Exponential Correlation Model Research Articles

Spatially correlated gamma-gamma scintillation in atmospheric optical channels.

In this paper, novel analytical closed-form expressions are derived for the probability density function of the sum of identically distributed correlated gamma-gamma random variables that models an optical atmospheric channel communication with receiver spatial diversity. The mathematical expressions here proposed provide a general procedure to obtain information about the scintillation effects induced by turbulence over a diversity reception scheme implementing equal-gain combining method. Both, validity and accuracy of the obtained statistical distribution are corroborated by comparing the analytical results to numerical results obtained by Monte-Carlo simulations. These simulations are particularized for constant, exponential and circular correlation models, corresponding to three different receivers spatial configurations. In addition, the extreme situations of no correlation and fully correlated received signals are also studied. The presented expressions lead to a simple and easy-to-compute analytical procedure of analyzing atmospheric optical communications systems with correlated spatial diversity.

Modelling Geometric Imperfections of Spatial Latticed Structures Considering Correlations of Node Imperfections

The buckling loads of shell structures and shell-like space frames are very sensitive to initial geometric imperfections. Previous studies focused on estimating the lower bound of the load-carrying capacity of reticulated shells. This paper proposes a new method for modelling structural geometrical imperfections based on random field theory. The method can consider the correlation of imperfections of nodes. The correlation of imperfections relies on the number and length of the connecting members between the two nodes and decreases with the increase of members by an exponential correlation model. The influence of geometric imperfections on structural stability is studied using a probabilistic method by modelling structural geometrical imperfections with the proposed method.

Capacity Loss Due to Polarization-Mismatch and Space-Correlation on MISO Channel

This paper analyzes the effects of polarization-mismatch and space-correlation to a multiple-input and single-output (MISO) channel which is observable in the near future cellular communications environments such as large-scale antenna arrays and small cells. The analysis is based on a polarization-mismatched and space-correlated MISO channel which is modeled from the conventional dual-polarized channel. In the MISO channel, polarization-mismatch is described by the polarization-mismatch angle which is uniformly distributed from 0 to the maximum polarization-mismatch angle and space-correlation is described by the exponential correlation model. Assuming high SNR, approximate expressions of the ergodic capacity are derived as a function of the transmit power, number of transmit antennas, maximum polarization-mismatch angle, and space-correlation coefficient in four representative environments: narrowly or widely spread polarization-mismatch angles and slightly or highly correlated channels. Further, the capacity loss introduced by polarization-mismatch and space-correlation is derived with respect to the maximum polarization-mismatch angle and space-correlation coefficient. It is shown that the capacity loss introduced by polarization-mismatch is upper bounded by 2 bit/s/Hz. Whereas, the capacity loss introduced by space-correlation increase with the number of transmit antennas and is upper bounded by 0.832 bit/s/Hz. Required resources to compensate for the capacity loss is derived as well.

Collaborative Spectrum Sensing under Suburban Environments

Collaborative spectrum sensing for detection of white spaces helps in realizing reliable and efficient spectrum sensing algorithms, which results in efficient usage of primary spectrum in secondary fashion. Collaboration among cognitive radios improves probability of detecting a spectral hole as well as sensing time. Available literature, in this domain, uses Gudmundson’s exponential correlation model for correlated lognormal shadowing under both urban and suburban environments. However, empirical measurements verify that the suburban environment can better be modeled through double exponential correlation model under suburban environments in comparison to Gudmundson’s exponential correlation model. Collaboration among independent sensors provides diversity gains. Asymptotic detection probability for collaborating users under suburban environments using double exponential correlation model has been derived. Also, the Region of Convergence performance of collaborative detection is presented which agrees well with analytical derivations.

Effects of the correlation model, the trend model, and the number of training points on the accuracy ofKriging metamodels

AbstractThis paper explores the effects of the correlation model, the trend model, and the number of training points on the accuracy ofKriging metamodels.Gaussian correlation models are found to be superior to exponential and linear correlation models. No particular trend model is found to be better than the other models. The number of training points used in constructing theKriging metamodels is observed to change the relative performances of the trend and the correlation functions. The leave‐one‐out cross‐validation error is found to become a better surrogate for the actual error, as the number of training points is increased. Finally, the use of an ensemble of metamodels is discussed and it is found that using an ensemble may improve the accuracy.

Performance analysis of selection diversity over exponentially correlated α– µ fading environment

AbstractAn approach to the performance analysis of multibranch selection combiner (SC) receiver operating over fading channels is presented. High level of generality for the proposed analysis is achieved by considering correlated α– µ fading environment. The effect of correlation is studied by assuming exponential correlation model of the signals in each diversity branch. The whole analysis is observed in the interference‐limited fading environments (SIR‐based diversity system is assumed). The important performance measures are considered. Closed form of formulae for the output SIR's probability density function and cumulative distribution function are derived. In order to check the accuracy of the complete proposed formulation, some numerical results are presented. Copyright © 2011 John Wiley & Sons, Ltd.

