The combination of unmanned aerial vehicles (UAVs) and millimeter wave (mmWave) multiple-input multiple-out (MIMO) system is regarded as a key enabling technology for beyond 5G networks, as it provides high data rate aerial links. However, establishing UAV-enabled mmWave MIMO communication is quite challenging due to the high hardware cost in terms of radio frequency (RF) chains. As a cost-effective alternative, a beamspace precoding with discrete lens arrays (DLA) architecture has received considerable attention. However, the underlying optimal design in beamspace precoding has not been fully exploited in UAV-enabled communication scenario. In this paper, the joint design of the UAV's altitude and hybrid beamspace precoding is proposed for the UAV-enabled multiuser MIMO system, in which the DLA is exploited to reduce the number of the RF chain. In the proposed scheme, the optimization problem is formulated as a minimum weighted mean squared error (MWMSE) method. Then an efficient algorithm with the penalty dual decomposition (PDD) is proposed that aims to jointly optimize the altitude of UAV, beam selection and digital precoding matrices. Simulation results confirm the comparable performance of the proposed scheme and perform close to full-digital beamforming in terms of achievable spectral efficiency
