherent time is insufficiently large. By contrast, even for extremely short channel coherent time, our scheme can still be implemented to significantly reduce PC. This is particularly beneficial for high velocity scenarios. Our simulation results demonstrate the efficiency of the proposed scheme.