Nakagami Model Research Articles

Bayesian estimation of some reliability characteristics for Nakagami model using adaptive progressive censoring

The focus of this research is to clarify both conventional and Bayesian parametric estimation methods for the Nakagami distribution making use of adaptive progressive Type II censored data. From a classical estimation perspective, two estimation methods are considered: maximum likelihood and least squares estimations. Along with the model parameters, three reliability metrics are estimated using point and interval estimation. Bayes estimates with gamma and inverse gamma priors are investigated by employing the squared error loss function. The Bayes computations are created using the Markov Chain Monte Carlo technique. Moreover, the classical and Bayesian intervals are also taken into consideration. For evidence of the effectiveness of the given methodologies, a simulation study and three applications from the physics, chemistry, and engineering domains are explored. Lastly three optimality criteria are applied to the stated data sets to pick the best progressive censoring strategy.

Edge blurring suppression of ultrasonic reflection coefficients in contact state measurement

Ultrasonic reflection coefficient is the key to contact state evaluation of mechanical devices. Edge blurring can lead to contact state (such as stress concentrations) measurement errors. This reduces the reliability of performance evaluations and introduces potential security risks. In this study, an edge blurring suppression method based on matching pursuit algorithm was proposed. Firstly, the interference signal prediction model is built based on the Nakagami model. Then, a blurred signal separation algorithm based on matching pursuit is proposed to obtain the effective signal. Finally, the reflection coefficient with and without edge blurring effect were obtained. The simulation results show that the maximum relative error of the reflection coefficient is reduced from 219 % to 15 %. The effectiveness of the proposed method is also verified by experiments. The experimental results show that the relative error of the reflection coefficient after edge blurring suppression is reduced from 64 % to 16 %. This indicates that the proposed method can effectively suppress edge blurring, which provides an effective method for edge blurring suppression in various application fields of ultrasonic measurement and improve the reliability of product quality evaluation.

Relationship between transmission/reception conditions of high-frequency plane wave compounding and evaluation accuracy of extended amplitude envelope statistics

The double–Nakagami (DN) model provides a method for analyzing the amplitude envelope statistics of quantitative ultrasound (QUS). In this study, the relationship between the sound field characteristics and the robustness of QUS evaluation was evaluated using five HF linear array probes and tissue-mimicking phantoms. Compound plane-wave imaging (CPWI) was used to acquire echo data. Five phantoms containing two types of scatterers were used to mimic fatty liver tissue. After clarifying the relationship between the sound field characteristics of the probes and QUS parameters, DN QUS parameters in 10 rat livers with different lipidification were evaluated using one HF linear array probe. For both phantom and in situ liver analyses, correlations between fat content and multiple QUS parameters were confirmed, suggesting that the combination of CPWI using a HF linear array probe with the DN model is a robust method for quantifying fatty liver and has potential clinical diagnostic applications.

Increasing the probability of transfer GMDSS broadcast messages when transmitted over HF channel in case fading

Improving the quality of communication in the Global Maritime Distress and Safety System of navigation is one of the components of the development of the Arctic zone of the Russian Federation in terms of information support. At the same time, the most difficult is to ensure communication in the A3 and A4 areas, where a communication HF channel plays a not small role. The transfer of messages over HF channel in the broadcasting mode of SITOR-B is considered. To improve probabilistic characteristics in the work, a statistical analysis of the decisions of the demodulator is carried out. It is shown that the probability density functions are “noisy”, which is associated with the non-zero probability of a bit error. Models of Rayleigh, Rice and Nakagami distributions were used for statistical analysis. It is shown that in the case of low values of the signal-to-noise ratio, which is characteristic of high latitude tracks, a Nakagami model is preferable. The symbol error rate and message error rate in a fading communication channel, as well as the probability of receiving an erroneous message are shown. The results presented in this work can significantly improve the probabilistic characteristics of the HF radiolines when transmitting messages in SITOR-B mode.

