Autocorrelation Properties of OFDM Timing Synchronization Waveforms Employing Pilot Subcarriers

We investigate the autocorrelation properties of timing synchronization waveforms that are generated by embedded frequency domain pilot tones in orthogonal frequency division multiplex (OFDM) systems. The waveforms are composed by summing a selected number of OFDM subcarriers such that the autocorrelation function (ACF) of the resulting time waveform has desirable sidelobe behavior. Analytical expressions for the periodic and aperiodic ACF sidelobe energy are derived. Sufficient conditions for minimum and maximum aperiodic ACF sidelobe energy for a given number of pilot tones are presented. Several useful properties of the pilot design problem, such as invariance under transformations and equivalence of complementary sets are demonstrated analytically. Pilot tone design discussion is expanded to the ACF sidelobe peak minimization problem by including various examples and simulation results obtained from a genetic search algorithm.