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In this paper, we analyze the cross-correlation properties for Chu sequences, which provide information on the distribution of the maximum magnitudes of the cross-correlation function. Furthermore, we can obtain the number of available sequences for a given maximum magnitude of the cross-correlation function and the sequence length.

In this paper, optimal pilot sequence designs for MIMO-OFDM systems in multi-cell environments are provided. The proposed multi-cell optimality criterion is to minimize the worst-case MSE of an LS-based channel estimator. To satisfy the multi-cell optimality, it is found that the pilot sequence set, having the perfect auto-correlation property, should meet the Welch bound and the maximum magnitude of the crosscorrelation function should be further minimized. Multi-cell optimal pilot sequence designs for various pilot types and their DFT representations are proposed by adopting Chu sequences and a tight upper-bound on the maximum size of the pilot sequence set is derived for a given pilot sequence length and the maximum allowed cross-correlation value. Simulation results show that the proposed pilot sequences can improve both the MSE performance and the system performance in multi-cell environments.

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