Compressed sensing (CS) deals with the problem of reconstructing a sparse vector from an under-determined set of observations. Approximate message passing (AMP) is a technique used in CS based on iterative thresholding and inspired by belief propagation in graphical models. Due to the high transmission rate and a high molecular absorption, spreading loss and reflection loss, the discrete-time channel impulse response (CIR) of a typical indoor THz channel is very long and exhibits an approximately sparse characteristic. In this paper, we develop AMP based channel estimation algorithms for indoor THz communications. The performance of these algorithms is compared to the state of the art. We apply AMP with soft- and hard-thresholding. Unlike the common applications in which AMP with hard-thresholding diverges, the properties of the THz channel favor this approach. It is shown that THz channel estimation via hard-thresholding AMP outperforms all previously proposed methods and approaches the oracle based performance closely.
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