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Channel estimation is a challenging and timely issue for the 3rd Generation Partnership Project (3GPP) standardized low power wide-area network technology named narrowband Internet of Things (NB-IoT). Channel estimation is crucial to achieve extended radio coverage, energy efficiency, coherent detection, and channel equalization for signal repetition dominated NB-IoT uplink transmission. The NB-IoT inherits simplified baseband radio frequency processing, physical channels, reference signal structure, and numerology from existing Long Term Evolution (LTE) systems to save power and costs. Thus, channel estimation methods extensively employed in LTE systems may not be applied to the NB-IoT uplink systems. In this paper, efficient discrete cosine transform type-I (DCT-I)-based transform-domain channel estimation approaches are proposed by modifying the original definition of DCT-I. The proposed …