  This paper addresses carrier frequency offset (CFO) estimation and training
sequence design for multiple-input multiple-output (MIMO) orthogonal frequency
division multiplexing (OFDM) systems over frequency selective fading channels.
By exploiting the orthogonality of the training sequences in the frequency
domain, integer CFO (ICFO) is estimated. {With the uniformly spaced non-zero
pilots in the training sequences} and the corresponding geometric mapping,
fractional CFO (FCFO) is estimated through the roots of a real polynomial.
Furthermore, the condition for the training sequences to guarantee estimation
identifiability is developed. Through the analysis of the correlation property
of the training sequences, two types of sub-optimal training sequences
generated from the Chu sequence are constructed. Simulation results verify the
good performance of the CFO estimator assisted by the proposed training
sequences.
