  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.
