Optimal Fusion Rule Research Articles

Joint Activity Detection and Channel Estimation for Intelligent-Reflecting-Surface-Assisted Wireless IoT Networks

Intelligent reflecting surfaces (IRSs) provide the ability to tune the wireless environments by introducing passive scattering elements between the base station (BS) or access points (APs) and users, and it is a promising technology for next generation wireless networks. In this paper, we consider joint activity detection and channel estimation in both centralized and distributed IRS assisted IoT networks. We determine the explicit distribution for the equivalent channel coefficients from the BS or APs to the users. It is shown that this distribution can be equivalently represented with a Gaussian scale mixture (GSM) model. With generalized approximate message passing (GAMP) algorithm, the received pilot signals at the BS or APs are decoupled into scalar Gaussian noise corrupted versions of the effective channel coefficients. Subsequently, minimum mean square error (MMSE) estimate of the effective channel coefficients and threshold detection rules are acquired. Finally, the optimal fusion rule is used to obtain the activity detection results of each user. As an additional low-complexity approach, we approximate the equivalent channel coefficients with a Gaussian approximation (GA) model. We derive the theoretical mean square error for the MMSE estimate of the effective channel coefficients using the GA model and the state evolution equations of the GAMP algorithm, under the assumption that the direct links from the BS to the users can be neglected due to unfavorable propagation conditions. Numerical results show that the Gaussian approximation for the distribution of the equivalent channel coefficients is accurate even for moderate number of elements at the IRS. And the theoretical mean square error for the MMSE estimate of the effective channel coefficients under the assumption that direct link is negligible is shown to overlap with the corresponding numerical simulations.

A Novel Bacterial Foraging Optimization Based Multimodal Medical Image Fusion Approach

Multimodal medical image fusion (MIF) is the procedure of integrating different images in single into multiple imaging modalities for increasing the image quality by preserving a certain feature. Medical image combination covered a tremendous count of hot topic areas, involving pattern recognition, image processing, artificial intelligence (AI), computer vision (CV), and machine learning (ML). In addition, MIF was more commonly applied in clinical for physicians to understand the lesion by the combination of various modalities of medicinal image. This article introduces a novel bacterial foraging optimization-based multimodal medical image fusion approach (BFO-M3IFA). The presented BFO-M3IFA technique considered two distinct patterns of the images as the input of systems and the outcome will be the fused image. Primarily, the BFO-M3IFA technique exploits Weiner filtering (WF) technique as an image pre-processing step to get rid of the noise. Besides, discrete wavelet transform (DWT) was applied for decomposing the image into distinct subbands. Afterward, the estimated coefficients of modality 1 and comprehensive coefficients of modality 2 are integrated and vice versa. At last, a fusion rule is generated to fuse the details of two image modalities and the optimal fusion rule parameter is chosen with utilize of BFO algorithm. The experimental validation of the BFO-M3IFA system was tested and outcomes ensured the improved performance of the BFO-M3IFA system on existing models.

Fast copula-based fusion of correlated decisions for distributed radar detection

Distributed sensor networks with multiple antenna arrays are widely utilized for radar detection systems. When observations of network nodes are correlated, an optimal copula-based fusion (termed CBF) rule is designed for correlated binary decisions under the Neyman–Pearson (NP) framework. However, the CBF rule needs to determine the weights of all decisions in combination. Therefore, the high computational complexity of the CBF rule is unavoidable as the number of nodes increases. In this paper, we propose a fast copula-based fusion (F-CBF) algorithm for a multi-node radar system. The correlation between node decisions is simplified at the fusion center (FC) by taking logarithms of the weighted sum of node decisions. Specifically, the node decisions are weighted by a constant associated with the number of nodes. Thus the proposed method does not need to exhaust the weights of all combinations. Simulation results demonstrate that the proposed algorithm can efficiently reduce computational complexity. The detection performance of the proposed F-CBF method is significantly better than the independent detection method, although it is slightly inferior to the CBF method.

Deep Learning-Based Medical Image Fusion Using Integrated Joint Slope Analysis with Probabilistic Parametric Steered Image Filter

Medical image fusion plays a significant role in medical diagnosis applications. Although the conventional approaches have produced moderate visual analysis, still there is a scope to improve the performance parameters and reduce the computational complexity. Thus, this article implemented the hybrid fusion method by using the novel implementation of joint slope analysis (JSA), probabilistic parametric steered image filtration (PPSIF), and deep learning convolutional neural networks (DLCNNs)-based SR Fusion Net. Here, JSA decomposes the images to estimate edge-based slopes and develops the edge-preserving approximate layers from the multi-modal medical images. Further, PPSIF is used to generate the feature fusion with base layer-based weight maps. Then, the SR Fusion Net is used to generate the spatial and texture feature-based weight maps. Finally, optimal fusion rule is applied on the detail layers generated from the base layer and approximate layer, which resulted in the fused outcome. The proposed method is capable of performing the fusion operation between various modalities of images, such as MRI-CT, MRI-PET, and MRI-SPECT combinations by using two different architectures. The simulation results show that the proposed method resulted in better subjective and objective performance as compared to state of art approaches.

