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This paper investigates the 3-D massive multiple-input multiple-output (MIMO) for air-to-ground transmission, where an air platform (AP) is equipped with a 2-D rectangular antenna array and communicates with a number of user equipments (UEs) on the ground. By exploiting the slow timevarying parameters, such as channel correlation and angles of departure (AoDs) of UEs, we first propose a location-assisted two-layer precoding scheme for downlink transmission. The first-layer precoding aims to decompose the original massive MIMO system into several low-dimension MIMO systems, with each operating on the orthogonal subspace. Through proper UE clustering, we show that the first-layer precoding matrix can be approximated using a constant-envelope matrix, which results in significant reduction on hardware complexity of AP. The second-layer precoding is designed to eliminate the multi-UE interference within each low-dimension MIMO system. Since the AoD information is usually not perfectly known at AP, we then investigate the effect of AoD uncertainty on the performance of the proposed precoding scheme. In particular, we propose a new analytic method to fast estimate approximately the power loss due to AoD error. Numerical simulations are presented to evaluate the performance of location-assisted precoding under different system parameters, including Rician factor, altitude of AP, and AoD uncertainty. The results show that the location-assisted precoding outperforms match filter precoding and basis expansion-based precoding in the air-to-ground transmission scenarios significantly.

Three-Dimension Massive MIMO for Air-to-Ground Transmission: Location-Assisted Precoding and Impact of AoD Uncertainty