MIMO-OFDM channel estimation in presence of carrier frequency offsets

Optimal pilot design and placement for channel estimation in Multiple-input Multiple-output (MIMO) Orthogonal Frequency-Division Multiplexing (OFDM) systems in the presence of frequency offset are discussed. Both the singlefrequency-offset case and the multiple-frequency-offset case are treated. Constant-Envelope (CE) is shown to be a sufficient but not necessary condition for optimizing the mean square error (MSE). When the CE condition is relaxed, i.e., pilots with multiple envelope values, the power allocation and placement rules for the optimal MSE performance are derived. The Least-Squares (LS) and Linear Minimum Mean Square Error (LMMSE) estimators are designed for uncorrected and correlated MIMO-OFDM channels, respectively. Both optimal adaptive pilot power allocation and suboptimal uniform pilot power allocation strategies 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]. The proposed LMMSE estimator significantly outperforms the LS estimator.