Study of Spatial Reuse in IEEE 802.11ax Networks over Propagation Models

The paper studies the spatial reuse in IEEE 802.11ax networks over propagation models in ns3. The propagation models used in the study include the Friis model, the Nakagami model, and the combination of the two models. The results show that not all access points in an area benefit from the spatial reuse, and some even lose throughput. These results introduce the question of how to justify the spatial reuse for those access points who lose throughput, although the total throughput of the access points in the area benefits from the spatial reuse in general. The results also show that the total throughput gains heavily depend on the physical environment of the networks as the environment determines the signal propagation in the networks. The results show that an environment of significant attenuation plus multipath fading offers significant throughput gains for the access points as a whole. Our main contributions in the paper are the results of the ns3 simulations which were not found in the literature.

Polarization-Enabled MIMO Bidirectional Device-to-Device Communications via RIS

In future wireless networks, device-to-device (D2D) communications are expected to play an important role to support a plethora of applications. To meet the target quality of service while ensuring high reliability, and high spectral and energy efficiencies, manipulation of the radio waves by reconfigurable intelligent surfaces (RIS) will be critical. In this context, leveraging concepts of polarization, this paper proposes a framework for bidirectional D2D communications, where the data exchange between a central node and devices operating in distinct polarization states, is multiple-input multiple-output in nature and takes place via a dual-polarized RIS, in the presence of hardware impairments and imperfect interference cancellation, as well as impairments caused by the spatial correlation and cross-polarization. Performance evaluation of such a framework is conducted in terms of key metrics, namely, bit error rate, outage probability, channel capacity, and energy efficiency, for which closed-form expressions are obtained considering transmissions over Nakagami fading channels. An asymptotic analysis is also conducted to evaluate the achievable diversity gains, by approximating the Nakagami model with a tractable Gamma model. Further, the impact of imperfect channel estimation on performance is also investigated. Comparative numerical results are provided, and the effects of the main system parameters on performance are analyzed. The proposed framework is shown to provide significant performance improvements as compared to D2D communications via non-polarized RIS.

Ultrasound Backscatter Envelope Statistics Parametric Imaging for Liver Fibrosis Characterization: A Review.

Early detection and diagnosis of liver fibrosis is of critical importance. Currently the gold standard for diagnosing liver fibrosis is biopsy. However, liver biopsy is invasive and associated with sampling errors and can lead to complications such as bleeding. Therefore, developing noninvasive imaging techniques for assessing liver fibrosis is of clinical value. Ultrasound has become the first-line tool for the management of chronic liver diseases. However, the commonly used B-mode ultrasound is qualitative and can cause interobserver or intraobserver difference. Ultrasound backscatter envelope statistics parametric imaging is an important group of quantitative ultrasound techniques that have been applied to characterizing different kinds of tissue. However, a state-of-the-art review of ultrasound backscatter envelope statistics parametric imaging for liver fibrosis characterization has not been conducted. In this paper, we focused on the development of ultrasound backscatter envelope statistics parametric imaging techniques for assessing liver fibrosis from 1998 to September 2019. We classified these techniques into six categories: constant false alarm rate, fiber structure extraction technique, acoustic structure quantification, quantile-quantile probability plot, the multi-Rayleigh model, and the Nakagami model. We presented the theoretical background and algorithms for liver fibrosis assessment by ultrasound backscatter envelope statistics parametric imaging. Then, the specific applications of ultrasound backscatter envelope statistics parametric imaging techniques to liver fibrosis evaluation were reviewed and analyzed. Finally, the pros and cons of each technique were discussed, and the future development was suggested.

A Framework for the Lower Bound on the BER of DCSK Systems Over Multi-Path Nakagami-m Fading Channels

In this brief, a generalized closed-form approach for the evaluation of the lower bound on the BER of differential chaos-shift-keying (DCSK) systems over multi-path Nakagami- $m$ fading channels is presented. A closed-form lower bound is derived for all configurations of the Nakagami- $m$ channel model which extends to all fading profiles covered by the Nakagami model. In contrast to previous works where very specific models were targeted and only numerical analyses of the DCSK systems were presented, we provide an approach that analytically unifies the performance analysis of DCSK systems over more generalized fading models. A similar analytical development is generalized for Quadrature Chaos Shift Keying (QCSK) and Multi-carrier Differential Chaos Shift Keying (MC-DCSK) systems. A lower bound is applied on the Q-function to extract an exponential expression of the BER. Afterwards, a bound on the exponential function is used to derive a simple polynomial expression which is easily integrable using basic integration techniques for all multi-path Nakagami- $m$ fading channels. The final expression of the newly derived lower bound is forwarded in terms of the Gaussian hypergeometric functions. Comparative simulations conducted for the different systems under consideration show a tight gap between the BER of the simulated systems and their respective lower bounds.

