## 1 Introduction
The paper [12] focuses on a UAV full duplex (FD) relay with joint beamforming and power allocation to optimize the instantaneous data rate when the UAV flight follows a circular trajectory. FD relaying allows for a relay node to simultaneously transmit and receive in the same band, unlike half-duplex (HD) mode [10; 13]. Therefore, a natural choice is to combine FD relays with NOMA to enhance spectral efficiency. A UAV-supported clustered-NOMA system for the 6G-enabled IoT is detailed in [14], where the numerous terminals are partitioned into clusters and the UAV provides services to the clusters by using wireless-powered communication (WPC) to optimize the uplink average achievable sum rate of all terminals by designing the UAVs' trajectory. In [15], a multiple-UAV-aided NOMA scheme is proposed to improve spectral and energy efficiency for cellular uplinks. In particular, half of users are partitioned in clusters served by multiple UAV relays, and the other ones communicate with the BS directly. A location-based user pairing (UP) scheme associates the clustered users with the multiple-UAV-aided NOMA to minimize the resource allocation problem. However, all the aforementioned works focus on UAV-relay-aided NOMA without considering mmWave communications. The severe signal power attenuation in the mmWave band impacts UAV connectivity performance, especially when very long communications distances exist between the ground users and the associated UAV which serves them. Therefore, this paper addresses the design of a UAV-enabled FD relaying network in the mmWave band to aid an uplink NOMA cellular system. In detail, a multiple-UAV-relaying network supports NOMA technology, and hybrid mmWave beamforming is considered at the base station (BS), which can estimate the DoA information of UAVs to improve the overall sum rate of the system. Indeed, the DoAs are unknown and the MUltiple SIgnal Classification (MUSIC) method [16] considered in this paper estimates directly the DoAs at the hybrid mmWave beamformer. In [17], a beamspace MUSIC algorithm is used to estimate path directions for mmWave channel estimation problem showing that the hybrid precoding structure can avoid the spectrum ambiguity and maximize the number of resolvable path directions. The mmWavechannel estimation problem is also considered in [18] by using MUSIC for the hybrid analog/digital beamformer with 2D co-prime arrays where the directions can be uniquely estimated by finding the common peaks of the 2 decomposed subarrays. Deep-learning approaches are considered to evaluate the angle-of-arrival (AoA) information in the uplink of an mmWave communication system based on MUSIC to enhance classification accuracy in [19]. The above papers use the MUSIC algorithm to derive the DoA information in mmWave hybrid beamforming, but they do not deploy an UAV-relay network, as in this paper. To the best of our knowledge, this paper is the first contribution that considers jointly (i) the UL mmWave communications, (ii) the hybrid beamforming with DoA estimation based on the MUSIC method and (iii) multiple UAVs acting as an aerial BS to relay NOMA transmissions and, consequently, achieve better data rate for users who can suffer severe channel conditions. Moreover, a novel maximization design of the overall sum-rate is proposed for the uplink mmWave transmission of the multiple-UAV-relay-aided NOMA 6G system.