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Millimeter wave (mmWave) channels can provide new frequency bands for communications together with improved accuracy and resolution for sensing and target localization. Those require parametric channel estimation methods capable of operating with very short coherence times in case of large Doppler spread. In this paper, we address this problem in orthogonal frequency division multiplexing (OFDM) uplink channel estimation. We first observe that it is a variation of the multidimensional harmonic retrieval (MHR) problem in which one has no direct access to the channel tensor due to the strongly time-varying channel. We then derive an improvement of the OFDM space-alternating generalized expectation-maximization (SAGE) algorithm for channel estimation. It is able to solve the problem under intense Doppler spreads and carrier frequency offset (CFO). The proposed method exploits the shift-invariance properties of the OFDM channel tensor to perform efficient coordinate descent steps. We also derive a threshold with probability of false alarm (PFA) guarantees to probe the quality of path initializations. The algorithm estimates the number of significant multipath components by progressively adding paths until the likelihood function reaches a threshold value derived from the noise distribution. We show via numerical examples that the proposed method outperforms the state-of-the-art methods both in channel tensor estimation accuracy as well as in the model order estimation performance.
Pinto et al. (Thu,) studied this question.