High altitude platform station (HAPS) communications have made a tremendous impact on recent research into sixth-generation (6G) and beyond wireless networks. The large coverage area and significant computational capability of HAPS systems enable many areas of utilization in 6G and beyond applications, including Internet of Things (IoT) services, augmented reality, and connected autonomous vehicles. In addition, non-orthogonal multiple access (NOMA) is a cutting-edge technology that can be utilized to enhance spectral efficiency in HAPS systems. In this paper, we exploit NOMA-based HAPS communications and multiple antennas to meet the connectivity, reliability, and high-data-rate requirements of 6G and beyond applications. We propose a user selection and correlation-based user pairing algorithm for a NOMA-based multi-user HAPS system. Moreover, we investigate the codebook design for HAPS communication and adapt the polar-cap codebook (PCC) to the HAPS channel which shows Rician fading propagation characteristics dominated by the line-of-sight (LOS) component. Performance evaluations show that the proposed user selection algorithm is perfectly suited to the HAPS channel and that the PCC provides a remarkable spectral efficiency.
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