Maximum A Posterior Research Articles

On the Performance of Training-Based IRS-Assisted Communications Under Correlated Rayleigh Fading

The channel state information (CSI) is crucial in communication systems assisted by intelligent reflecting surfaces (IRSs). This paper is on the phase estimation of individual channels in IRS-assisted communication systems with single-antenna transceivers under the correlated Rayleigh fading. We consider both the fully-active-IRS where all IRS elements are active and the hybrid-IRS where partially IRS elements are active, where an active IRS element is equipped with a sensing device for pilot signal reception. We derive the maximum likelihood (ML) estimator for channel phases of all IRS elements based on the observations on active IRS elements. This estimator is also proved to be the minimum mean square error (MMSE), maximum a posterior (MAP) and minimum mean absolute error (MMAE) estimators. Then we conduct performance analysis in terms of the gain and the capacity of the cascaded transmitter-IRS-receiver channel with perfectly known and estimated individual channel phases. Numerical results are provided to show that the performance of IRS-assisted communication systems with our proposed phase estimator is close to that with perfect CSI and validate our theoretical analysis.

Concatenated Permutation Codes under Chebyshev Distance

Permutation codes are error-correcting codes over symmetric groups. We focus on permutation codes under Chebyshev (ℓ∞) distance. A permutation code invented by Kløve et al. is of length n, size 2n-d and, minimum distance d. We denote the code by φn,d. This code is the largest known code of length n and minimum Chebyshev distance d > n/2 so far, to the best of the authors knowledge. They also devised efficient encoding and hard-decision decoding (HDD) algorithms that outperform the bounded distance decoding. In this paper, we derive a tight upper bound of decoding error probability of HDD. By factor graph formalization, we derive an efficient maximum a-posterior probability decoding algorithm for φn,d. We explore concatenating permutation codes of φn,d=0 with binary outer codes for more robust error correction. A naturally induced pseudo distance over binary outer codes successfully characterizes Chebyshev distance of concatenated permutation codes. Using this distance, we upper-bound the minimum Chebyshev distance of concatenated codes. We discover how to concatenate binary linear codes to achieve the upper bound. We derive the distance distribution of concatenated permutation codes with random outer codes. We demonstrate that the sum-product decoding performance of concatenated codes with outer low-density parity-check codes outperforms conventional schemes.

Bayesian geoacoustic parameters inversion for multi-layer seabed in shallow sea using underwater acoustic field

Seabed geoacoustic parameters play an important role in underwater acoustic channel modeling. Traditional methods to determine these parameters, for example, drilling, are expensive and are being replaced by acoustic inverse technology. An inversion method based on Bayesian theory is presented to derive the structure and geoacoustic parameters of a layered seabed in a shallow sea. The seabed was considered a layered elastic medium. The objective of this research was to use the sound pressure detected by underwater acoustic sensors at different positions and to use nonlinear Bayesian inversion to estimate the geoacoustic parameters and their uncertainties in the multi-layer seabed. Specifically, the thickness, density, compression wave speed, shear wave speed, and the attenuation of these two wave speeds were determined. The maximum a posterior (MAP) model and posterior probability distribution of each parameter were estimated using the optimized simulated annealing (OSA) and Metropolis-Hastings sampling (MHS) methods. Model selection was carried out using the Bayesian information criterion (BIC) to determine the optimal model that thoroughly explained the experimental data for different parameterizations. The results showed that the OSA is much more capable of delivering high-accuracy results in multi-layer seabed models. The compression wave speed and shear wave speed were less uncertain than the other parameters, and the parameters in the upper layer had less uncertainty than those in the lower layer.

