EM-Based Phase Noise Estimation in Vector OFDM Systems Using Linear MMSE Receivers

Vector orthogonal frequency-division multiplexing (V-OFDM) for single-transmit-antenna systems is a generalization of OFDM where single-carrier frequency-domain equalization and OFDM are just two special cases. Phase noise in a V-OFDM system leads to a common vector block phase error (CVBPE) and an intervector block carrier interference effect. Severe performance degradation may occur if these two effects are not estimated and compensated well. In this paper, blind and semiblind phase noise estimation and compensation in a V-OFDM system is investigated by using the expectation-maximization (EM) algorithm. This is motivated by the fact that the conventional frequency-domain phase noise suppression schemes based on pilot-aided common phase error (CPE) or CVBPE estimation and compensation are not spectrally efficient as the vector block size is increased. Two novel schemes are proposed: One estimates the CVBPE only, and the other estimates the entire phase noise sequence in the time domain. General closed-form formulas for the maximization step of the EM algorithm for the two schemes are derived, and their computational complexity values are analyzed. The performances of the two schemes are investigated by using linear-minimum-mean-square-error (LMMSE) receivers. Simulations show that the two proposed schemes are very effective in estimating and compensating for phase noise in V-OFDM systems. It turns out that the second proposed scheme not only outperforms the traditional CPE or CVBPE schemes but is computationally efficient as well when applied to V-OFDM systems.