In high data rate wireless communication systems, the robust synchronization is one of the critical criterions. Since OFDM and a single carrier system with frequency domain equalizer (SC-FDE) have a lot of similarities, the synchronization tasks and methods can be comparable. For the reasonable synchronization performance, applying a preamble part to the transmission format is a well-known approach. The preamble consists of training symbols which are used for different synchronization tasks at the receiver. Carrier frequency offset (CFO) estimation is one of the synchronization problems. CFO is caused by the frequency mismatch between the local oscillators at the transmitter and receiver and the Doppler frequency shift due to relative motion between transmitter and receiver. There will always be some remaining CFO after the initial preamble based carrier frequency synchronization. While this remaining offset in OFDM causes inter-carrier-interference (ICI) which could lead to severe performance degradation and introduces a rotation of the constellation diagram, it causes a rotation of the whole constellation diagram from one received block to the other in SC-FDE. This rotation cause a random spreading of the constellation points and the constellation points of the individual symbols experience a spreading along circles.
To compensate this residual CFO, the phase tracking is required. In the cyclic prefix based systems including OFDM and a single carrier system with CP (CP-SC), the pilot symbols are inserted in data frame regularly. However, using CP based systems with the preamble and additional pilot symbols would be inefficient approach. Thus, we consider a SC-FDE system with unique word (UW) instead of the CP. The main advantage of UW based SC-FDE is the fact that UW can be equalized together with the data symbols since the UW is part of the FFT block. Therefore the equalized UW symbols can effectively be used to improve the estimation accuracy. Moreover, im...