Optimal fusion rule for distributed detection with channel errors taking into account sensors' unreliability probability when protecting coastlines

In this paper, algorithms that make decisions on the presence or absence of penetration on a protected object with both ideal and non-ideal communication channels are synthesised and analysed. Local sensor decision rules based on an energy detector and its performance characteristics are presented. We determine the dependencies of the total error probability on the energy parameter taking into account the energy emitted from the target at the level of local sensors and the channel's signal-to-noise ratio. The gain of the optimal fusion rule in efficiency compared to known fusion rules such as the LRT-BER and Chair-Varshney fusion rule is shown. The detection algorithm under possible sensor failure and its detection performance is also presented. With the unknown target location on a coastline, the detection rules are given and the detection performance is analysed.

Joint Activity Detection and Channel Estimation in Cell-Free Massive MIMO Networks With Massive Connectivity

Cell-free massive MIMO is one of the key technologies for future wireless communications, in which users are simultaneously and jointly served by all access points (APs). In this paper, we investigate the minimum mean square error (MMSE) estimation of effective channel coefficients in cell-free massive MIMO systems with massive connectivity. To facilitate the theoretical analysis, only single measurement vector (SMV) based MMSE estimation is considered in this paper, i.e., the MMSE estimation is performed based on the received pilot signals at each AP separately. Inspired by the decoupling principle of replica symmetric postulated MMSE estimation of sparse signal vectors with independent and identically distributed (i.i.d.) non-zero components, we develop the corresponding decoupling principle for the SMV based MMSE estimation of sparse signal vectors with independent and non-identically distributed (i.n.i.d.) non-zero components, which plays a key role in the theoretical analysis of SMV based MMSE estimation of the effective channel coefficients in cell-free massive MIMO systems with massive connectivity. Subsequently, based on the obtained decoupling principle of MMSE estimation, likelihood ratio test and the optimal fusion rule, we perform user activity detection based on the received pilot signals at only one AP, or cooperation among the entire set of APs for centralized or distributed detection. Via theoretical analysis, we show that the error probabilities of both centralized and distributed detection tend to zero when the number of APs tends to infinity while the asymptotic ratio between the number of users and pilots is kept constant. We also investigate the asymptotic behavior of oracle estimation in cell-free massive MIMO systems with massive connectivity via random matrix theory. Moreover, in order to demonstrate the potential performance loss of SMV based MMSE estimation, which does not employ the correlation between the received pilot signals at different APs, the multiple measurement vector (MMV) based MMSE estimation, i.e., joint MMSE estimation with pilot signals from all APs, is analyzed via numerical results. Numerical analysis shows that the theoretical analyze with our decoupling principle for the SMV based MMSE estimation of sparse signal vectors with i.n.i.d. non-zero components matches well with the numerical results.

Enhanced Audit Bit Based Distributed Bayesian Detection in the Presence of Strategic Attacks

This paper employs an audit bit based mechanism to mitigate the effect of Byzantine attacks on distributed Bayesian detection systems. In this framework, the optimal attacking strategy for strategic attackers is investigated for the traditional audit bit based scheme (TAS) to evaluate the robustness of the system. We show that it is possible for a strategic attacker to degrade the performance of TAS to the system without audit bits. To enhance the robustness of the system in the presence of strategic attackers, we propose an enhanced audit bit based scheme (EAS). The optimal fusion rule for the proposed scheme is derived and the detection performance of the system is evaluated via the probability of error for the system. Simulation results show that the proposed EAS improves the robustness and the detection performance of the system. Moreover, based on EAS, another new scheme called the reduced audit bit based scheme (RAS) is proposed which further improves system performance. We derive the new optimal fusion rule and the simulation results show that RAS outperforms EAS and TAS in terms of both robustness and detection performance of the system. Then, we extend the proposed RAS for a wide-area cluster based distributed wireless sensor networks (CWSNs). Simulation results show that the proposed RAS significantly reduces the communication overhead between the sensors and the FC, which prolongs the lifetime of the network.

