Spatial Cross-correlation Function Research Articles

A Novel UAV Air-to-Air Channel Model Incorporating the Effect of UAV Vibrations and Diffuse Scattering

In this paper, we propose a geometric channel model for air-to-air (A2A) unmanned aerial vehicle (UAV) communication scenarios. The model is established by incorporating line-of-sight, specular reflection, and diffuse scattering components, and it can capture the impacts of UAV vibrations induced by the propeller’s rotation. Based on UAV heights and ground scatterer density, a closed-form expression is derived to jointly capture the zenith and azimuth angular distributions of diffuse rays. The power of diffuse rays is modeled according to the grazing angle of the rays and the electrical properties and roughness of the ground materials. Key statistics, including the temporal autocorrelation function, spatial cross-correlation function, Doppler power spectrum density, and coherence time are derived, providing an in-depth understanding of the time-variant characteristics of the channel. The results indicate that the presented model is capable of capturing certain A2A channel characteristics, which align with the corresponding theoretical analysis. The findings suggest that the scattering effect of the A2A channel is significantly influenced by the altitude of the UAV. Additionally, it is shown that UAV vibrations can introduce extra Doppler frequencies, notably decreasing the temporal correlation and coherence time of the channel. This effect is more prominent when the system operates at high-frequency bands. The effectiveness of the presented model is confirmed through a comparison of its statistics with those of an existing model and with available measurement data.

A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands

High-altitude platforms (HAPs) are considered to be the most important equipment for next-generation wireless communication technologies. In this paper, we investigate the channel characteristics under the configurations of massive multiple-input multiple-output (MIMO) space and large bandwidth at millimeter-wave (mmWave) bands, along with the moving essence of the HAP and ground terminals. A non-stationary three-dimensional (3D) geometry-based stochastic model (GBSM) is proposed for a HAP communication system. We use a cylinder-based geometric modeling method to construct the channel and derive the channel impulse response (CIR). Additionally, the birth–death process of the scatterers is enclosed using the Markov process. Large-scale parameters such as free space loss and rainfall attenuation are also taken into consideration. Due to the relative motion between HAP and ground terminals, the massive MIMO space, and the wide bandwidth in the mmWave band, the channel characteristics of HAP exhibit non-stationarities in time, space, and frequency domains. By deriving the temporal auto-correlation function (ACF), we explore the non-stationarity in the time domain and the impact of various parameters on the correlations across the HAP-MIMO channels. The spatial cross-correlation function (CCF) for massive MIMO scenarios, and the frequency correlation function (FCF) in the mmWave bands are also considered. Moreover, we conduct simulation research using MATLAB. Simulation results show that the theoretical results align well with the simulation results, and this highlights the fact that the constructed 3D GBSM can characterize the non-stationary characteristics of HAP-MIMO channels across the time, space, and frequency domains.

Hybrid Far- and Near-Field Modeling for Reconfigurable Intelligent Surface Assisted V2V Channels: A Sub-Array Partition Based Approach

Reconfigurable intelligent surface (RIS)-assisted communications has been a hot topic due to its promising advantages for future wireless networks. Existing works on RIS-assisted channel modeling have mainly focused on far-field propagation condition with planar wavefront assumption. In essence, the far-field condition does not always hold because the RIS array dimension may be comparable to the terminal distance, especially in RIS-assisted mobile networks. To this end, we propose a hybrid far- and near-field stochastic channel model for characterizing a RIS-assisted vehicle-to-vehicle (V2V) propagation environment, which takes into account both far-field and near-field propagation conditions. To achieve the balance between the modeling accuracy and complexity for the investigation of the RIS-assisted V2V propagation characteristics, we develop a sub-array partitioning scheme to dynamically divide the entire RIS array into several smaller sub-arrays, which makes planar wavefront assumption applicable for the sub-arrays. Important channel statistical properties, including spatial cross-correlation functions (CCFs), temporal auto-correlation functions (ACFs), and frequency correlation functions (FCFs), are derived and investigated. Simulation results are provided to show the performance of the proposed sub-array partition based hybrid far- and near-field modeling solution for RIS-assisted V2V channels.