Decadal variability and scales of the sea surface structure in the northern Ionian

The variability and scales of the sea surface structure of the northern Ionian Sea from January 1993 to December 2007 were studied by means of altimeter remotely-sensed weekly Sea Level Anomaly (SLA) objective maps. Variability in the sea surface structure was addressed by means of empirical orthogonal function (EOF) analysis and, assuming an exponential correlation model, scales of the SLA field were quantified as e-folding distances of the SLA autocorrelation function. The variability in the sea surface structure, described by the first three EOFs, which cumulatively explain 60.3% of the data set variance, is characterized by a large-scale structure with variability on a time scale of ∼10–13 years and, on shorter scales, an eddy system with variability on an annual scale. The variability in the large-scale structure describes an overturning of the SLA field, which took place in 1997, and determines a reversal of the geostrophic upper-layer circulation. As the large-scale circulation transition takes place, time-dependent spectral analysis of EOF coefficients shows a redistribution of the spectral energy from inter-annual to semi-annual and monthly components. Spatial scales display variability on an annual and inter-annual time scale. On the annual time scale, variability in spatial scales is characterized by longer values in summer–fall and shorter in winter–spring. Inter-annual variability in spatial scales is demonstrated by a remarkable drop in the values during fall in the period 1998–2000. We propose an explanation of the variability in horizontal scales in terms of the redistribution of water masses and related modifications of the vertical structure of the water column associated with different regimes of the basin-scale circulation.

Soil erosion and sediment yield and their relationships with vegetation cover in upper stream of the Yellow River

Soil erosion is a significant concern when considering regional environmental protection, especially in the Yellow River Basin in China. This study evaluated the temporal-spatial interaction of land cover status with soil erosion characteristics in the Longliu Catchment of China, using the Soil and Water Assessment Tool (SWAT) model. SWAT is a physical hydrological model which uses the RUSLE equation as a sediment algorithm. Considering the spatial and temporal scale of the relationship between soil erosion and sediment yield, simulations were undertaken at monthly and annual temporal scales and basin and sub-basin spatial scales. The corresponding temporal and spatial Normalized Difference Vegetation Index (NDVI) information was summarized from MODIS data, which can integrate regional land cover and climatic features. The SWAT simulation revealed that the annual soil erosion and sediment yield showed similar spatial distribution patterns, but the monthly variation fluctuated significantly. The monthly basin soil erosion varied from almost no erosion load to 3.92 t/ha and the maximum monthly sediment yield was 47,540 tones. The inter-annual simulation focused on the spatial difference and relationship with the corresponding vegetation NDVI value for every sub-basin. It is concluded that, for this continental monsoon climate basin, the higher NDVI vegetation zones prevented sediment transport, but at the same time they also contributed considerable soil erosion. The monthly basin soil erosion and sediment yield both correlated with NDVI, and the determination coefficients of their exponential correlation model were 0.446 and 0.426, respectively. The relationships between soil erosion and sediment yield with vegetation NDVI indicated that the vegetation status has a significant impact on sediment formation and transport. The findings can be used to develop soil erosion conservation programs for the study area.

Analytical second‐order statistics of maximal‐ratio diversity over spatially correlated nakagami fading channels

To evaluate the performance of antenna diversity with maximal‐ratio combining (MRC) over spatially correlated Nakagami fading channels, the average level crossing rate (LCR) and the average fade duration (AFD) of the signal envelope are derived. To characterize the dependence among antenna branches, both the exponential and equal correlation models are considered. Numerical results of the average LCR and AFD are presented for various channel parameters and different numbers of branches.

Scales and variability of the sea surface temperature distribution in the Adriatic Sea

Scales and variability of the Adriatic sea surface temperature (SST) distribution in the period January 1991 to December 2000 are studied by means of 8‐day composite, 4‐km resolution, SST data. Scales of the SST are defined as scales of the SST autocorrelation function. Assuming an exponential correlation model, scales of the SST are quantified as e‐folding times and distances of the SST autocorrelation function. Variability in the SST is analyzed through empirical orthogonal function (EOF) analysis. From summer to winter, spatial scales of the SST in the along‐basin direction remain unchanged while in the across‐basin direction they decrease, resulting in scales that are slightly shorter (10–15%) in winter than in summer. The spatial distribution of temporal scales displays two patterns: the first, characterized by low values, is located in the northern part of the basin and along the Italian coast, and the second, characterized by high values, covers the rest of the basin. The SST variability is dominated by the annual signal, which explains 45% of the overall variance. The main structures of the Adriatic circulation leave their signature on the first three EOFs, whose spatial variability occurs on wavelengths longer than 200 km in the along‐basin direction and, in the across‐basin direction, in the band 25–50 km and at 80 and 100 km. EOF coefficients are characterized by oscillating components with periods of 20 days to 6 months.

