  Phase noise correction is crucial to exploit full advantage of orthogonal
frequency division multiplexing (OFDM) in modern high-data-rate communications.
OFDM channel estimation with simultaneous phase noise compensation has
therefore drawn much attention and stimulated continuing efforts. Existing
methods, however, either have not taken into account the fundamental properties
of phase noise or are only able to provide estimates of limited applicability
owing to considerable computational complexity. In this paper, we have
reformulated the joint estimation problem in the time domain as opposed to
existing frequency-domain approaches, which enables us to develop much more
efficient algorithms using the majorization-minimization technique. In
addition, we propose a method based on dimensionality reduction and the
Bayesian Information Criterion (BIC) that can adapt to various phase noise
levels and accomplish much lower mean squared error than the benchmarks without
incurring much additional computational cost. Several numerical examples with
phase noise generated by free-running oscillators or phase-locked loops
demonstrate that our proposed algorithms outperform existing methods with
respect to both computational efficiency and mean squared error within a large
range of signal-to-noise ratios.
