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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 single-frequency-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.
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