Numerical and experimental investigation of impacts of nonlinear scattering encapsulated microbubbles on Nakagami distribution.

The Nakagami statistical model and Nakagami shape parameter m have been widely used in linear tissue characterization and preliminarily characterized the envelope distributions of nonlinear encapsulated microbubbles (EMBs). However, the Nakagami distribution of nonlinear scattering EMBs lacked a systematical investigation. Thus, this study aimed to investigate the Nakagami distribution of EMBs and illustrate the impact of EMBs' nonlinearity on the Nakagami model. A group of simulated EMB phantoms and in vitro EMB dilutions with an increasing concentration distribution under various EMB nonlinearities, as regulated by acoustic parameters, were characterized by using the window-modulated compounding Greenwood-Durand estimator. Raw envelope histograms of simulated and in vitro EMBs were well matched with the Nakagami distribution with a high correlation coefficient of 0.965±0.021 (P<0.005). The mean values and gradients of m parameters of simulated and in vitro EMBs were smaller than those of linear scatterers due to the stronger nonlinearity. These m values exhibited a quasi-linear improvement with the increase in second harmonic nonlinear-to-linear component ratio regulated by pulse lengths and excitation frequencies at low- and high-concentration conditions. The Nakagami distribution was suitable for the EMBs characterization but the corresponding m parameter was affected by the EMBs' nonlinearity. These validations provided support and nonlinear impact assessment for the EMBs' characterization using the Nakagami statistical model in the future.

Ultrasonic backscatter characterization of cancellous bone using a general Nakagami statistical model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11874289, 11827808, 11504057, 11525416, and 81601504) and the Fundamental Research Funds for the Central Universities.

The goal of this study is to analyze the statistics of the backscatter signal from bovine cancellous bone using a Nakagami model and to evaluate the feasibility of Nakagami-model parameters for cancellous bone characterization. Ultrasonic backscatter measurements were performed on 24 bovine cancellous bone specimens in vitro and the backscatter signals were compensated for the frequency-dependent attenuation prior to the envelope detection. The statistics of the backscatter envelope were modeled using the Nakagami distribution. Our results reveal that the backscatter envelope mainly followed pre-Rayleigh distributions, and the deviations of the backscatter envelope from Rayleigh distribution decreased with increasing bone density. The Nakagami shape parameter (i.e., m) was significantly correlated with bone densities (R=0.78–0.81, ) and trabecular microstructures (, ). The scale parameter (i.e., ) and signal-to-noise ratio (SNR) also yielded significant correlations with bone density and structural features. Multiple linear regressions showed that bone volume fraction (BV/TV) was the main predictor of the Nakagami parameters, and microstructure produced significantly independent contribution to the prediction of Nakagami distribution parameters, explaining an additional 10.2% of the variance at most. The in vitro study showed that statistical parameters derived with Nakagami model might be useful for cancellous bone characterization, and statistical analysis has potential for ultrasonic backscatter bone evaluation.

1P5-7 In vivo Application of Fatty Liver Progression Assessment Method by Double Nakagami Model

1P5-7 In vivo Application of Fatty Liver Progression Assessment Method by Double Nakagami Model

Associations between ultrasonic backscatter, bone density, and microstructure in cancellous bone characterization

Ultrasonic backscatter is related to the microstructure of cancellous bone. However, whether backscatter measurement can provide additional information independently of BMD remains speculative. In this study, we analyzed the independent contribution of cancellous bone densities and microstructure to apparent backscatter signals in vitro. The results showed that ultrasonic backscatter and the statistics of backscatter envelope were significantly correlated with bone densities and microstructure. After adjustment for BMD, some trabecular structures still contributed significantly to the adjusted correlations, with moderate additional variance explained. Multiple linear regressions revealed that both bone density and structure contributed significantly to the prediction of ultrasonic backscatter (adjusted R2 = 0.75–0.93, p&amp;lt;0.05), explaining an additional 14.0% of the variance at most, compared with that of BMD measurements alone. We also demonstrated that the Nakagami model had great potential in trabecular microstructure characterization. The results proved that ultrasonic backscatter was primarily determined by bone apparent density, but bone densities plus microstructure structure could achieve encouragingly better predictive performance than BMD alone. This study implied that ultrasonic apparent backscatter might provide additional density and structural features unrelated to current BMD measurement. Thus, we suggest that ultrasonic backscatter measurement could play a more important role in cancellous bone evaluation.

