Millimeter wave communication -mmWC- is a promising volunteer for 5G communication systems with high data rates. To subdue the channel propagation characteristics in this frequency band, high dimensional antenna arrays need to be deployed at transceiver. Employing such a deployment, prevents to use of ADC or RF chain in each branch of MIMO system because of power constraints. Thus, Such systems impose to have a hybrid analog/digital precoding/combining architecture. Hence, channel estimation revision seems to be essential. This paper propose new algorithms to estimate the mmW channel by exploiting the sparse nature of the channel and finding the subspace of received signal vectors based on MUSIC. By combining the multiple measurement vector -MMV- concept, MISIC , subspace augmentation -SA- and two-stage orthogonal subspace matching pursuit -TOSMP- approaches, we try to recover the indices of non-zero elements of an unknown channel matrix accurately even under the defective- rank condition. These indices are called support in the context. Simulation results indicate MUSIC-based approaches offer lower estimation error and higher sum rates compared with conventional MMV solutions.

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