Optimal fusion rule for distributed detection with channel errors taking into account sensors' unreliability probability when protecting coastlines

Optimal fusion rule for distributed detection with channel errors taking into account sensors' unreliability probability when protecting coastlines

Distributed Detection Fusion in Clustered Sensor Networks Over Multiple Access Fading Channels

In this paper, we tackle decision fusion for distributed detection in a randomly-deployed clustered Wireless Sensor Networks (WSNs) operating over a non-ideal multiple access channels (MACs), i.e. considering Rayleigh fading, path loss and additive noise. To mitigate fading, we propose the distributed equal gain transmit combining (dEGTC) and distributed maximum ratio transit combining (dMRTC). The first and second order statistics of the received signals were analytically computed via stochastic geometry tools. Then the distribution of the received signal over the MAC are approximated by Gaussian and log-normal distributions via moment matching. This enabled the derivation of moment matching optimal fusion rules (MOR) for both distributions. Moreover, suboptimal simpler fusion rules were also proposed, in which all the CHs data are equally weighed, which is termed moment matching equal gain fusion rule (MER). It is shown by simulations that increasing the number of clusters improve the performance. Moreover, MOR-Gaussian based algorithms are better under free-space propagation whereas their lognormal counterparts are more suited in the ground-reflection case. Also, the latter algorithms show better results in low SNR and SN numbers conditions. We have proved that the received power at the CH in MAC is proportional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\lambda ^{2} R^{2})$</tex-math></inline-formula> and to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(\lambda ^{2} \ln ^{2} R)$</tex-math></inline-formula> in the free-space propagation and the ground-reflection cases respectively, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> is SN deployment intensity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R$</tex-math></inline-formula> is the cluster radius. This implies that having more clusters decreases the required transmission power for a given SNR at the receiver.

Explicit Recursive Track-to-Track Fusion Rules for Nonlinear Multi-Sensor Systems

This letter presents explicit sub-optimal track-to-track fusion algorithms for Multi-Sensor Systems (MSS) estimating nonlinear processes. The individual tracks in an MSS are correlated due to the presence of a common process noise in the track estimation errors. Herein, we propose recursive formulae for consistent correlation estimation in mildly and highly nonlinear systems that respectively use Extended Kalman Filters (EKF) and Unscented Kalman Filters (UKF) for track estimation. In a mildly nonlinear system, the linearized model employed in the EKF-based MSS architecture offers a correlation propagation formula whose coupling with the optimal track fusion rule generates a sub-optimal fused estimate. On the other hand in highly nonlinear systems, the UKF-based architectures are proven effective for track estimation. The UKF works based on the unscented transform of deterministic sigma points, which is equivalent to the Statistical Linearization Regression (SLR) process. For UKF-based MSS architectures, we propose a consistent correlation propagation recursion according to the SLR technique that will be coupled with the optimal track fusion rule to generate a sub-optimal fused estimate. The performance of the developed fusion algorithms is demonstrated through conducting a statistical test and an average root mean square error analysis.

Analysis of energy‐efficient cooperative spectrum sensing with improved energy detectors and multiple antennas over Nakagami‐q/n fading channels

SummaryCognitive radio (CR) is an advanced technique used for the utilization of radio spectrum. A CR node uses the radio spectrum of a licensed user (called as primary user, PU) deviously. In this work, a cooperative sensing network (CSN) with improved energy detection (IED)‐based CR nodes is proposed. Each CR node consists of multiple antennas and perform themselves selection diversity (SC) technique. Each CR node senses a PU through erroneous sensing channel and reports its sensing data (1‐bit binary‐decision) to the fusion center (FC) through erroneous reporting channels. At FC, existence of PU (presence or absence) is identified using k‐out‐of‐N fusion rule. The novel expressions for detection probability over noise plus Nakagami‐q/n fading channels are derived and the mathematical frameworks for analysis of throughput and energy‐efficiency of the proposed network are developed. The simulation testbed is also developed and presented in this work to validate the analytically obtained performance characteristics. For several network parameters values, the investigation on comparison between IED and traditional energy detection method for various decision fusion rules is studied. Further, performance characteristics are analytically illustrated for throughput and energy‐efficiency over noise plus Nakagami‐q/n fading channels. The impact of diversity technique and effect of fading severity parameters on the throughput and energy‐efficiency are also investigated. The effect of channel error on total error performance for both proposed and conventional networks is shown. Finally, optimal fusion rule and optimal network parameters values correspond to maximum throughput and maximum energy‐efficiency are also identified.

