Asymptotic Cramér–Rao Bounds and Training Design for Uplink MIMO-OFDMA Systems With Frequency Offsets

In this paper, we address the data-aided joint estimation of frequency offsets and channel coefficients in the uplink transmission of multiple-input multiple-output orthogonal frequency-division multiple access systems. A compact and informative expression of the Cramer-Rao bound is derived for large training sequence sizes. It is proved that the asymptotic performance bounds depend on the choice of the training sequence only via the asymptotic covariance profiles. Moreover, it is shown that the asymptotic performance bounds do not depend on the number of users and the values of the frequency offsets. Next, we bring to the fore the training strategies which minimize the asymptotic performance bounds and which are, therefore, likely to lead to accurate estimates of the parameters. In particular, for a given user, it is shown that accurate frequency offset estimates are likely to be obtained by introducing relevant correlation between training sequences sent at different antennas. On the other hand, accurate channel estimation is achieved when training sequences sent at different antennas are uncorrelated. Simulation results sustain our claims.