Stationarity Region Research Articles

A General Bayesian Functional Spatial Partitioning Method for Multiple Region Discovery Applied to Prostate Cancer MRI.

Current protocols to estimate the number, size, and location of cancerous lesions in the prostate using multiparametric magnetic resonance imaging (mpMRI) are highly dependent on reader experience and expertise. Automatic voxel-wise cancer classifiers do not directly provide estimates of number, location, and size of cancerous lesions that are clinically important. Existing spatial partitioning methods estimate linear or piecewise-linear boundaries separating regions of local stationarity in spatially registered data and are inadequate for the application of lesion detection. Frequentist segmentation and clustering methods often require pre-specification of the number of clusters and do not quantify uncertainty. Previously, we developed a novel Bayesian functional spatial partitioning method to estimate the boundary surrounding a single cancerous lesion using data derived from mpMRI. We propose a Bayesian functional spatial partitioning method for multiple lesion detection with an unknown number of lesions. Our method utilizes functional estimation to model the smooth boundary curves surrounding each cancerous lesion. In a Reversible Jump Markov Chain Monte Carlo (RJ-MCMC) framework, we develop novel jump steps to jointly estimate and quantify uncertainty in the number of lesions, their boundaries, and the spatial parameters in each lesion. Through simulation we show that our method is robust to the shape of the lesions, number of lesions, and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using MRI.

A novel Bayesian functional spatial partitioning method with application to prostate cancer lesion detection using MRI.

Spatial partitioning methods correct for nonstationarity in spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning boundaries. This is inadequate for detecting an arbitrarily shaped anomalous spatial region within a larger area. We propose a novel Bayesian functional spatial partitioning (BFSP) algorithm, which estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct distribution or spatial process. Our method utilizes transitions between a fixed Cartesian and moving polar coordinate system to model the smooth boundary curves using functional estimation tools. Using adaptive Metropolis-Hastings, the BFSP algorithm simultaneously estimates the partitioning boundary and the parameters of the spatial distributions within each region. Through simulation we show that our method is robust to shape of the target zone and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using magnetic resonanceimaging.

A Novel B5G Frequency Nonstationary Wireless Channel Model

Frequency nonstationarity is an important statistical property of beyond fifth generation wireless communication channels due to extremely large bandwidths used in millimeter wave (mmWave) and teraherz communications. In this article, a general averaged power delay profile method is first introduced as a metric to determine the stationarity regions of wireless channels in the time, frequency, and spatial domains. Then, we apply this method to determine the frequency stationarity regions (FSRs) of channel measurements in a sub-6-GHz frequency band (2-4 GHz) and two mmWave frequency bands (14-16 GHz and 28-30 GHz). Frequency nonstationary (FnS) properties are found from all of the three bands. A novel FnS channel model is then proposed to model wireless channels in all frequency bands. We first split a FnS channel into a few frequency stationary (FS) subband channels and model them one by one, which are finally combined as an FnS channel model considering the cluster evolution in the frequency domain and the frequency consistency of subband channels. Simulation results show that the frequency correlation functions of the proposed FnS channel model fit well those of the measured FnS channels.

Modeling Panel Time Series with Mixture Autoregressive Model

This paper considers the mixture autoregressive panel (MARP) model. This model can capture the burst and multi-modal phenomenon in some panel data sets. It also enlarges the stationarity region of the traditional AR model. An estimation method based on the EM algorithm is proposed and the assumption required of the model is quite low. To illustrate the method, we fitted the MARP model to the gray-sided voles data. Another MARP model with less restriction is also proposed.

Analysis of Non-Stationarity for 5.9 GHz Channel in Multiple Vehicle-to-Vehicle Scenarios.

The vehicle-to-vehicle (V2V) radio channel is non-stationary due to the rapid movement of vehicles. However, the stationarity of the V2V channels is an important indicator of the V2V channel characteristics. Therefore, we analyzed the non-stationarity of V2V radio channels using the local region of stationarity (LRS). We selected seven scenarios, including three directions of travel, i.e., in the same, vertical, and opposite directions, and different speeds and environments in a similar driving direction. The power delay profile (PDP) and LRS were estimated from the measured channel impulse responses. The results show that the most important influences on the stationary times are the direction and the speed of the vehicles. The average stationary times for driving in the same direction range from 0.3207 to 1.9419 s, the average stationary times for driving in the vertical direction are 0.0359–0.1348 s, and those for driving in the opposite direction are 0.0041–0.0103 s. These results are meaningful for the analysis of the statistical characteristics of the V2V channel, such as the delay spread and Doppler spread. Small-scale fading based on the stationary times affects the quality of signals transmitted in the V2V channel, including the information transmission rate and the information error code rate.

