Impact of pilot pattern on carrier frequency recovery for TETRA-like multitone modulations

A study of maximum-likelihood pilot-aided frequency offset recovery for filtered multitone modulations such as that employed in the TETRA Release 2 Enhanced Data Service is presented. An approach is proposed to improve on previously published algorithms. When pilot symbols are arranged on a rectangular time-frequency grid, as envisaged by the cited standard, the acquisition range of a pilot-based frequency synchroniser may seem to be very narrow as it cannot exceed the inverse of pilot spacing in the time-domain. It is shown that the above drawback can be relieved by resorting to a pilot pattern where the pilot symbols are simply shifted in time along the subcarriers with respect to the rectangular arrangement.