## 1 Introduction  
Unmanned aerial vehicles (UAVs) have attracted significant attention in both military and industrial applications, ranging from reconnaissance and attacks to communications, delivery, and search operations, due to their affordability, versatility, and accessibility [1, 2, 3, 4, 5, 6]. Space-air-ground integrated networks (SAGINs) have emerged as a prominent research topic in the development of the sixth-generation cellular network (6G) [7], where UAVs and millimeter-wave (mm-wave) massive multiple-input-multiple-output (MIMO) systems are expected to play crucial roles [8, 9]. The unique characteristics of UAVs, such as their high maneuverability and potential for unmanned operations, necessitate advancements in communication technologies, leading to an increased interest from researchers, companies, and organizations [10, 11, 12, 13]. Recognizing the importance of UAVs, the third-generation partnership project (3 GPP) has proposed the new radio (NR) support for UAVs as a specialized category of user equipment (UE) [14, 15], highlighting the urgent need for research on UAV communication systems [16]. UAV communications encompass various modes, including air-to-ground (AG) communications, air-to-air (AA) communications, and UAV-assisted communications. In the context of UAV AG communication, researchers such as [PERSON] et al. [17] and [PERSON] et al. [18] have explored tensor-based joint channel estimation and symbol detection in UAV-assisted communication systems. [PERSON] et al. have summarized channel models for UAV AG communications [19], while [PERSON] et al. have provided a comprehensive survey on channel modeling for UAV communications [20]. As MIMO technology is expected to be employed in UAV communication systems, MIMO symbol detection has become crucial; although, limited research has been conducted in this area. MIMO detection is a crucial process in wireless communication systems that employ multiple antennas at both the transmitter and receiver. In MIMO systems, multiple spatial streams are transmitted simultaneously using different antenna configurations, allowing for increased data rates, improved reliability, and enhanced spectral efficiency. The goal of MIMO detection is to estimate the transmitted symbols or bits at the receiver by efficiently recovering the original data from the received signals affected by noise, interference, and channel impairments. This process involves solving the detection problem, where the receiver must determine the transmitted symbols based on the received signals and knowledge of the channel. Thus, the application of MIMO detection is necessary in any scenario where multiple antennas are employed at both the transmitter and receiver in UAV AG communications. Regarding MIMO detection, maximum likelihood (ML) detection exhibits an optimal performance but suffers from a prohibitively high complexity [21]. Linear minimum mean square error (LMMSE) detectors can reduce the complexity to an acceptable level but fail to match the performance of ML detection [22]. [PERSON] et al. introduced the iterative approximate message passing (AMP) algorithm for MIMO detection, which has been proven to be Bayes-optimal for independent and identically distributed (i.i.d.) sub-Gaussian channels [23]. [PERSON] and [PERSON] proposed orthogonal AMP (OAMP) for channel estimation, which outperforms AMP, particularly for ill-conditioned matrices [24]. By unfolding the structure of the OAMP algorithm and adding some trainable parameters, [PERSON] et al. introduced OAMP-Net [25] and OAMP-Net2 [26] for MIMO detection. [PERSON] et al. proposed conjugate gradient OAMP-Net (CG-OAMP-Net) for MIMO detection to reduce the complexity of OAMP [27]. [PERSON] et al. introduced MMNnet for channel estimation, which exhibits superior performance and has a lower computational complexity for realistic channels [28].