Near optimal training sequences for low complexity symbol timing estimation in MIMO systems
IEEE Transactions on Communications
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In this paper, the data aided (DA) and non-data aided (NDA) maximum likelihood (ML) symbol timing estimators and their corresponding conditional Cramer–Rao bound (CCRB) and modified Cramer–Rao bound (MCRB) in multiple-input-multiple-output (MIMO) correlated flat-fading channels are derived. It is shown that the approximated ML algorithm in References [4,13] is just a special case of the DA ML estimator; while the extended squaring algorithm in Reference [14] is just a special case of the NDA ML estimator. For the DA case, the optimal orthogonal training sequences are also derived. It is found that the optimal orthogonal sequences resemble the Walsh sequences, but present different envelopes. Simulation results under different operating conditions (e.g. number of antennas and correlation between antennas) are given to assess and compare the performances of the DA and NDA ML estimators with respect to their corresponding CCRBs and MCRBs. It is found that (i) the mean square error (MSE) of the DA ML estimator is close to the CCRB and MCRB, (ii) the MSE of the NDA ML estimator is close to the CCRB but not to the MCRB, (iii) the MSEs of both DA and NDA ML estimators are approximately independent of the number of transmit antennas and are inversely proportional to the number of receive antennas, (iv) correlation between antennas has little effect on the MSEs of DA and NDA ML estimators and (v) DA ML estimator performs better than NDA ML estimator at the cost of lower transmission efficiency and higher implementation complexity. Copyright © 2004 John Wiley & Sons, Ltd.