Memory-dependent noise-induced resonance and diffusion in non-Markovian systems.

We study random processes with nonlocal memory and obtain solutions of the Mori-Zwanzig equation describing non-Markovian systems. We analyze the system dynamics depending on the amplitudes ν and μ_{0} of the local and nonlocal memory and pay attention to the line in the (ν,μ_{0}) plane separating the regions with asymptotically stationary and nonstationary behavior. We obtain general equations for such boundaries and consider them for three examples of nonlocal memory functions. We show that there exist two types of boundaries with fundamentally different system dynamics. On the boundaries of the first type, diffusion with memory takes place, whereas on borderlines of the second type the phenomenon of noise-induced resonance can be observed. A distinctive feature of noise-induced resonance in the systems under consideration is that it occurs in the absence of an external regular periodic force. It takes place due to the presence of frequencies in the noise spectrum, which are close to the self-frequency of the system. We analyze also the variance of the process and compare its behavior for regions of asymptotic stationarity and nonstationarity, as well as for diffusive and noise-induced-resonance borderlines between them.

Identifying regions of inhomogeneities in spatial processes via an M-RA and mixture priors.

Soils have been heralded as a hidden resource that can be leveraged to mitigate and address some of the major global environmental challenges. Specifically, the organic carbon stored in soils, called soil organic carbon (SOC), can, through proper soil management, help offset fuel emissions, increase food productivity, and improve water quality. As collecting data on SOC are costly and time-consuming, not much data on SOC are available, although understanding the spatial variability in SOC is of fundamental importance for effective soil management. In this manuscript, we propose a modeling framework that can be used to gain a better understanding of the dependence structure of a spatial process by identifying regions within a spatial domain where the process displays the same spatial correlation range. To achieve this goal, we propose a generalization of the multiresolution approximation (M-RA) modeling framework of Katzfuss originally introduced as a strategy to reduce the computational burden encountered when analyzing massive spatial datasets. To allow for the possibility that the correlation of a spatial process might be characterized by a different range in different subregions of a spatial domain, we provide the M-RA basis functions weights with a two-component mixture prior with one of the mixture components a shrinking prior. We call our approach the mixture M-RA. Application of the mixture M-RA model to both stationary and nonstationary data show that the mixture M-RA model can handle both types of data, can correctly establish the type of spatial dependence structure in the data (e.g., stationary versus not), and can identify regions of localstationarity.

Real-Time Vehicular Wireless System-Level Simulation

Future automation and control units for advanced driver assistance systems (ADAS) will exchange sensor and kinematic data with nearby vehicles using wireless communication links to improve traffic safety. In this paper we present an accurate real-time system-level simulation for multi-vehicle communication scenarios to support the development and test of connected ADAS systems. The physical and data-link layer are abstracted and provide the frame error rate (FER) to a network simulator. The FER is strongly affected by the non-stationary doubly dispersive fading process of the vehicular radio communication channel. We use a geometry-based stochastic channel model (GSCM) to enable a simplified but still accurate representation of the non-stationary vehicular fading process. The propagation path parameters of the GSCM are used to efficiently compute the time-variant condensed radio channel parameters per stationarity region of each communication link during run-time. Five condensed radio channel parameters mainly determine the FER forming a parameter vector: path loss, root mean square delay spread, Doppler bandwidth, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -factor, and line-of-sight Doppler shift. We measure the FER for a pre-defined set of discrete grid points of the parameter vector using a channel emulator and a given transmitter-receiver modem pair. The FER data is stored in a table and looked up during run-time of the real-time system-level simulation. We validate our methodology using empirical measurement data from a street crossing scenarios demonstrating a close match in terms of FER between simulation and measurement.