Nakagami–m Parametric Imaging for Atherosclerotic Plaque Characterization Using the Coarse-to-Fine Method

The Nakagami model was used to analyze the statistical differences in ultrasound backscattered signals between different plaque types. To improve image resolution, Nakagami-m parametric imaging using the coarse-to-fine method based on the maximum likelihood estimation (CTF-BOW) was proposed for atherosclerotic plaque characterization. Simulation results confirmed that the CTF-BOW method significantly outperforms the sliding window method in precision, smoothness and resolution. Preliminary in vivo results (n = 45) indicated that the ranges of the m parameters for calcified, mixed and echolucent plaques are, respectively, 0.2852–0.5225, 0.6532–0.8784 and 0.8908–1.4011, with no overlap. Results revealed that the CTF-BOW method significantly improves image resolution without sacrificing accuracy and can distinguish between calcified, mixed and echolucent plaques. Moreover, it was found that the parameter m is related to the composition of the plaque, indicating that Nakagami-m parametric imaging has the potential to characterize plaques.

Viability Analysis of TwoRayGround and Nakagami Model for Vehicular Ad-Hoc Networks

VANETs are enhanced and upgraded versions of mobile ad-hoc networks which are fruitful for intercommunication vehicles. Communication can be vehicle-to-vehicle and between vehicles to side-fixed equipment known as roadside equipment. This network is self-organized, highly dynamic but separated without any infrastructure or client and server communication. The objective of this research is to examine the study of TwoRayGround and Nakagami radio propagation models for vehicular ad-hoc networks in Indian Scenarios as well as to find the best efficient model, which is more suitable in various scenarios. Output of this research will be beneficial for applying efficient models on the realistic highway scenario, especially traffic caused by four wheelers. This model will also be fruitful for avoiding heavy road congestion and highway road accidents caused by a high and unbalanced speed of traffic as well as other various road conditions, like pot holes and road barriers, etc.

Study of WMAN Physical Layer under Fading Channels

WMAN (wireless metropolitan area network) technology is based on the IEEE 802.16 air interface standard suite, which provides the wireless technology for fixed and nomadic data access. WMAN employs orthogonal frequency division multiplexing (OFDM), and supports adaptive modulation and coding depending on the channel conditions. The objective of this paper is to study the performance of the IEEE 802.16d WMAN physical layer under Nakagami model as a Multi-path and frequency-selective fading channel beside the additive white Gaussian noise (AWGN) and Doppler. Finally, we compared it with the Rayleigh fading model. The transmission bit rate, Probability of Error ( ) and estimated SNR have been compared under single/multi path propagation conditions.

Heterogeneous Tissue Characterization Using Ultrasound: A Comparison of Fractal Analysis Backscatter Models on Liver Tumors

Assessment of tumor tissue heterogeneity via ultrasound has recently been suggested as a method for predicting early response to treatment. The ultrasound backscattering characteristics can assist in better understanding the tumor texture by highlighting the local concentration and spatial arrangement of tissue scatterers. However, it is challenging to quantify the various tissue heterogeneities ranging from fine to coarse of the echo envelope peaks in tumor texture. Local parametric fractal features extracted via maximum likelihood estimation from five well-known statistical model families are evaluated for the purpose of ultrasound tissue characterization. The fractal dimension (self-similarity measure) was used to characterize the spatial distribution of scatterers, whereas the lacunarity (sparsity measure) was applied to determine scatterer number density. Performance was assessed based on 608 cross-sectional clinical ultrasound radiofrequency images of liver tumors (230 and 378 representing respondent and non-respondent cases, respectively). Cross-validation via leave-one-tumor-out and with different k-fold methodologies using a Bayesian classifier was employed for validation. The fractal properties of the backscattered echoes based on the Nakagami model (Nkg) and its extend four-parameter Nakagami-generalized inverse Gaussian (NIG) distribution achieved best results—with nearly similar performance—in characterizing liver tumor tissue. The accuracy, sensitivity and specificity of Nkg/NIG were 85.6%/86.3%, 94.0%/96.0% and 73.0%/71.0%, respectively. Other statistical models, such as the Rician, Rayleigh and K-distribution, were found to not be as effective in characterizing subtle changes in tissue texture as an indication of response to treatment. Employing the most relevant and practical statistical model could have potential consequences for the design of an early and effective clinical therapy.

