Tensor-Based compressed estimation of frequency-selective mmWave MIMO channels

This paper develops a novel channel estimation technique for frequency-selective mmWave MIMO channels using a hybrid analog-digital architecture. By adopting a tensor formalism to model the effective channel, we link the channel estimation problem to the theory of multi-way compressive sensing of sparse tensors via Parallel Factors (PARAFAC) analysis. By leveraging on this link, a joint estimation of the compressed channel bases (spatial transmit, spatial receive and delay) can be obtained by means of an alternating least squares algorithm. Once these bases are estimated, the channel parameters are extracted by solving a simpler compressive sensing (CS) problem for each basis. Some useful bounds on the minimum number of beams and pilot sequence length can be derived from Kruskal's uniqueness conditions for sparse PARAFAC models. Remarkable channel estimation performance is obtained with short pilot sequences and very few beams, as shown in our simulation results.