Experimental Study on the Impact of Antenna Characteristics on Non-Stationary V2I Channel Parameters in Tunnels

This paper analyses the experimentally-assessed dual-polarized (DP) mobile channel in a tunnel environment at 1.35 GHz under traffic conditions. We investigate the impact of antenna polarization and radiation pattern on the non-stationary vehicle-to-infrastructure (V2I) channel. Basic channel evaluation metrics are examined including path gain, co-polarization ratio (CPR), and cross-polarization discrimination (XPD). In addition, the stationarity region is estimated using the channel correlation function approach, and used to calculate the time-varying delay and Doppler power profiles. Statistical models are presented for parameters like CPR, XPD, RMS delay and Doppler spreads, where the lognormal distribution provides the best fit. The polarization and the opening angle of the antennas into the propagation channel are found to strongly influence the observed non-stationarity of the channel. They impact the degree of multipath richness that is captured, thus providing different path gain, delay and Doppler spreads. Based on our analysis, the directional antenna with vertical polarization provides the longest stationarity time of 400 ms at 90 km/h, as well as the highest path gain and lowest dispersion. Furthermore, the DP channel capacity is calculated and its dependence on different normalization approaches is investigated. We propose a more accurate normalization for the DP channels that takes the conservation of energy into account. Moreover, the subchannels correlation coefficients are determined. While the condition number is found to be low on average, the correlation results show high correlation among the DP subchannels. As conclusion, we show how the CPR and XPD play the main role in providing multiplexing gain for DP tunnel channels.

Measured User Correlation in Outdoor-to-Indoor Massive MIMO Scenarios

The performance of a multi-user multiple-input multiple-output (MIMO) system is mainly determined by the correlation of user channels. Applying channel models without spatial correlation or spatially inconsistent channel models for performance analysis leads to an under-estimation of spatial correlation and therefore to overly optimistic system performance. This is especially pronounced when the wireless channel is modeled as i.i.d. Rayleigh fading for users in a rich scattering environment, for example, for indoor users. To analyze the spatial channel correlation in massive MIMO systems, we performed wireless channel measurements in three different scenarios. In each scenario, we measure 148 receiver positions, spread over a length of almost 9m. Since the wireless channel statistics change with receiver position, we perform a stationarity analysis. We provide a statistical analysis of the measured channel in terms of amplitude distribution and user-side spatial correlation within the region of stationarity. This analysis shows that, even for a deep-indoor user location, the spatial correlation is significantly higher compared to a Rician channel model with the same $K$ factor. We model the measured channel by means of a Rician channel model and a spatially consistent channel model, which is based on the scenario geometry, to provide an insight for the observed propagation phenomena. Results show that the user correlation is not negligible for massive MIMO in outdoor-to-indoor scenarios. The achievable spectral efficiency with linear precoding is 20% lower compared to the Rician channel model, even for large inter-user distances of 6m.

Stationarity Analysis of V2I Radio Channel in a Suburban Environment

Due to rapid changes in the environment, vehicular communication channels no longer satisfy the assumption of wide-sense stationary uncorrelated scattering. The non-stationary fading process can be characterized by assuming local stationarity regions with finite extent in time and frequency. The local scattering function (LSF) and channel correlation function (CCF) provide a framework to characterize the mean power and correlation of the non-stationary channel scatterers, respectively. In this paper, we estimate the LSF and CCF from measurements collected in a vehicle-to-infrastructure radio channel sounding campaign in a suburban environment in Lille, France. Based on the CCF, the stationarity region is evaluated in time as 567 ms and used to capture the non-stationary fading parameters. We obtain the time-varying delay and Doppler power profiles from the LSF, and we analyze the corresponding root-mean-square delay and Doppler spreads. We show that the distribution of these parameters follows a lognormal model. Finally, application relevance in terms of channel capacity and diversity techniques is discussed. Results show that the assumption of ergodic capacity and the performance of various diversity techniques depend on the stationarity and coherence parameters of the channel. The evaluation and statistical modeling of such parameters can provide a way of tracking channel variation, hence, increasing the performance of adaptive schemes.

Real-Time Geometry-Based Wireless Channel Emulation

Connected autonomous vehicles and industry 4.0 production scenarios require ultrareliable low-latency communication links. The varying positions of transmitter, reflecting objects, and receiver cause a nonstationary time- and frequency-selective fading process. In this paper, we present the necessary hardware architecture and signal processing algorithms for a real-time geometry-based channel emulator, that is needed for testing of wireless control systems. We partition the nonstationary fading process into a sequence of local stationarity regions and model the channel impulse response as sum of propagation paths with time-varying attenuation, delay, and Doppler shift. We implement a subspace projection of the propagation path parameters, to compress the time-variant channel impulse response. This enables a low data-rate link from the host computer, which computes the geometry-based propagation paths, to the software defined radio unit, that implements the convolution on a field programmable gate array (FPGA). With our new architecture, the complexity of the FPGA implementation becomes independent of the number of propagation paths. Our channel emulator can be parametrized by all known channel models. Without loss of generality, we use a parameterization by a geometry-based stochastic channel model, due to its nonstationary nature. We provide channel impulse response measurements of the channel emulator, using the RUSK Lund channel sounder for a vehicular scenario with 617 propagation paths. A comparison of the time-variant power delay profile and Doppler spectral density of simulated and emulated channel impulse response showed a close match with an error smaller than -35 dB. The results demonstrate that our channel emulator is able to accurately emulate nonstationary fading channels with continuously changing path delays and Doppler shifts.

