Multipath Model Research Articles

A Physical Model for GPS Multipath Caused by Land Reflections: Toward Bare Soil Moisture Retrievals

Reflected Global Positioning System (GPS) signals can be used to infer information about soil moisture in the vicinity of the GPS antenna. Interference of direct and reflected signals causes the composite signal, observed using signal-to-noise ratio (SNR) data, to undulate with time while the GPS satellite ascends or descends at relatively low elevation angles. The soil moisture change affects both the phase of the SNR modulation pattern and its magnitude. In order to more thoroughly understand the mechanism of how the soil moisture change leads to a change in the SNR modulation, we built an electrodynamic model of GPS direct and reflected signal interference, i.e., multipath, that has a bare-soil model as the input and the total GPS received power as the output. This model treats soil as a continuously stratified medium with a specific composition of material ingredients having complex dielectric permittivity according to well-known mixing models. The critical part of this electrodynamic model is a numerical algorithm that allows us to calculate polarization-dependent reflection coefficients of such media with various profiles of dielectric permittivity dictated by the soil type and moisture. In this paper, we demonstrate how this model can reproduce and explain the main features of experimental multipath modulation patterns such as changes in phase and amplitude. We also discuss the interplay between true penetration depth and effective reflector depth. Based on these modeling comparisons, we formulate recommendations to improve the performance of bare soil moisture retrievals from the data obtained using GPS multipath modulation.

Network coding based reliable disjoint and braided multipath routing for sensor networks

This paper presents network coding based reliable disjoint and braided multipath routing (NC-RMR ) for sensor networks, which forms multipath by hop-by-hop method and only maintains local path information of each node without establishing end-to-end paths. Neighbors of each local node are divided into groups according to their hops to sink nodes to improve the network load balancing. For further performance improvement of NC-RMR with disjoint multipath model, local nodes select their own backup nodes in neighbor nodes to form additional logical paths, which implement a braided multipath model. Security advantages of NC-RMR with multipath and network coding mechanisms are analyzed. Analytical and simulation results prove that braided multipath routing model has better performance over disjoint model, and NC-RMR protocol can reduce the required number of transmission paths, ensure load balance of sensor network system, reduce the energy consumption of nodes.

Forwarding via checkpoints: Geographic routing on always-on sensors

Data forwarding is an essential function in wireless sensor networks (WSNs). It is well-known that geographic forwarding is an efficient scheme for WSNs as it requires maintaining only local topology information to forward data to a central gathering point, called the sink (or base station), for further analysis and processing. In this paper, we propose an energy-efficient data forwarding protocol for WSNs, called Weighted Localized Delaunay Triangulation-based data forwarding (WLDT), with a goal to extending the network lifetime. Specifically, WLDT selects as forwarders the sensors with high remaining energy and whose locations lie nearer the shortest path between source sensors and a single sink, thus helping the sensors minimize their average energy consumption. More precisely, WLDT defines checkpoints to build energy-efficient data forwarding paths and uses a 1-lookahead scheme to guarantee data delivery to the sink. We show that WLDT, which favors data forwarding through short Delaunay edges, achieves an energy gain percentage in the order of 55% for the free space model and close to 100% for the multi-path model compared to BVGF and GPSR, which forward data through long distances and which we have slightly updated to account for energy in the selection of next forwarders. We prove that these checkpoints yield an energy gain percentage in the order of 30% in comparison with a similar protocol, called WLDT-w/c (or WLDT without checkpoints), which forwards data via short distances but does not use checkpoints.

Sidereal filtering based on single differences for mitigating GPS multipath effects on short baselines

Carrier-phase multipath effects are one of the most significant error sources in precise Global Positioning System (GPS) positioning applications. A new sidereal filtering algorithm based on single differences is developed to mitigate multipath effects for short-baseline high-rate GPS applications such as structural deformation monitoring. This method differs from traditional sidereal filtering in that our method operates on the single differences rather than the coordinates or double differences. A multipath model for the single differences on the reference day is established for each satellite and is used to remove multipath errors from observations of subsequent days by taking advantage of the sidereal repeatability of multipath signals. Using both simulated and real GPS observations, we demonstrate that this method is insensitive to different weighting strategies used in computing single differences from double differences. Applying the proposed method can reduce the root mean square (RMS) of positioning noises by 82% on average. Compared to sidereal filtering (in either coordinate or double differences domain) and aspect repeat time adjustment, this method can further reduce the RMS values by 13 and 7%, respectively. Wavelet spectra have shown that the proposed method is more effective in mitigating multipath errors of both long and short periods. This method is also more advantageous in that it is applicable when different GPS satellites are observed on different days.

