New data-aided frequency estimators are introduced for phase shift keying (PSK) or quadrature amplitude modulation (QAM) transmitted over frequency-selective fading channels. The estimators are developed based on a maximul likelihood (ML) or a least squares (LS) criterion.
The ML-based estimator assumes the use of a special class of pilots, called near-iid (independent identically distributed) sequences, with impulsive 4-th order moments. By the help of such pilots, the ML based estimator can estimate frequency offsets without the need for channel information. The pilots of GSM and IS-136 mobile communication systems have been observed as are near-iid, and statistical analysis indicates that the ML based estimate is almost unbiased if the pilot is near-iid.
The LS-based estimator is developed from differentially decoded signals. Using these signals, the channel autocorrelations containing a frequency offset are first estimated by LS criterion. Among the elements of the estimated autocorrelations, useful terms for frequency estimation are collected, and from which the frequency offset is estimated. The LS based estimator is robust to the preamble pattern, and it also does not require any channel information.
The proposed estimators are applied to transmissions with antenna diversity. In addition, a space-time (ST) block coding for frequency estimation is investigated, and we propose a condition that the code matrix should satisfy, called cyclically orthogonal matrix. If the code matrix is cyclically orthogonal, the frequency offset can be easily estimated from the inner product between different received signal vectors without any channel information.