Non-Stationarity Characterization and Geometry-Cluster-Based Stochastic Model for High-Speed Train Radio Channels

In time-variant high-speed train (HST) radio channels, the scattering environment changes rapidly with the movement of terminals, leading to a serious deterioration in communication quality. In the system-and link-level simulation of HST channels, this non-stationarity should be characterized and modeled properly. In this paper, the sizes of the quasi-stationary regions are quantified to measure the significant changes in channel statistics, namely, the average power delay profile (APDP) and correlation matrix distance (CMD), based on a measurement campaign conducted at 2.4 GHz. Furthermore, parameters of the multi-path components (MPCs) are estimated and a novel clustering-tracking-identifying algorithm is designed to separate MPCs into line-of-sight (LOS), periodic reflecting clusters (PRCs) from power supply pillars along the railway, and random scattering clusters (RSCs). Then, a non-stationary geometry-cluster-based stochastic model is proposed for viaduct and hilly terrain scenarios. Furthermore, the proposed model is verified by measured channel statistics such as the Rician K factor and the root mean square delay spread. The temporal autocorrelation function and the spatial cross-correlation function are presented. Quasi-stationary regions of the model are analyzed and compared with the measured data, the standardized IMT-Advanced (IMT-A) channel model, and a published non-stationary IMT-A channel model. The good agreement between the proposed model and the measured data demonstrates the ability of the model to characterize the non-stationary features of propagation environments in HST scenarios.

Physics-Based 3D End-to-End Modeling for Double-RIS Assisted Non-Stationary UAV-to-Ground Communication Channels

In this paper, we propose a three-dimensional (3D) physics-based double reconfigurable intelligent surface (RIS) cooperatively assisted multiple-input multiple-output (MIMO) stochastic channel model for unmanned aerial vehicle (UAV)-to-ground communication scenarios. The double-RIS is distributed on the surface of buildings can assist the UAV transmitter to reflect its own signals to the ground receiver (GR), and simultaneously enhance the propagation by passive beamforming on the RISs. In the proposed channel model, we derive the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">path power gains</i> for different propagation links between the UAV and GR, thus enabling the proposed channel model to effectively characterize both large- and small-scale fading characteristics of realistic UAV-to-ground communication systems. Furthermore, we derive the critical propagation properties of the proposed channel model, including the spatial cross-correlation functions (CCFs), temporal auto-correlation functions (ACFs), and frequency correlation functions (FCFs), with respect to different RIS reflection phase configurations as well as different RIS orientation angles. Numerical simulation results demonstrate the propagation characteristics of the proposed double-RIS assisted UAV-to-ground channel model behave better than those of traditional channel models with single-RIS link or LoS link, thereby validating the necessity of introducing double-RIS into UAV-to-ground communication.

Channel Modeling and Characteristics Analysis under Different 3D Dynamic Trajectories for UAV-Assisted Emergency Communications.

This study involved channel modeling and characteristics analysis of unmanned aerial vehicles (UAVs) according to different operating trajectories. Based on the idea of standardized channel modeling, air-to-ground (AG) channel modeling of a UAV was carried out, taking into consideration that both the receiver (Rx) and the transmitter (Tx) ran along different types of trajectories. In addition, based on Markov chains and a smooth-turn (ST) mobility model, the influences of different operation trajectories on typical channel characteristics-including time-variant power delay profile (PDP), stationary interval, temporal autocorrelation function (ACF), root mean square (RMS) delay spread (DS), and spatial cross-correlation function (CCF)-were studied. The multi-mobility multi-trajectory UAV channel model matched well with actual operation scenarios, and the characteristics of the UAV AG channel could be analyzed more accurately, thus providing a reference for future system design and sensor network deployment of sixth-generation (6G) UAV-assisted emergency communications.

