The system (700), apparatus (600), and method of the present invention provide an hierarchical pseudo-circularly symmetric and full circularly symmetric training sequence structure (100) for high-speed communication system. The hieratical pseudo-circularly symmetric part (101) is preferably used for burst detection, coarse frequency and timing error estimation and AGC gain setting. The full circularly symmetric part (102) is preferably used for channel estimation, fine frequency error estimation. The resulting sequence has a very good peak-to-average power (PAPR) property, making it suitable for many applications. The bandwidth efficiency is also improved due to using symmetric sequences.