Guaranteed Open-loop Channel Estimation for mmWave Hybrid MIMO Communications, Using Orthogonal Matching Pursuit (OMP) Algorithm

Channel estimation for millimeter wave (mmWave) hybrid MIMO communications, is challenging because of the complexities associated with the large antenna arrays at the transceivers and with the higher propagation lossess of the mmWaves. However, with open-loop training and exploiting the inherent sparse nature of the mmWave channel, it becomes easier by formulating the channel estimation problem in compressive sensing (CS) theory, and solving the problem using orthogonal matching pursuit (OMP) algorithm. In the CS theory, coherence and restricted isometry property (RIP) of sensing matrices, and restricted isometry constant (RIC) based k-sparse signal recovery exactly in k iterations, are significant conditions for guaranteed recoverability. Most of the earlier works are focused on coherence only, because of the impracticality of computation of RICs for the larger dimensional mmWave channel. In this paper, a novel technique, for the first time different from the earlier works, is devised to achieve guaranteed open-loop training based channel estimation. As there is hurdle for computation of RIC for the channel, smaller dimensional sensing (DFT) matrices are synthesized and are subjected for guaranteed recoverability conditions. From the simulation results of recoverability with synthesized and channel matrices, guarantee of the mmWave channel estimation is achieved.