A 3-D Semi-Deterministic MIMO Beam Channel Model for Cellular-Assisted Millimeter-Wave Vehicular Communications

The multiple-input multiple-output (MIMO)-based millimeter-wave (mmWave) propagation is envisioned as a key technology to offer greater bandwidths than previously available for vehicular communications. In this paper, we propose a three-dimensional (3-D) semi-deterministic MIMO beam channel model to characterize the fading properties of cellular-assisted mmWave communications. First, we analyze the digital beamforming effects on multipaths and find that beams act like spatial filters. Then, we propose a cluster generation method, which assemblies single-bounce (SB)-based reflection points and surrounding scatterers into a group. On this basis, the SB reflection and scattering propagation mechanisms via clusters are realized by using ray tracing (RT) and propagation-graph (PG) models, respectively. Furthermore, we use the directive scattering model to enhance modeling accuracy regarding scattering components. Based on our proposal, position and beamwidth-based channel statistical properties, including power delay profile (PDP), spatial cross-correlation function (CCF), Doppler power spectrum density (PSD), and additional path loss (PL) are fully investigated considering perfect beam alignment. Numerical results show that our proposal is capable of emulating beam-dependent mmWave channel and narrow beamwidths cause few multipaths and higher PL. Besides, it can capture the non-stationarities for given scenarios, which can be adapted to various communication scenarios by establishing the corresponding digital maps.

Collective photon emission of two correlated atoms in free space

By preparing two distant emitters in entangled Dicke states via detection of a single photon, the subsequent spatiotemporal photon emission is investigated. Depending on the parity of the established quantum state, emission patterns for the second scattered photon are observed featuring spatial superradiance as well as subradiance. We employ ultrafast single-photon resolving cameras with high spatial resolution disclosing the spatiotemporal emission characteristics. By recording the first photon in one direction and the second photon in another, revealing the spatial two-photon cross-correlation function ${g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})$, we characterize the collective spontaneous emission behavior of two ions in free space. We explain the observed contrast of ${g}^{(2)}({\mathbf{r}}_{1},{\mathbf{r}}_{2})$ considering independently derived experimental parameters. Our results show how the detection of a single photon can profoundly modify the collective spontaneous emission dynamics of an atomic ensemble.

A General 3-D Nonstationary GBSM for Underground Vehicular Channels

Reliable and efficient communications are indispensable for vehicles in underground environments. Underground wireless channels present a number of unique properties, such as guided propagation, rich scatterers, and near-field/far-field effect. In this article, a 3-D twin cluster geometry-based stochastic model (GBSM) is proposed to describe underground vehicular channel characteristics in both pillar and tunnel scenarios. The proposed model supports arbitrary trajectory mobility of vehicles and multiple antenna configurations at the transmitter (Tx) and the receiver (Rx). The cluster time evolution is modeled by different scatterer generation and updating methods to simulate the channel characteristics such as nonstationarity, near-field/far-field differences, and waveguide effects. Based on the proposed channel model, the statistical characteristics of the channel are derived and simulated, including the temporal autocorrelation function (ACF), spatial cross-correlation function (CCF), delay power spectrum density (PSD), Doppler PSD, and so on. Besides, underground channel measurements at 2.5/3.5 GHz are conducted in a garage scenario. Comparison results of channel measurements and simulations validate the accuracy and usefulness of the proposed GBSM.