A Hybrid Ray and Graph Model for Simulating Vehicle-to-Vehicle Channels in Tunnels

Wave propagation in tunnels for vehicle-to-vehicle (V2V) communications scenarios is characterized by multiple diffuse reflections on tunnel surfaces as well as specular reflections on other objects inside the tunnel, leading to a nonstationary fading process. Such a fading process is difficult to model by ray tracing (RT), requiring a prohibitively high computational complexity due to the large number of diffuse reflections. In this paper, we propose two new ideas for modeling diffuse reflections in nonstationary scenarios: 1) We partition the nonstationary fading process into multiple stationarity regions with a given extent in time and frequency for which approximate wide-sense stationarity can be assumed; 2) we propose a hybrid model, tightly interlinking RT with a propagation graph, such that vertices for the propagation graph are obtained from interaction points calculated by RT for each stationarity region. We compare our hybrid model with measurement data in terms of the time-variant power-delay and the Doppler-power spectral-density as well as the root-mean square delay- and Doppler-spread. This analysis shows, that our hybrid model is the first numerical simulation model that is able to model diffuse reflections inside a tunnel with correct nonstationary (i.e., time-variant) temporal correlation for a nonstationary V2V communication link.

Real‐Time Emulation of Nonstationary Channels in Safety‐Relevant Vehicular Scenarios

This paper proposes and discusses the architecture for a real‐time vehicular channel emulator capable of reproducing the input/output behavior of nonstationary time‐variant radio propagation channels in safety‐relevant vehicular scenarios. The vehicular channel emulator architecture aims at a hardware implementation which requires minimal hardware complexity for emulating channels with the varying delay‐Doppler characteristics of safety‐relevant vehicular scenarios. The varying delay‐Doppler characteristics require real‐time updates to the multipath propagation model for each local stationarity region. The vehicular channel emulator is used for benchmarking the packet error performance of commercial off‐the‐shelf (COTS) vehicular IEEE 802.11p modems and a fully software‐defined radio‐based IEEE 802.11p modem stack. The packet error ratio (PER) estimated from temporal averaging over a single virtual drive and the packet error probability (PEP) estimated from ensemble averaging over repeated virtual drives are evaluated and compared for the same vehicular scenario. The proposed architecture is realized as a virtual instrument on National Instruments™ LabVIEW. The National Instrument universal software radio peripheral with reconfigurable input‐output (USRP‐Rio) 2953R is used as the software‐defined radio platform for implementation; however, the results and considerations reported are of general purpose and can be applied to other platforms. Finally, we discuss the PER performance of the modem for two categories of vehicular channel models: a vehicular nonstationary channel model derived for urban single lane street crossing scenario of the DRIVEWAY’09 measurement campaign and the stationary ETSI models.

Evaporation in action sensed by multiwavelength Doppler radars

AbstractThis work documents a rain case dominated by evaporation which occurred at the Atmospheric Radiation Measurement site in Oklahoma on 15 September 2011. A recently developed algorithm, applied to radar Doppler spectra measured at Ka and W band, provides the vertical evolution of binned drop size distributions (DSDs) and of the vertical wind. Such retrieved quantities are used in connection with relative humidity (RH) profiles to derive evaporation rates and atmospheric cooling rates. In addition, in regions of stationarity and of light rain, when other microphysical processes are negligible, the presented case study suggests the possibility of retrieving RH profiles from the vertical evolution of the drop size distributions. The key is to characterize the gradient of the rain mass flux between successive levels. Such signal is particularly weak and can be enhanced thanks to a substantial averaging of the retrieved DSD over approximately 5 min and 250 m (eight range gates). The derived profile agrees with the retrieval from coincident Raman lidar observations within a 10% RH difference. These results suggest that other rain microphysical processes could be studied by combining the radar‐based DSD retrieval with ancillary RH observations.