A Stochastic Model of the Time-Variant MIMO Channel Based on Experimental Observations

This paper proposes a stochastic multipath model that is useful for generating multiple-input-multiple-output (MIMO) channel matrices in time-variant environments. The multipath model is developed by first extracting the relevant multipath cluster characteristics from measured indoor channel data and subsequently capturing these characteristics in an autoregressive stochastic model. This model is then used to generate channel matrices whose space-time characteristics closely match those of realistic scenarios, particularly when birth and death of multipath clusters are included in the stochastic representation. Computational examples reveal the applicability and the accuracy of the approach. While the current implementation is based on data taken assuming that propagation is confined to the horizontal plane, this paper also discusses the extension of the model to describe 3-D propagation, enabling its application to a wide range of physical scenarios and antenna characteristics.

Carrier phase multipath error characterization and reduction in single aircraft relative positioning

This paper describes GPS carrier phase (CP) multipath characterization and error reduction techniques and their application in single aircraft relative positioning. In particular, the single aircraft relative positioning scenario has applications for high-accuracy multi-sensor stabilization where CP multipath is a major error source that limits system performance. We will briefly review the requisite multipath theory and discuss models for quantifying the error characteristics. Field-test data will be used to validate the multipath models considering the underlying assumptions. A basic geometric reflection point theory will be presented to demonstrate the physical environmental sensitivity of CP multipath to parameters such as surface flatness and antenna height. Several different quantities will be described as multipath indicators for time-domain detection and will be compared with a frequency-domain technique. A new multipath detection approach will be introduced that is suitable to track multipath from time-varying reflection/diffraction points. Finally, the narrow-lane antenna baseline processing technique will be presented as a real-time approach to mitigate CP noise and multipath errors that is well suited for a very short baseline single aircraft high accuracy relative positioning system. Field-test results and analysis will be used to illustrate the key concepts in this paper and to help characterize the total navigation system performance.

A Double-Angular Propagation Model With Cluster Scattering

A statistical multipath propagation model is developed in the double-angular domain to include effects of both angle of departure and angle of arrival. The model is characterized by a discrete stochastic double-angular spectrum of the Green's function between two volumes that communicate with each other in the presence of cluster scattering. The whole modeling process is a combination of theories, assumptions, and numerical verification by rigorous full wave electromagnetic simulations. Notably, an uncorrelated scattering assumption for received fields is extended to the double-angular domain, and the transport theory plays a key role defining the statistical properties of the spectrum of the Green's function. The spectrum is eventually modeled as a random matrix whose entries are uncorrelated zero-mean complex Laplacian random variables. The real and imaginary parts of the matrix entries are independent and identically distributed, and the variance profile follows the reduced incident intensity of the waves through random media. The parameters of the model are completely obtained from bulk statistical knowledge of the scattering environments, and the resulting model demonstrates good performance on EM DOF and MIMO capacity estimation.

Ultra-Wideband Channel Modeling for Intravehicle Environment

With its fine immunity to multipath fading, ultra-wideband (UWB) is considered to be a potential technique in constructing intravehicle wireless sensor networks. In the UWB literature, extensive measuring and modeling work have been done for indoor or outdoor propagation, but very few measurements were performed in intravehicle environments. This paper reports our effort in measuring and modeling the UWB propagation channel in commercial vehicle environment. In our experiment, channel sounding is performed in time domain for two environments. In one environment, the transmitting and the receiving antennas are put beneath the chassis. In another environment, both antennas are located inside the engine compartment. It is observed that paths arrive in clusters in the latter environment but such clustering phenomenon does not exist in the former case. Different multipath models are used to describe the two different propagation channels. For the engine compartment environment, we describe the multipath propagation with the classical S-V model. And for the chassis environment, the channel impulse response is just represented as the sum of multiple paths. Observation reveals that the power delay profile (PDP) in this environment does not start with a sharp maximum but has a rising edge. A modified S-V PDP model is used to account for this rising edge. Based on the analysis of the measured data, channel model parameters are extracted for both environments.

Using GPS-based link exclusion to reduce overhead and increase route reliability in FTP/TCP-based MANETs

In this paper, we show that the use of global positioning system (GPS) information in a mobile ad hoc network (MANET) running the file transfer protocol (FTP) over the transmission control protocol (TCP) can be used to block the inclusion of unreliable links within a discovered route by not allowing the nodes outside of a given distance to participate in their formation. In doing so, this creates more reliable routes over time and lowers the amount of network overhead necessary to maintain the flow of data packets. This approach to route formation is validated using the NS-2.31 network simulator under different types of multipath fading models as well as varying network dimensions and node densities. While this GPS blocking scheme has been explored previously in a constant bit rate (CBR) over a user datagram protocol (UDP) setting, it has not yet been tested previously under the more common real-world conditions of FTP running over TCP.

