Frequency synchronization algorithms for MIMO-OFDM systems with periodic preambles

This paper addresses the problem of frequency synchronization in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems with periodic preambles. Two Maximum Likelihood Estimators (MLEs) and four low complexity Best Linear Unbiased Estimators (BLUEs) are proposed. When cyclic shift delay is applied to periodic preambles, MLEs can adopt a unique structure which employs diversity and correlation calculation in the estimator. We first propose a multiple-antenna estimator named as MLE-MA, which has an estimation range of the entire signal bandwidth. MLE-MAS is a simplified version of MLE-MA, which reduces the computational load at the cost of a narrower estimation range. Moreover, phases or differential phases obtained from the autocorrelation of periodic sequences with different delays can be used to estimate carrier frequency offset (CFO). The weighting coefficients of all BLUEs are derived in closed form and shown to be independent from the signal-to-noise ratio (SNR). BLUEs have asymptotically consistent variances. Theoretical and simulation results demonstrate that all estimators can asymptotically approach the theoretical Cramer Rao Lower bound (CRLB) at different SNRs.