Ultra-Massive MIMO Channel Measurements at 5.3 GHz and a General 6G Channel Model

Ultra-massive multiple-input multiple-output (MIMO) technology will bring unique channel characteristics that need to be fully explored through channel measurements and channel modeling. In this paper, single-user and multi-user channel measurements using ultra-massive MIMO antenna arrays with different configurations are conducted at 5.3 GHz band. The non-stationarity, spherical wavefront, channel hardening, and sparse properties are validated by the channel measurements. Correspondingly, a general three-dimensional (3D) sixth generation (6G) non-stationary geometry-based stochastic model (GBSM) for ultra-massive MIMO communication systems is proposed. The statistical properties of channel measurements and the corresponding channel model are studied, including delay power spectral density (PSD), angular PSD, spatial cross-correlation function (SCCF), normalized user-side correlation matrix, singular value spread (SVS), degrees of freedom (DoF), and diversity level. In addition, channel capacities of channel measurements and the corresponding channel model are studied. The accuracy of the proposed general channel model is validated by the consistency of simulation results and measurement results, which indicates that the proposed model can be applied to ultra-massive MIMO communication systems.

A Non-Stationary 3D-GBSM V2V Channel Model for Wideband Massive MIMO Systems

This letter presents a non-stationary 3D-GBSM vehicle to vehicle (V2V) channel model in tunnel environment based on massive multiple-input multiple-output (MIMO) antenna arrays. Instead of plane wavefront assumptions used in traditional MIMO systems, the proposed channel model considers spherical wavefront assumption for V2V communications. Firstly, the channel impulse response (CIR) and closed-form expression for probability density function (PDF) of angle-of-departure (AoD) and angle-of-arrival (AoA) in elevation and azimuth planes are derived. Afterwards, the expressions for the spatial cross-correlation function (S-CCF) and doppler power spectrum density (DPSD) due to the non-stationarity of transmitting (NT) and receiving (MR) antenna arrays are derived by considering different time separation, antenna arrays spacing, moving velocity, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -factor for line of sight (LoS) and non-line of sight (NLoS) propagation paths. The statistical characteristics of the proposed V2V wideband massive MIMO model are validated by measurement, analytical, and simulation results, verifying the effectiveness and adaptability of the proposed model in high-speed train (HST) environment.

Channel Characterization for Hyperloops Using the Nonstationary Geometry-Based Model

As a novel means of high-speed transportation, the Hyperloop can proceed at an ultra-high speed (more than 1000 km/h) in the long and narrow pipelines. In this paper, the channel characteristic of the Hyperloop wireless communication systems is the main objective. Based on the geometric scattering theories, a novel nonstationary channel model is proposed to investigate the channel characteristics for Hyperloop train-to-ground communications. According to this model, the channel impulse response (CIR) is obtained, and the closed-form expressions of the multi-link spatial-temporal correlation functions, including the spatial cross-correlation function (CCF) and the temporal autocorrelation function (ACF) are derived and analyzed. Simulation results show that a high correlation between the multi-link channels in vacuum tube scenario can be observed. The relevant research results will contribute to the design of future Hyperloop wireless communication system.

A stochastic confocal ellipsoid channel model for high speed railway MIMO communication systems

This paper investigates the channel model for multiple-input multiple-output (MIMO) communication systems in high speed railway (HSR) networks. Specially, a three-dimensional (3D) confocal stochastic geometry ellipsoid model is proposed for modeling the MIMO channels. Normalized space–time correlation function(ST CF), Spatial cross correlation function (CCF) and level crossing rate (LCR) of both theoretical and simulation model are have been derived and analyzed. As a 3D GBSM, the proposed confocal ellipsoid model has lower correlation in spatial cross-correlation function (CCF) compared with that of the corresponding two-dimensional (2D) ellipse model. Measurement data of different HSR scenarios verify the applicability of the confocal ellipsoid model.