MIMO Precoder Designs for Frequency-Selective Fading Channels Using Spatial and Path Correlation

Multiple-input-multiple-output (MIMO) precoder design for frequency-selective fading channels using partial channel information based on the spatial and path correlation matrices is presented. By representing a frequency-selective fading channel as a multipath model with L effective paths, a general precoding structure is proposed and used to derive optimum precoding designs that maximize Jensen's upper bound on the channel ergodic capacity under the transmitted power constraint for two cases, i.e., uncorrelated and correlated channel paths. Analytical results show that, in the uncorrelated case, the precoder structure consists of a number of parallel precoders for frequency-flat fading channels. The power assignment to each precoder and the power allocation over the eigenmodes of each precoder are calculated based on the power of channel paths and the eigenvalues of the transmit correlation matrix. In the correlated case, the precoder structure is an eigenbeamformer with the beams referred to a function of eigenvectors of the Kronecker product of path and transmit correlation matrices. Furthermore, the power allocated to each eigenmode can be obtained from a statistical water-pouring policy that is specified by the product of eigenvalues of the transmit antenna and path correlation matrices. Simulation results for different scenarios indicate that the proposed precoder can increase the ergodic capacity of MIMO systems in a frequency-selective fading environment with spatial and path correlations, and its offered capacity gain is increased with the level of correlation and numbers of antennas and channel paths.

Multipath multihop routing analysis in mobile ad hoc networks

This paper proposes an analytical modeling framework to investigate multipath routing in multihop mobile ad hoc networks. In this paper, a more generalized system has been considered and mathematically analyzed to observe some of the related performance measures of the ad hoc network. Each node in the network is assumed to have finite buffer. The single-path model is approximated to be a multi-node M/M/1/B tandem network, and the multi-path model as a set of multiple parallel paths. This proposed model allows us to investigate issues such as end-to-end delivery delay, throughput and routing reliability in mobile ad hoc networks. Theoretical results have been verified by numerical results. An optimal path selection strategy has been proposed to select a minimized delay path among the available multiple paths between source-destination pair.

Analysis of airborne GPS multipath effects using high-fidelity EM models

Airborne GPS systems are being upgraded to provide sufficient positioning accuracy to support automatic landing operations in low visibility conditions. This is made possible by differential GPS (DGPS), in which the errors common to the airborne receiver and ground station are removed by knowledge of the latter's precise location. However, errors specific to the airborne system remain, of which the dominant components are receiver noise and multipath. To support the assessment of the integrity of the signal in space, these residual errors are incorporated in a statistically based error model, designated as the "standard model." The standard model is defined as the standard deviation of a Gaussian distribution that overbounds the residual pseudo-range (PR) error. It relates the standard deviation of the overbounding distribution to the elevation angle of the satellite relative to the local level coordinate system. The international community is currently developing improved standards to enable DGPS systems to support landings in the worst visibility conditions (i.e., CAT III). As a part of this development, the standard model for multipath is being re-evaluated and an improved model is sought. In order to better characterize the residual multipath errors, tools for accurate calculation of the airframe scattering effects are needed. Development of such tools is the subject of this paper. A new method for accurately computing pseudo-range error, based on the use of high-fidelity EM models, is described. This approach provides new insight into the mechanisms causing multipath error.

The Performance Analysis of Backward Compatible Modulation With Higher Spectrum Efficiency for DAB Eureka 147

Based on the standard of digital audio broadcasting (DAB) Eureka 147 system to improve structures of transmitter/receiver, this paper proposes a physical layer transmission technique capable of boosting the spectrum efficiency up to two times of that of the DAB-Eureka 147 system while the backwards compatibility is guaranteed. The proposed transmission technique comprises the development of both the modulation and demodulation schemes. In the developed modulation scheme, differential 16-level amplitude/ phase shift keying (D16 APSK) is adopted to replace the differential quadrature-phase-shift-keying (DQPSK) used in the DAB Eureka 147 system. In the developed demodulation scheme, on the other hand, a detector for two-level differential amplitude-shift-keying (DASK) signal is proposed which can be implemented with rather low hardware costs. The performance is presented by the Simulink platform in multipath fading channel model.

A GNSS Code Multipath Model for Semi-Urban, Aircraft, and Ship Environments

ABSTRACT: The University of Colorado Advanced GNSS Multipath Model integrates 3D structure models, electromagnetic ray-tracing algorithms, antenna pattern measurements, and detailed receiver tracking loop models to simulate code multipath errors. This article presents results for three environments – a semi-urban rooftop, an F-18 aircraft, and the aircraft carrier USS Eisenhower. Model accuracy is evaluated on the basis of multipath error statistics as well as time history amplitude and frequency content. In general, 1-s error statistics for all scenarios match the experimental data to within 15 cm, and time history comparisons often show good agreement in terms of amplitude and temporal variability. Frequency content is compared on the basis of a cross-correlation metric, with values of 0.57 or better for at least 67% of the data points. We also demonstrate the application of the modeling tools for the evaluation of additional antenna placements, reflector identification, and the characterization of key multipath signal properties.