Space-Time Spreading Aided Distributed MIMO-WSNs

In this letter, we consider the plaguing, yet rarely handled problem of interference resulting from superposition of multiple sensor signals in time, when sent over a multiple access channel (MAC) in wireless sensor networks (WSNs). We propose space-time spreading (STS) of local sensor decisions before reporting them over a MAC to i) minimize interference and ii) reduce energy required for combating interference due to superposition of sensor decisions. Each sensor decision is encoded on appropriately indexed space-time block of fixed duration using dispersion vectors, such that a single sensor is activated over each space-time block while all the other sensors are silent. At the receive side of the reporting channel, we assume a multi-antenna decision fusion center (DFC), thereby representing a distributed multiple-input-multiple-output (MIMO) communication scenario. We formulate and compare optimum and sub-optimum fusion rules for fusing sensor decisions at the DFC to arrive at a reliable conclusion. Simulation results demonstrate gain in fusion performance with STS-aided transmission by 3 to 6 times over performance without STS.

Multi-Party Dynamic State Estimation That Preserves Data and Model Privacy

In this paper we focus on the dynamic state estimation which harnesses a vast amount of sensing data harvested by multiple parties and recognize that in many applications, to improve collaborations between parties, the estimation procedure must be designed with the awareness of protecting participants’ data and model privacy, where the latter refers to the privacy of key parameters of observation models. We develop a state estimation paradigm for the scenario where multiple parties with data and model privacy concerns are involved. Multiple parties monitor a physical dynamic process by deploying their own sensor networks and update the state estimate according to the average state estimate of all the parties calculated by a cloud server and security module. The paradigm taps additively homomorphic encryption which enables the cloud server and security module to jointly fuse parties’ data while preserving the data privacy. Meanwhile, all the parties collaboratively develop a stable (or optimal) fusion rule without divulging sensitive model information. For the proposed filtering paradigm, we analyze the stabilization and the optimality. First, to stabilize the multi-party state estimator while preserving observation model privacy, two stabilization design methods are proposed. For special scenarios, the parties directly design their estimator gains by the matrix norm relaxation. For general scenarios, after transforming the original design problem into a convex semi-definite programming problem, the parties collaboratively derive suitable estimator gains based on the alternating direction method of multipliers (ADMM). Second, an optimal collaborative gain design method with model privacy guarantees is provided, which results in the asymptotic minimum mean square error (MMSE) state estimation. Finally, numerical examples are presented to illustrate our design and theoretical findings.

Dynamic Spatial Fusion of Cloud Vertical Phase from CALIPSO and CloudSat Satellite Data

Cloud phase is a core parameter of inversion of cloud characteristics. The accuracy of cloud phase affects the results of cloud optical and microphysical characteristics. In this study, we obtain the cloud vertical phase (CVP ) products of CALIPSO and CloudSat satellites, then we put forward a dynamic spatial fusion algorithm for the fusion of the two products. A series of spatial optimal CVP fusion rules are presented for dual-source data, and we realize CVP fusion using these rules. We took Typhoon Lupit in the Pacific Ocean as an experimental object. The results show that the total cloud pixel amount increased by 124.09% and 10.54%, respectively, compared to those of CALIPSO and CloudSat. The recognition of different CVP is 7.97% and 1.37%. The results show that this method can improve the accuracy of multi-source CVP inversion effectively, and provide new ways for the synergy of multi-sensor satellites.

Distributed Sensor Local Linear Fusion Detection of Weak Pulse Signal in Chaotic Background

This paper combines the distributed sensor fusion system with the signal detection under chaotic noise to realize the distributed sensor fusion detection from chaotic background. First, based on the short‐term predictability of the chaotic signal and its sensitivity to small interference, the phase space reconstruction of the observation signal of each sensor is carried out. Second, the distributed sensor local linear autoregressive (DS‐LLAR) model is constructed to obtain the one‐step prediction error of each sensor. Then, we construct a Bayesian risk model and also obtain the corresponding conditional probability density function under each sensor’s hypothesis test which firstly needs to fit the distribution of prediction errors according to the parameter estimation. Finally, the fusion optimization algorithm is designed based on the Bayesian fusion criterion, and the optimal decision rule of each sensor and the optimal fusion rule of the fusion center are jointly solved to effectively detect the weak pulse signal in the observation signal. Simulation experiments show that the proposed method which used a distributed sensor combined with a local linear model can effectively detect weak pulse signals from chaotic background.

