In this letter, we study user grouping and beamforming for high altitude platform (HAP) massive multiple-input multiple-output (MIMO) systems. We first exploit the fact that the signal power mainly concentrates on statistical-eigenmode (SE), and we then use it to perform user grouping and design the outer beamformer. The user grouping is realized based on the average chordal distance between the SEs instead of the chordal distance between the covariance eigenspaces of the users in the same group. In this case, the complexity of a singular value decomposition is avoided. The outer beamformer is designed using reduced-dimensional SEs of the users, and the computational complexity is lower than in the case where the statistical correlation matrix is used. Numerical results demonstrate the performance enhancement of the proposed beamforming scheme in HAP massive MIMO systems compared to the existing schemes based on channel correlation matrix.

The measurement results in land mobile satellite (LMS) communication scenario have shown that the propagation characteristic of LMS channel is a non-stationary process. In this paper, a non-stationary three-dimensional (3-D) wideband geometry-based stochastic model (GBSM) and the corresponding simulation model are proposed for high-altitude platform (HAP) multiple-input multiple-output (MIMO) communication system. The proposed GBSM uses two-dimensional (2-D) one-ring and 3-D multi-cylinders to model moving scatterers and near and far stationary scatterers, respectively. In the proposed GBSM, we assume that the multipath components (MPCs) scattering from the far stationary scatterers could appear again after their disappearance, and a two-state continuous-time Markov process is used to model the dynamic properties of MPCs such as MPCs appearance and disappearance, and the closed-form expressions of the survival probabilities of MPCs are derived. In the proposed GBSM, the long distance and small-scale time-variant parameters are also used to investigate the non-stationarities of HAP-MIMO channel. Using the survival probabilities of MPCs, the statistical properties of the proposed 3-D GBSM are derived. The numerical results demonstrate that the proposed 3-D GBSM is more practical to characterize the HAP-MIMO channel.

In the indoor environment, where global positioning system (GPS) fails, the presence of multipath, non-line-of-sight (NLOS), and dense scatterer yield unreliable position estimation. In the massive multiple-input multiple-output (massive MIMO) system, the sparse channel property is exploited here for user localization as an integral part of the network to reduce the power of user equipment (UE). In this study, a novel spatial spectrum fusion estimation and localization (SSFEAL) algorithm using the uniform circular array (UCA) structure is proposed, which is based on the two-dimensional (2D) direction of arrival (DOA) estimation. The spatial spectrum of the incoherent narrowband uplink pilot signal on each frequency bin received at the distributed massive MIMO base stations is used for spectrum fusion. The main contributions of this research work are as follows: (1) The channel’s sparse characteristics at individual base stations are used to synthesize the covariance matrix of the received signal at the central fusion center. (2) The proposed method has 2D spatial information measurement fusion to generate informative spatial spectrum followed by grid refinement processing to reduce the localization error to sub-meter level. It is demonstrated that the proposed method using UCA gives higher-resolution estimation performance compared with the rectangular array in the localization accuracy. Comprehensive Monte Carlo simulation and real application test results show the validity and sub-meter precision in the indoor environment.

Intelligent reflecting surface (IRS) composed of unit cells with tunable reflection coefficients, amplitude, phase, and frequency has received great interest from wireless communication communities. In this paper, a non-stationary three-dimensional (3-D) wideband IRS-assisted channel model, including spatial and temporal non-stationarity, is proposed for high altitude platform (HAP) multiple-input multiple-output (MIMO) communication systems. The proposed channel model considers the propagation environment around the receiver (Rx) and that around both the IRS and Rx, which are modeled using multiple 3-D cylinders and confocal elliptic-cylinders, respectively. In the proposed model, the optimal reflection phases of the IRS reflection units are proposed, and the number and the size of the IRS reflection units are also considered, which are used to investigate received signal strength, multipath fading effect, and spatial non-stationarity of IRS-aided communication systems. The numerical results show that the IRS reflection units can improve the received signal strength by adjusting the reflection phases and multipath fading effect can be effectively reduced by increasing the number and the size of IRS reflection units. Also, it is found that the spatial correlation significantly decreases with the increase of the number and size of the IRS reflection units, and the proposed IRS-aided channel model presents spatial non-stationarity. These observations can provide guidelines and references for systems design and performance analysis of IRS-aided HAP-MIMO communication systems.

In this article, a nonstationary 3-D wideband geometry-based stochastic model (GBSM) is proposed for low-altitude unmanned aerial vehicle (UAV) multiple-input–multiple-output (MIMO) communication systems. The proposed GBSM is a combination of Line-of-Sight (LoS) components, local multipath components (MPCs) scattering from the scatterers around the receiver (Rx), named as local scatterers, and far MPCs scattering from far scatterers, defined as not local scatterers, and uses 2-D one-ring and 3-D cylinder to mimic local scatterers as well as 3-D multiple confocal elliptic cylinders to mimic far scatterers. In this article, two-state continuous-time Markov chains (CTMCs) are introduced to model appearances or disappearances of the LoS components, local MPCs at the transmitter (Tx) installed on UAV, and far MPCs at the Tx and Rx, and the evolution process of the far MPCs is also investigated. The concept of the visibility region (VR) is introduced to model the birth and death processes of the local MPCs at the Rx, and the effect of the size of the VR on channel statistics is also considered. In the proposed GBSM, the inherited nature of the LoS components, the local MPCs and far MPCs, is considered, and the corresponding statistical properties are derived. The proposed nonstationary 3-D GBSM is validated by the measured results in terms of temporal correlation, and the numerical results show that the proposed 3-D GBSM is suitable for describing nonstationarity of the 3-D UAV-MIMO channel.

In this letter, we study an energy-efficient algorithm for beamspace high altitude platform with non-orthogonal multiple access (HAP-NOMA) systems over Rician fading channels. We first derive the non-line-of-sight (NLOS) theorem of beamspace HAP channel in large scale array regime according to the asymptotic property of the Toeplitz matrix. Then, we propose the beamspace HAP-NOMA scheme based on the derived NLOS theorem, which can be partitioned into two stages, i.e. user grouping scheme and power optimization scheme. The statistical channel state information (CSI) is only required in the proposed algorithm, which avoids acquiring instantaneous CSI. NOMA can serve users in each beam simultaneously to compensate for the loss of spectral efficiency due to the beamspace HAP. The digital precoder can be obtained by zero forcing (ZF) based on the equivalent channel. Numerical results show the performance enhancement of the proposed beamspace HAP-NOMA algorithm.