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This paper proposes a low complexity channel estimation algorithm for unmanned aerial vehicle three dimension multi-user multiple-input-multiple-output (3D MIMO) systems with the uniform planar array (UPA) at base station using paired spatial signatures. With the aid of antenna array theory and array signal processing, 3D channel is firstly modeled based on the angles between the direction of arrival along x - and y -axis of the UPA. And 3D MIMO channels can be projected onto the x - and y -directions, respectively. Then, channel estimation for multi-user uplinks using small amount of training resources is divided into two phases. At the first uplink preamble phase, each user is assigned the orthogonal pilot, and the paired spatial signatures and optimal rotation angle of each user through the same pilot sequence are obtained. We also propose a user grouping strategy based on three-dimension angle-division multiple access (3D-ADMA) to ensure that the user's spatial signatures do not overlap. At the second phase during several coherence times, the same pilot sequence within a group and orthogonal pilot sequences between groups are assigned, then, the channel state information of the user's x - and y -directions are recovered by the paired space signatures and optimal rotation angle of each user obtained in the preamble phase, respectively. And dynamically updating the user's paired spatial signatures and optimal rotation angle utilizes the obtained channel parameter of x - and y -directions. Finally, the channel parameter of the x - and y -directions are reconstructed by the updated user's space signatures and the optimal rotation angle, and the 3D MIMO channel estimation is obtained through the Kronecker product. Compared with the conventional channel estimation method of the 3D MIMO system under UPA using a low-rank model, the proposed methods reduce the computational complexity without degrading the estimated performance to a large extent. Furthermore, it is carried out with limited training resources, and the pilot resource overhead of the system is greatly reduced by the 3D-ADMA packet and the two-stage pilot allocation. Simulation results verified that the proposed algorithm is effective and feasible.

Low complexity channel estimation algorithm using paired spatial signatures for UAV 3D MIMO systems