Medium-Contention Based Energy-Efficient Distributed Clustering (MEDIC) for Wireless Sensor Networks

In this paper, we utilize clustering to organize wireless sensors into an energy-efficient hierarchy. We propose a Medium-contention based Energy-efficient DIstributed Clustering (MEDIC) scheme, through which sensors self-organize themselves into energy-efficient clusters by bidding for cluster headship. This scheme is based on a new criterion that can be used by each sensor node to make a distributed decision on whether electing to be a cluster head or a non-head member, which is a fully distributed approach. Although MEDIC uses only local information, it achieves better performance in terms of effective lifetime and its Data/Energy Ratio is 25% higher than native LEACH (Low-Energy Adaptive Clustering Hierarchy), which relies on other routing algorithms to access global information. A complementary exponential data correlation model is also introduced to simulate different data aggregation effect.

Poverty determinants of acute respiratory infections among Mapuche indigenous peoples in Chile's Ninth Region of Araucania, using GIS and spatial statistics to identify health disparities

BackgroundThis research concerns Araucanía, often called the Ninth Region, the poorest region of Chile where inequalities are most extreme. Araucanía hasn't enjoyed the economic success Chile achieved when the country returned to democracy in 1990. The Ninth Region also has the largest ethnic Mapuche population, located in rural areas and attached to small agricultural properties. Written and oral histories of diseases have been the most frequently used methods to explore the links between an ancestral population's perception of health conditions and their deprived environments. With census data and hospital records, it is now possible to incorporate statistical data about the links between poverty and disease among ethnic communities and compare results with non-Mapuche population.Data sourcesHospital discharge records from Health Services North N = 24,126 patients, year 2003, and 7 hospitals), Health Services South (N = 81,780 patients and 25 hospitals); CAS-2/Family records (N = 527,539 individuals, 439 neighborhoods, 32 Comunas).MethodsGiven the over-dispersion of data and the clustered nature of observations, we used the global Moran's I and General G Gettis-Ord procedures to test spatial dependence. These tests confirmed the clusters of disease and the need to use spatial regression within a General Linear Mixed Model perspective.ResultsHealth outcomes indicate significantly higher morbidity rates for the Mapuche compared to non-Mapuche in both age groups < 5 and 15–44, respectively; for the groups 70–79 and 80 + years of age, this trend is reversed. Mortality rates, however, are higher among Mapuches than non-Mapuches for the entire Ninth Region and for all age groups. Mortality caused by respiratory infections is higher among Mapuches than non-Mapuches in all age-groups. A major finding is the link between poverty and respiratory infections.ConclusionPoverty is significantly associated with respiratory infections in the population of Chile's Ninth Region. High deprivation areas are associated with poverty, and poverty is a predictor of respiratory infections. Mapuches are at higher risk of deaths caused by respiratory infections in all age groups. Exponential and spherical spatial correlation models were tested to estimate the previous association and were compared with non-spatial Poisson, concluding that significant spatial variability was present in the data.

On the capacity of doubly correlated MIMO channels

In this paper, we analyze the capacity of multiple-input multiple-output (MIMO) Rayleigh-fading channels in the presence of spatial fading correlation at both the transmitter and the receiver, assuming the channel is unknown at the transmitter and perfectly known at the receiver. We first derive the determinant representation for the exact characteristic function of the capacity, which is then used to determine the trace representations for the mean, variance, skewness, kurtosis, and other higher-order statistics (HOS). These results allow us to exactly evaluate two relevant information-theoretic capacity measures - ergodic capacity and outage capacity - and the HOS of the capacity for such a MIMO channel. The analytical framework presented in the paper is valid for arbitrary numbers of antennas, and generalizes the previously known results for independent and identically distributed or one-sided correlated MIMO channels to the case when fading correlation exists on both sides. We verify our analytical results by comparing them with Monte Carlo simulations for a correlation model based on realistic channel measurements as well as a classical exponential correlation model

Spatial scales of tropical precipitation inferred from TRMM microwave imager data

The local spatial scales of tropical precipitating systems were studied using Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) rain rate imagery from the TRMM satellite. Rain rates were determined from TMI data using the Goddard Profiling (GPROF) Version 5 algorithm. Following the analysis of Ricciardulli and Sardeshmukh (RS), who studied local spatial scales of tropical deep convection using global cloud imagery (GCI) data, active precipitating months were defined alternatively as those having greater than either 0.1 mm/h or 1 mm/h of rain for more than 5% of the time. Spatial autocorrelation values of rain rate were subsequently computed on a 55/spl times/55 km grid for convectively active months from 1998 to 2002. The results were fitted to an exponential correlation model using a nonlinear least squares routine to estimate a spatial correlation length at each grid cell. The mean spatial scale over land was 90.5 km and over oceans was 122.3 km for a threshold of 0.1 mm/h of rain with slightly higher values for a threshold of 1 mm/h of rain. An error analysis was performed which showed that the error in these determinations was of order 2% to 10%. The results of this study should be useful in the design of convective schemes for general circulation models and for precipitation error covariance models for use in numerical weather prediction and associated data assimilation schemes. The results of the TMI study also largely concur with those of RS, although the more direct relationship between the TMI data and rain rate relative to the GCI imagery provide more accurate correlation length estimates. The results also confirm the strong impact of land in producing short spatial scale convective rain.