A 3D Non-Stationary Wideband Massive MIMO Channel Model Based on Ray-Level Evolution

In this paper, a novel space-time non-stationary three-dimensional (3D) wideband massive multiple-input multiple-output (MIMO) channel model is proposed. We then propose a ray-level process to model the spatial-temporal evolution of individual multipath components (MPCs), including near-field effects and (dis)appearance, and cluster-level large-scale fading. The proposed evolution process can flexibly control rays&#x2019; lifespans and smoothness of (dis)appearance in both space and time domains. In addition, we propose an improved Rayleigh-distance criterion to determine the most adequate wavefront for each cluster and ray. Existing models can easily implement the proposed criterion and make a more efficient use of computation resources. Also, a Gamma-Poisson mixture distribution is introduced to model the distribution of the number of clusters when multiple locations of the mobile station are considered. Key statistical properties of the channel, including the autocorrelation function (ACF), Doppler power spectral density (PSD), spatial cross-correlation function (S-CCF), and frequency correlation function (FCF), are derived and the impact of the ray-level evolution process on them is analyzed. We demonstrate the correctness of the derived statistical properties through numerical and simulation results.

A 3-D Nonstationary Wideband V2V GBSM With UPAs for Massive MIMO Wireless Communication Systems

This article proposes a novel 3-D nonstationary wideband vehicle-to-vehicle (V2V) geometry-based stochastic model (GBSM) with uniform planar antenna arrays (UPAs) for massive multiple-input–multiple-output (MIMO) wireless communication systems. In the proposed GBSM, a novel method, so-called birth–death (BD) process and seed algorithm-based selective cluster evolution, is developed to capture the space nonstationarity of V2V massive MIMO with UPA channels. The time nonstationarity is further mimicked by employing this novel method over the entire timeline. In addition, the proposed GBSM not only models the reflection of the ground, but also divides clusters into static clusters and dynamic clusters to sufficiently investigate the impact of vehicular traffic density (VTD) on channel statics. The channel parameters are properly calculated by 3-D vectors, resulting in the proposed GBSM with high accuracy and low complexity. Important statistical properties, such as the space-time correlation function (S-T CF), spatial cross-correlation function (CCF), temporal auto-correlation function (ACF), and Doppler power spectrum density (PSD) are derived and thoroughly investigated. Simulation results show that the space-time nonstationarity is successfully mimicked and the VTD has a significant impact on channel statistics. Finally, an excellent agreement is achieved between simulation results and measurements, validating the accuracy of the proposed GBSM.

Three-Dimensional Geometry-Based Stochastic Channel Modeling for Intelligent Reflecting Surface-Assisted UAV MIMO Communications

In this letter, a three-dimensional (3D) geometry-based stochastic multiple-input multiple-output (MIMO) channel model for intelligent reflecting surface (IRS)-assisted unmanned aerial vehicle (UAV) communications is proposed. The IRS is distributed on the surface of buildings to assist the UAV transmitter to reflect its signals to the receiver on the ground level and to improve the communication quality by passive beamforming at the IRS. In such a channel model, the signals transmitted from the UAV transmitter will first get scattered by the clusters between the UAV and IRS before arriving at the IRS, and subsequently arrive at the ground receiver. We separate this channel model into a subchannel model between the UAV and the IRS, as well as a subchannel model between the IRS and the receiver. Based on the derivations of complex channel coefficients for the above two subchannel models, we investigate the impact of IRS on the underlying propagation channel by studying the spatial cross-correlation functions (CCFs). Simulation results are provided to show the statistical propagation characteristics of the IRS-assisted UAV MIMO channels.

A Novel Non-Stationary 6G UAV Channel Model for Maritime Communications

To achieve space-air-ground-sea integrated communication networks for future sixth generation (6G) communications, unmanned aerial vehicle (UAV) communications applying to maritime scenarios serving as mobile base stations have recently attracted more attentions. The UAV-to-ship channel modeling is the fundamental for the system design, testing, and performance evaluation of UAV communication systems in maritime scenarios. In this paper, a novel non-stationary multi-mobility UAV-to-ship channel model is proposed, consisting of three kinds of components, i.e., the line-of-sight (LoS) component, the single-bounce (SB) components resulting from the fluctuation of sea water, and multi-bounce (MB) components introduced by the waveguide effect over the sea surface. In the proposed model, the UAV as the transmitter (Tx), the ship as the receiver (Rx), and the clusters between the Tx and Rx, can be seen as moving with arbitrary velocities and arbitrary directions. Then, some typical statistical properties of the proposed UAV-to-ship channel model, including the temporal autocorrelation function (ACF), spatial cross-correlation function (CCF), Doppler power spectrum density (PSD), delay PSD, angular PSD, stationary interval, and root mean square (RMS) delay spread, are derived and investigated. Finally, by comparing with the available measurement data, the accuracy of proposed channel model is validated.

