  In this paper, we consider a downlink orthogonal frequency division
multiplexing (OFDM) system from a base station to a high-speed train (HST)
equipped with fully/partly calibrated massive uniform linear antenna-array
(ULA) in wireless environments with abundant scatterers. Multiple Doppler
frequency offsets (DFOs) stemming from intensive propagation paths together
with transceiver oscillator frequency offset (OFO) result in a fast
time-varying frequency-selective channel. We develop an angle domain carrier
frequency offset (CFO, general designation for DFO and OFO) estimation
approach. A high-resolution beamforming network is designed to separate
different DFOs into a set of parallel branches in angle domain such that each
branch is mainly affected by a single dominant DFO. Then, a joint estimation
algorithm for both maximum DFO and OFO is developed for fully calibrated ULA.
Next, its estimation mean square error (MSE) performance is analyzed under
inter-subarray mismatches. To mitigate the detrimental effects of
inter-subarray mismatches, we introduce a calibration-oriented beamforming
parameter (COBP) and develop the corresponding modified joint estimation
algorithm for partly calibrated ULA. Moreover, the Cramer-Rao lower bound of
CFO estimation is derived. Both theoretical and numerical results are provided
to corroborate the proposed method.