On the capacity of spatially correlated mimo rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.

BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

AbstractExact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Error Performance Evaluation of Wireless Communication Systems Using Maximal Ratio Combining with Multiple Interferers

In this paper we evaluate the error performance of wireless communication systems using M-branch maximal ratio combining (MRC) with multiple cochannel interference. Three cochannel interference models are considered: (A) L independent identically distributed (i.i.d.) Nakagami-m cochannel interferers; (B) L independent cochannel interferers consisting of L-N Nakagami-m interferers and N Rayleigh interferers; (C) L independent cochannel interferers in which each interferer follows Nakagami-m distribution for a fraction of time and Rayleigh distribution for the remaining time. In addition, the desired signal assumes Nakagami-m fading. This paper considers that an exponential correlation model is assumed for the desired signals received on each branch, while the interferers are assumed independent. Closed-form expressions are derived for the probability density functions (PDFs) of the instantaneous signal-to-interference power ratio (SIR) at the output of the MRC for the three interference models. Using these SIR PDFs, further closed-form expressions to evaluate the outage probability (OTP) and the average bit error probability (BEP) of differential phase-shift keying (DPSK) are derived. Numerical results showing the impacts of the system parameters on the OTP and the average BEP are then presented.

Generalized Least Squares With Ignored Errors in Variables

We present data, both real and simulated, that show generalized least squares (GLS) estimation, intended to account for correlated response error structure, can produce gross biasing in regression parameter estimates under misspecified models with ignored errors in explanatory-variable measurements. The bias, and its subsequent effect on mean squared error (MSE), can be much more severe than the apparently less appropriate ordinary least squares (OLS) estimator. This article provides a theoretical basis for these effects by deriving expressions for the bias and MSE for the general GLS estimator through Taylor-series expansions. The results are compared with simulations for two specific weight matrices and applied to a dataset relating atmospheric pollutant levels in Los Angeles with average recorded wind speed. We show that the bias (with subsequent implications for the MSE) is always worse for the exponential correlation model with equally spaced explanatory-variable observations and present a simple test to decide a preference for OLS or GLS in practice.

Random coding error exponents for flat fading channels with realistic channel estimation

There has been a considerable interest in determining the limits to communications over multipath fading channels. However, most studies have assumed that the channel is perfectly known at the receiver. In this paper, the random coding error exponent for flat fading channels with realistic channel state information (CSI) is studied. It is assumed that the CSI is obtained via some practical technique which utilizes a linear estimation scheme. Two commonly used techniques for channel estimation are considered in this paper, namely pilot tone extraction and pilot symbol transmission. The degradation in the achievable performance due to partial CSI is assessed and comparison of the different channel estimation methods is made. The focus of this paper is on the Jake's mobile Rayleigh flat fading model. Although Jake's model does not have a Markov property, such as that found in the commonly used exponential correlation model, which is usually attractive from the mathematical tractability point of view, Jake's model has a physical basis. Also, this model is considered herein from the standpoint of the random coding exponent. The results in this paper shed light on the amount of degradation in the achievable performance that is expected when the receiver has partial CSI. Finally, the sensitivity of the loss in achievable performance for the various channel estimation techniques with respect to channel parameters, such as Doppler spread and signal-to-noise ratio (SNR), is studied.

Technical Notes: Spatial Variation of Daily Rainfall and Network Design

A high-density pilot network of 10 rain gauges was implemented in the Everglades Nutrient Removal (ENR) Project to quantify areal rainfall over the site for accurate computation of water budget. The ENR Project, located in south Florida, is a 1500 ha wetland that was constructed to reduce phosphorus loads in agricultural runoff from the Everglades Agricultural Area (EAA) that enters the Water Conservation Areas (WCAs). The first 158 days of wet season daily rainfall data were used to evaluate the adequacy (or redundancy) of the network. A spatial correlation function was developed to characterize the spatial variation of wet season rainfall over the site. An exponential spatial correlation model was fitted to the data with an R2 value of 0.74. A method that compares relative error to rain gauge density was applied to determine the required minimum gauge density. It was determined that a five rain gauge network with uniform distribution was the most efficient design.