A Clustering Algorithm to Improve the Scan Statistic in Sensor Detection Systems

The success of the scan statistic in detecting anomalies in georeferenced data has motivated its use in distributed sensor systems to detect an emitter at an unknown location. Sensors are grouped into clusters, cluster statistics are produced, and the scan statistic decides that the emitter is present if any cluster statistic is above a threshold. Although the scan statistic is not the optimal fusion rule, it avoids combining strong measurements from sensors near the emitter with weak measurements from sensors far from the emitter. The question that motivates this paper is: could a clustering algorithm improve the detection performance of the scan statistic? Previous studies on the scan statistics considered that the set of clusters is given or is the product of a scanning process; and previous studies on clustering algorithms for wireless sensor networks have not considered forming clusters specifically for the scan statistic. Our first goal is to highlight the opportunity of improving the scan statistic by carefully designing the cluster set. We discuss how the cluster set influences not only the detection performance, but also processing and communication in the system. Our second goal is to propose and study a new clustering algorithm to build the cluster set for the scan statistic. Although suboptimal, our algorithm produces cluster sets that reach similar or better detection performance than the usually considered cluster sets with a significantly lower number of clusters, which results in less processing and communication in the system.

Optimal power allocation for M-ary distributed detection in the presence of channel uncertainty

We consider a wireless sensor network (WSN), consisting of several sensors and a fusion center (FC), which is tasked with detecting M known signals in Gaussian noise. Sensors make M-ary decisions and transmit their digitally modulated decisions over orthogonal fading channels to the FC. Considering two coherent and non-coherent systems, we study how to distribute the total transmit power among the sensors such that J-divergence at the FC is maximized, subject to cumulative and individual transmit power constraints. To fairly compare the two systems, we consider the cost of channel estimation for coherent systems via introducing trade off between pilot and data transmission. We develop power allocation schemes and provide the optimal fusion rule for both systems. Our numerical results show that, the coherent system does not necessarily outperform the non-coherent system, when the cost of channel estimation (required transmit power for pilot) is considered. In particular, when the total transmit power is low (and the effect of channel estimation is more severe) the non-coherent system outperforms the coherent one. The proposed power allocation schemes for the coherent system allow us to reduce the total transmit power consumption up to 80%, compared with uniform power allocation.

Energy efficiency maximization by optimal fusion rule in frequency-flat-fading environment

In cognitive radio networks, cooperative spectrum sensing improves the reliability of decision about the primary user channel condition. However, the challenge is to optimize the energy efficiency, as energy consumption is high with cooperative spectrum sensing due to multiple secondary users. In this paper, energy efficiency for cooperative spectrum sensing by optimal fusion rule is investigated and maximized by minimizing the number of secondary users. Here, decision fusion rule for the number of secondary users, is optimized and compared for the fading and non-fading environment. The energy efficiency is maximized and compared for frequency flat-fading channel with non-fading Additive White Gaussian Noise channel. The detection quality metrics as the measure of probability of detection and probability of false alarm, are also considered as constraints. The exhaustive numerical results achieved after simulation in MATLAB, illustrate that the energy efficiency is maximum for non-fading channel and k-out-of-N rule is the best among all fusion rules.

Detection of a recurrent static target using binary sensor networks

The authors address the problem of decentralised detection of a recurrent event produced by a static uncooperative target in a wireless network of spatially distributed sensors. The presence or absence of the target is determined by applying fusion rules on local binary decisions of individual sensors. Optimal fusion rules require complete statistical knowledge about local detection and false alarm probabilities; hence, in practice they are infeasible. Previous works, such as the counting rule test, scan statistics and the generalised likelihood ratio test, have suggested sub-optimal fusion rules based on the total number of detecting sensors. Neither method takes full advantage of the spatial or temporal correlation between adjacent sensors. In practice, the decisions of adjacent sensors are dependent both in space (as the target is static) and in time (as the event reoccurs). Herein, the authors propose an approach that capitalises on the temporal and spatial arrangement of the local decisions. Simulation examples demonstrate that the detection probability of the proposed spatio-temporal rule is significantly higher than that of the common methods, and also achieves a lower probability of false alarm. Moreover, real data results show that the proposed approach is robust to strong environmental noises.

The verification model of multi-focus image fusion by simulating subjective evaluation

We present a model to simulate the subjective evaluation and compare various fusion algorithms. First, we produce an all-focus image and two multi-focus images by the help of two filters. Second, we fuse two multi-focus images with two representative algorithms WT and CT. Third, we decide the optimal fusion rules of WT and CT by comparing the fused images with an all-focus image. Finally, we improve the performances of fused images by combining several algorithms. Simulation shows the verification model can compare various fusion algorithms or rules. Meanwhile, our fusion model can get better performances than other algorithms or rules.