Dual-Polarized Narrowband MIMO LMS Channel Measurements in Urban Environments

This paper presents the postprocessing results of a dual-polarized multiple-input-multiple-output (MIMO) channel measurement campaign, investigating two land mobile satellite link scenarios in urban environments. Basic channel evaluation metrics are examined to facilitate the selection of the appropriate communication technique. The ergodic channel capacity is found between 4.1 and 6.1 b/s/Hz and varies significantly with the elevation angle. The capacity is highly correlated with the terminal trajectory and signal reception. The cross-polarization discrimination (XPD) is found between 14.2 and 22.5 dB, whereas the cross-polarization isolation (XPI) is found between 12.8 and 21 dB, respectively. Furthermore, the correlation statistics and channel capacities are well approximated by existing stochastic channel models. Finally, from the channel stationarity analysis, large stationarity regions are found, the existence of which is also correlated with the terminal trajectory. The mean quasi-stationarity time is found between 41 and 66 s for different environments.

A stochastic recurrence equations approach for score driven correlation models

ABSTRACTWe describe stationarity and ergodicity (SE) regions for a recently proposed class of score driven dynamic correlation models. These models have important applications in empirical work. The regions are derived from sufficiency conditions in Bougerol (1993) and take a nonstandard form. We show that the nonstandard shape of the sufficiency regions cannot be avoided by reparameterizing the model or by rescaling the score steps in the transition equation for the correlation parameter. This makes the result markedly different from the volatility case. Observationally equivalent decompositions of the stochastic recurrence equation yield regions with different shapes and sizes. We use these results to establish the consistency and asymptotic normality of the maximum likelihood estimator. We illustrate our results with an analysis of time-varying correlations between U.K. and Greek equity indices. We find that also in empirical applications different decompositions can give rise to different conclusions regarding the stability of the estimated model.

Stationarity Regions for Ultrawideband Channels

In this letter, extracting the stationarity regions (SRs), where the channel statistics changes are insignificant, for ultrawideband (UWB) channel is achieved. SRs are found based on the correlation between consecutive power delay profiles (PDPs). The PDPs are found from channel measurement data for a frequency range of 3.1-5.3 GHz. The measured channel exhibits the sparsity behavior. Results show that the obtained SRs are between 0.27-0.32 m, where short distances show the variability of the channel. Moreover, the results are compared to standard probability density functions (PDFs). The generalized extreme value, Weibull, and exponential distributions are seen as the best fitted PDFs.

Spatial Stationarity of Ultrawideband and Millimeter Wave Radio Channels

For radio channels with broad bandwidth resource, such as those often used for ultrawideband (UWB) and millimeter wave (mmwave) systems, the Wide-Sense Stationary Uncorrelated Scattering (WSSUS) and spatial stationary assumptions are more critical than typical cellular channels with very limited bandwidth resource. This paper studies spatial stationarity and bandwidth dependency of the Multipath Component (MPC) parameters, and the concept of local region of stationarity (LRS) is used as the measure of the physical stationarity region. LRS calculation results based on channel measurements show that the size of LRS is bandwidth dependent in all measured bands, 2–4 GHz, 14–16 GHz, and 28–30 GHz. The results in this paper point out that an inappropriate choice of bandwidth in channel parameter estimation could violate spatial stationary assumptions. The paper indicates LRS sizes for different bandwidths in the three bands.

A Dynamic Wideband Directional Channel Model for Vehicle-to-Vehicle Communications

Vehicle-to-vehicle (V2V) communications have received a lot of attention due to their numerous applications in traffic safety. The design, testing, and improvement of the V2V system hinge critically on the understanding of the propagation channels. An important feature of the V2V channel is the time variance. To statistically model the time-variant V2V channels, a dynamic wideband directional channel model is proposed in this paper, based on measurements conducted at 5.3 GHz in suburban, urban, and underground parking environments. The model incorporates both angular and delay domain properties and the dynamic evolution of multipath components (MPCs). The correlation matrix distance is used to determine the size of local wide-sense stationary (WSS) region. Within each WSS time window, MPCs are extracted using the Bartlett beamformer. A multipath distance-based tracking algorithm is used to identify the “birth” and “death” of such paths over different stationarity regions, and the lifetime of MPC is modeled with a truncated Gaussian distribution. Distributions for the number of multipaths and their positions are statistically modeled. Within each path lifetime, the initial power is found to depend on the excess delay, and a linear polynomial function is used to model the variations within the lifetime. In addition, a Nakagami distribution is suggested to describe the fading behavior. Finally, the model implementation is validated by comparison of second-order statistics between measurements and simulations.