OFDMA uplink frequency offset estimation via cooperative relaying
IEEE Transactions on Wireless Communications
IEEE Transactions on Communications
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Optimal pilot design and placement for channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with frequency offsets are considered. Both the single-frequency- offset case and the multiple-frequency-offset case are treated. We show that the constant-envelope (CE) condition is sufficient but not necessary for pilot design, and that pilots with multiple envelopes can also achieve the optimal performance in terms of the mean square error (MSE) minimization, provided that an additional constraint on the pilot placement is satisfied simultaneously. New pilot designs, which take into account the multiple-frequency-offset case, are proposed to eliminate inter- pilot-interference (IPI) and to optimize the MSE performance. The least-squares (LS) and linear minimum mean square error (LMMSE) channel estimators for the multiple-frequency- offset case are designed for uncorrelated and correlated MIMO-OFDM channels, respectively. The LMMSE estimator requires the channel covariance matrix. Both optimal adaptive pilot power allocation and suboptimal uniform pilot power allocation are developed for the proposed LMMSE estimator. The adaptive allocation performs 4 dB better than the uniform allocation in the high noise region, but they both perform identically in the low noise region. Performance comparisons are made against several previous pilot designs due to [1], [2]. The proposed LMMSE estimator significantly outperforms the LS estimator.