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 Cramér-Rao lower bound of CFO estimation is derived. Both theoretical and numerical results are provided to corroborate the proposed method.
Index TermsHigh-mobility OFDM, massive MIMO, partly calibrated antenna array, multiple carrier frequency offsets (CFOs), angle-domain approach, calibration-oriented beamforming parameter (COBP).