A Dynamic 3-D Wideband GBSM for Cooperative Massive MIMO Channels in Intelligent High-Speed Railway Communication Systems

Coordinated multipoint (CoMP) and massive multiple-input multiple-output (mMIMO) are two of promising technologies in future intelligent high-speed railway (HSR) communication systems, whose performance is fundamentally determined by the characteristics of cooperative mMIMO channels. This article proposes a dynamic three-dimensional (3-D) wideband geometry-based stochastic model (GBSM) for HSR cooperative mMIMO channels. The proposed GBSM employs a sphere model and two elliptic-cylinder models to describe common and uncommon clusters for different links, and integrates the dynamic cluster evolution in both time and array domains. Statistical properties of the cooperative mMIMO model are investigated, such as multi-link spatial cross-correlation function and sum rate capacity. A corresponding dynamic 3-D wideband simulation model for the HSR cooperative mMIMO channel is also proposed. Finally, numerical results of the statistical properties are analyzed, and the proposed model is validated by realistic HSR channel measurement data, in terms of dual-link spatial cross-correlation and channel capacity. This model is more practical and will be helpful for facilitating the design and performance evaluation of future intelligent HSR communication systems.

A 32 × 32-Pixel CMOS Imager for Quantum Optics With Per-SPAD TDC, 19.48% Fill-Factor in a 44.64-μm Pitch Reaching 1-MHz Observation Rate

This article reports the design and characterization of a 32 $\times $ 32 single-photon avalanche diode (SPAD) time-resolved image sensor for quantum imaging applications fabricated in a 150-nm CMOS standard technology. A per-SPAD time-to-digital converter (TDC) records the spatial cross correlation functions of a flux of entangled photons. Each 44.64- $\mu \text{m}$ pixel with 19.48% fill-factor features a 210.2-ps resolution, 50-ns (8-bit) range TDC with 1.28-LSB differential and 1.92-LSB integral nonlinearity (DNL/INL). The sensor achieves an observation rate of up to 1 MHz through a current-based mechanism that avoids reading empty frames when the photon rates are low. A row-skipping mechanism detects the absence of SPAD activity in a row to increase the duty cycle. These two features require only three transistors in each pixel. The sensor functionality is demonstrated in a quantum imaging experiment that achieves super-resolution.

A Novel 3D UAV Channel Model for A2G Communication Environments Using AoD and AoA Estimation Algorithms

In this article, we propose a three-dimensional (3D) multi-input multi-output (MIMO) channel model for air-to-ground (A2G) communications in unmanned aerial vehicles (UAV) environments, where the UAV transmitter and ground receiver are in motion in the air and on the ground, respectively. A novel angular estimation algorithm is proposed to estimate the real-time azimuth angle of departure (AAoD), elevation angle of departure (EAoD), azimuth angle of arrival (AAoA), and elevation angle of arrival (EAoA) based on the non-stationary nature of the channel model. In the model, we investigate the time-varying spatial cross-correlation functions (CCFs) and temporal auto-correlation functions (ACFs) with respect to the different moving directions and velocities of the UAV transmitter and ground receiver. Furthermore, we derive and study the Doppler power spectral densities (PSDs) and power delay profiles (PDPs) of the proposed channel model. Numerical results show that characteristics of the proposed channel model are very close to those of practical measurements, which provide a new and practical approach to evaluate the performance of next generation UAV-MIMO communication systems.