Evaluation of mobile ultra wideband modems in dense multipath-part 1: channel model

The WSSUS channel model has provided a useful tool for modeling random time variant linear channels in the four decades since its introduction. However, with the advent of UWB (Ultra Wideband) communications, it is necessary to replace this model which is valid for Narrowband (NB) channels. This paper develops such a replacement. The development is based upon the tapped delay line model of a linear time- variant channel, which is valid for any ratio of bandwidth to carrier frequency. For simplicity, the analysis assumes a dense multipath environment such as may be experienced in outdoor and indoor urban environments. The thrust of this study is to derive an UWB channel model for dense multipath that will allow a meaningful comparative modem performance evaluation rather than to develop a new precise characterization of UWB channels. Such a model should be useful in preparation of UWB communication standards for mobile links.

Understanding K-feldspar 40 Ar/ 39 Ar data: reconciling models, methods and microtextures

Several descriptions of argon diffusion in K-feldspar have been developed, including the quantitative multiple-diffusion-domain (MDD) and multipath models and the qualitative ‘recrystallization’ model. These models remain contentious and the natural range in behaviour remains poorly understood. Feldspars from the Klokken syenite intrusion show a systematic relationship between 40 Ar/ 39 Ar age and microtexture suggesting that the loss of argon from different feldspars operates via different mechanisms such that the existing models represent only end-member scenarios. The MDD model can yield reliable thermal history information only for feldspars with pristine microtexture, with this model best viewed as a cipher for the real (but unknown) domain structure in such samples.

Performance prediction of packet mobile communication through wireless multipath fading channel modeling

This paper presents a software simulator applicable to multipath fading channels in urban environments of mobile communication networks. The simulator is constructed by a two-state Markov model and several statistical models for simulating the characterizations of different environments. A core idea of the simulator is to construct a Rice distribution-based multipath fading module produced by a modified Gans Doppler power spectrum, and in combination with a Markov model to predict the time-dependent characteristics of packet in different radio circumstances. It can simply predict the packet performance of the future channel and evaluate the relations between the radio channel and the modulation schemes, error control protocols and channel coding. Simulation results demonstrate that it is a reliable and efficient method.

A scalable QoS routing model for diffserv over MPLS networks

In this paper, we present a new Quality of Service (QoS) routing model for Differentiated Services (Diffserv) over Multiprotocol Label Switching (MPLS) networks. We use a pre-established multi-path model in which several MPLS label switching paths (LSPs) are established between each ingress-egress router pair in advance. Ingress routers perform per-request admission control and bulk-type resource reservation based on the resource availability on the associated LSPs. We use a utilization-based dynamic load balancing scheme to increase resource utilization across LSPs. The proposed model increases signaling and state scalability in the network core. It also provides hard QoS guarantees and minimizes admission control time. The experimental results verify the achievements of our model under various network topologies and traffic conditions.

Development and testing of a new ray-tracing approach to GNSS carrier-phase multipath modelling

Multipath is one of the most important error sources in Global Navigation Satellite System (GNSS) carrier-phase-based precise relative positioning. Its theoretical maximum is a quarter of the carrier wavelength (about 4.8 cm for the Global Positioning System (GPS) L1 carrier) and, although it rarely reaches this size, it must clearly be mitigated if millimetre-accuracy positioning is to be achieved. In most static applications, this may be accomplished by averaging over a sufficiently long period of observation, but in kinematic applications, a modelling approach must be used. This paper is concerned with one such approach: the use of ray-tracing to reconstruct the error and therefore remove it. In order to apply such an approach, it is necessary to have a detailed understanding of the signal transmitted from the satellite, the reflection process, the antenna characteristics and the way that the reflected and direct signal are processed within the receiver. This paper reviews all of these and introduces a formal ray-tracing method for multipath estimation based on precise knowledge of the satellite–reflector–antenna geometry and of the reflector material and antenna characteristics. It is validated experimentally using GPS signals reflected from metal, water and a brick building, and is shown to be able to model most of the main multipath characteristics. The method will have important practical applications for correcting for multipath in well-constrained environments (such as at base stations for local area GPS networks, at International GNSS Service (IGS) reference stations, and on spacecraft), and it can be used to simulate realistic multipath errors for various performance analyses in high-precision positioning.

Estimation of GPS Carrier Phase Multipath Signals Based on Site Environment

This paper presents a method that is based on Electromagnetic Modeling (EM) technique for modelling GPS carrier phase multipath signals. A commercial software plus modules developed in-house are used for modeling and processing carrier phase multipath error parameters. Static multipath modeling experiments show that up to about 35% carrier phase errors and about 25% 3D positioning errors can be reduced.