  Channel interpolation is an essential technique for providing high-accuracy
estimation of the channel state information (CSI) for wireless systems design
where the frequency-space structural correlations of multi-antenna channel are
typically hidden in matrix or tensor forms. In this letter, a modified extreme
learning machine (ELM) that can process tensorial data, or ELM model with
tensorial inputs (TELM), is proposed to handle the channel interpolation task.
The TELM inherits many good properties from ELMs. Based on the TELM, the Tucker
decomposed extreme learning machine (TDELM) is proposed for further improving
the performance. Furthermore, we establish a theoretical argument to measure
the interpolation capability of the proposed learning machines. Experimental
results verify that our proposed learning machines can achieve comparable mean
squared error (MSE) performance against the traditional ELMs but with 15%
shorter running time, and outperform the other methods for a 20% margin
measured in MSE for channel interpolation.
