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This paper considers the beamspace channel estimation problem in 3D lensantenna array under a millimeter-wave communication system. We analyze thefocusing capability of the 3D lens antenna array and the sparsity of thebeamspace channel response matrix. Considering the analysis, we observe thatthe channel matrix can be treated as a 2D natural image; that is, the channelis sparse, and the changes between adjacent elements are subtle. Thus, for thechannel estimation, we incorporate an image reconstruction technique calledsparse non-informative parameter estimator-based cosparse analysis AMP forimaging (SCAMPI) algorithm. The SCAMPI algorithm is faster and more accuratethan earlier algorithms such as orthogonal matching pursuit and supportdetection algorithms. To further improve the SCAMPI algorithm, we model thechannel distribution as a generic Gaussian mixture (GM) probability and embedthe expectation maximization learning algorithm into the SCAMPI algorithm tolearn the parameters in the GM probability. We show that the GM probabilityoutperforms the common uniform distribution used in image reconstruction. Wealso propose a phase-shifter-reduced selection network structure to decreasethe power consumption of the system and prove that the SCAMPI algorithm isrobust even if the number of phase shifters is reduced by 10%.

Beamspace Channel Estimation in mmWave Systems via Cosparse Image Reconstruction Technique