Adaptive codebook based channel estimation for hybrid mm-Wave massive MIMO systems

Channel estimation is challenging for millimeter wave (mmWave) massive multiple-input and multiple-output (MIMO) systems, because the number of antennas is much larger than the number of radio frequency (RF) chains and the signal-to-noise ratio (SNR) is low before beamforming. In this paper, we design a typical adaptive codebook based channel estimation by applying adaptive compressive sensing tools to generate beamforming vectors before channel estimation, which yields better performance than the conventional compressive sensing based channel estimation methods without beamforming at low SNRs. To reduce the computational load of hybrid codebook design and improve the channel estimation accuracy, a simultaneous multi-grid orthogonal matching pursuit method, called the S-MG-OMP method, is proposed to generate all the baseband training beamforming vectors simultaneously. In addition, for non-uniform linear arrays (non-ULAs), a random search algorithm is proposed to generate the candidate matrix containing all the RF beamforming vectors and determine the distribution of the antenna arrays by minimizing the newly defined modified mutual coherence. Simulation results show that the channel estimation accuracy is improved via the proposed S-MG-OMP method for uniform linear arrays (ULAs), and the S-MG-OMP method with non-ULAs has a better performance than that with ULAs.