Performance of Analysis Cognitive Radio with Cooperative Sensing under Malicious Attacks over Nakagami Faded Channels

The different realistic propagation channels are faced frequently the multipath fading environments. The main goal of this system design (cognitive radio network) is to improve the efficiency of spectrum access on a non-interfering basis. This system achieves high utilization for the limited spectrum in order to fulfill needs for all users’ demands which are considered as a problem in wireless communications due to rapidly increasing in wireless applications and service. This system is exposed to attack due to the vulnerabilities existence in this system. So, the main outcome of this paper is to investigate the performance of the cooperative sensing in cognitive radio networks under malicious attacks over different channel impairments, and to illustrate the most suitable individual probability of detection in real faded channel by using Nakagami model. This paper illustrates the effectiveness of the attacks and fading on the performance of spectrum sensing process.

Nakagami-based total variation method for speckle reduction in thyroid ultrasound images.

A good statistical model is necessary for the reduction in speckle noise. The Nakagami model is more general than the Rayleigh distribution for statistical modeling of speckle in ultrasound images. In this article, the Nakagami-based noise removal method is presented to enhance thyroid ultrasound images and to improve clinical diagnosis. The statistics of log-compressed image are derived from the Nakagami distribution following a maximum a posteriori estimation framework. The minimization problem is solved by optimizing an augmented Lagrange and Chambolle's projection method. The proposed method is evaluated on both artificial speckle-simulated and real ultrasound images. The experimental findings reveal the superiority of the proposed method both quantitatively and qualitatively in comparison with other speckle reduction methods reported in the literature. The proposed method yields an average signal-to-noise ratio gain of more than 2.16 dB over the non-convex regularizer-based speckle noise removal method, 3.83 dB over the Aubert-Aujol model, 1.71 dB over the Shi-Osher model and 3.21 dB over the Rudin-Lions-Osher model on speckle-simulated synthetic images. Furthermore, visual evaluation of the despeckled images shows that the proposed method suppresses speckle noise well while preserving the textures and fine details.

Statistics of Boundaries in Ultrasonic B-Scan Images

The existence of edges and boundaries in regions of interest (ROIs) in B-scan images alters the statistics of the backscattered echo from the ROI. Boundaries are the result of at least two different types of scattering scenarios in tissue, and the Nakagami model, which is being used extensively in ultrasound, is unlikely to fit the statistics of the backscattered echo under these conditions. Furthermore, there are very few other statistical models exist that describe the statistics of the backscattered echo from regions containing boundaries. In this work, the gamma mixture density and the recently proposed McKay density are explored as two viable models to fill this void. Justifications of these models are presented along with methods for estimating their parameters. Random number simulations and studies on tissue-mimicking phantoms indicate that the McKay and gamma mixture densities are the best for the modeling of the backscattered echo intensity when boundaries are present in the regions of interest.

Diversity in cascaded N*Nakagami channels

Short term fading conditions that are worse than those existing in typical Nakagami channels can be modeled using the cascaded approach where the received signal-to-noise ratio is treated as the product of N identical or nonidentical random variables that are either dependent or independent. Cascaded channels also permit the modeling of fading seen in amplify and forward relaying channels as well as keyhole channels. The simplest of these models, referred to as the N*Nakagami model, assumes that the received signal to noise ratio is the product of N independent and identically distributed gamma variables. The fading mitigation achieved in such cascaded channels through diversity is studied in this work. Through analytical approach and simulation, the performance of wireless channels is examined for the selection combining, equal gain combining, generalized selection combining, and maximal ratio combining algorithms. Results demonstrate the existence of severe degradations in cascaded fading channels and the comparative usefulness of the various algorithms in improving the data transmission capabilities. Even though the analysis was undertaken for the case of a coherent binary shift keying modem, results can easily be extended to other modems.