An efficient unfolding network with disentangled spatial-spectral representation for hyperspectral image super-resolution

Hyperspectral image super-resolution (HSI SR) is dramatically impacted by high spectral dimensionality, insufficient spatial resolution, and limited availability of training samples. Current approaches mainly rely on complex data-driven models to address some of these challenges, and the characteristics of HSI are not fully considered in the model design. In this paper, we propose an efficient unfolding network with disentangled spatial-spectral representation (EUNet) for HSI SR by combining domain knowledge (i.e., spectral correlation, degradation model, and structure prior) with deep learning. Specifically, the optimization process of the super-resolution prior-driven Maximum A Posterior (MAP) framework is unfolded into an interpretable multi-stage network, which inherits the advantages of deep learning-based image super-resolution (e.g., feature extraction in low-resolution space) and explicitly imposes the degradation model constraint. To well incorporate the structure prior of HSI, spatial and spectral feature extraction is disentangled by a variant of depthwise separable convolution, and spectral correlation is embedded by a lightweight spectral attention mechanism, so that the difficulty and computational complexity of feature learning are greatly reduced. Experiments on benchmark datasets with different degradation models demonstrate the feasibility and superiority of the proposed EUNet over other state-of-the-art methods in terms of evaluation metrics and computational complexity. The source code is available at https://github.com/denghong-liu/EUNet.

The Feasibility of Biologically Guided Radiation Therapy Implemented in a Small-Animal Radiation Therapy Platform Integrated with Quad-Modal On-Board Imaging

<h3>Purpose/Objective(s)</h3> Unparallel evolution between clinical radiation therapy (RT) paradigms and preclinical RT techniques, especially in biologically guided RT, has posed a challenge to completely validate the benefits and pitfalls of novel RT techniques prior to their translation to bedside practices. In this study, we firstly investigated the feasibility of biologically guided RT implemented within a small animal radiation therapy (SART) platform, with quad-modal on-board positron emission tomography (PET), single-photon emission computed tomography (SPECT), spectral CT, and cone-beam computed tomography (CBCT) imaging integrated, in a Monte Carlo model as a proof-of-concept. <h3>Materials/Methods</h3> The SART platform with quad-modal imaging guidance was modeled by using a planning tool. A preclinical biologically guided RT workflow with quad-modal imaging guidance was designed, in which image-guided RT and emission-guided radiation therapy (EGRT) can be implemented. To demonstrate the potential of contrast-enhanced spectral CT used in biologically guided RT for simultaneously guiding dose prescription based on tracer uptakes and dose calculation based on underlying tissue electron densities in the platform, iodine uptake fractions and virtual non-contrast electron densities in the Kidney1 inserts within a simulated phantom, mixed with an iodine contrast agent at electron fractions of 0.02 and 0.03, were decomposed quantitatively by using the Bayesian eigen tissue decomposition method and the maximum a posterior (MAP) estimation. To demonstrate EGRT implemented in the platform, the preliminary algorithm of EGRT was illustrated by introducing a 2-mm setup error to a target in the simulated phantom. The dose calculation was implemented after the set of binary micro-multileaf collimator (bmMLC) configurations was determined. The dose distributions delivered by EGRT were compared to that delivered by the conventional RT method with three treatment beams with and without setup error. <h3>Results</h3> For the Kidney1 insert with an iodine contrast agent fraction of 0.02, the average relative errors in the iodine contrast agent fraction and the underlying electron density estimated were 0.64% and 0.95%, respectively. In EGRT, the simulations resulted in 4339 and 5197 beamlet responses in an exemplary dose slice delivery with and without the 2-mm setup error, respectively. Compared to the conventional RT method, EGRT scheme introduced into the SART platform was validated to be more robust to setup errors while providing improved tumor targeting and a lesser dose burden on normal tissues during the treatment beam delivery in preclinical RT setting. <h3>Conclusion</h3> The results demonstrated the successful implementation of biologically guided RT within the SART platform with quad-model imaging guidance. With the comprehensive image- and emission-guided RT schemes integrated, this novel SART platform affords one-stop preclinical RT studies.

Image restoration for optical synthetic aperture system via patched maximum–minimum intensity prior and unsupervised DenoiseNet

Optical synthetic aperture system improves spatial resolution significantly. However, the image will be degraded and blurred because of the sparse sub-mirror arrangement. Therefore, it is of great significance to exploit the restoration method to obtain an ideal latent image. A method combining maximum a posterior (MAP) framework model optimization with deep learning is presented to enhance imaging quality. The model is optimized by patched maximum–minimum intensity (PMMI) to alleviate insufficient representation of existing priors, while DenoiseNet is designed to train the device and eliminate noise interference. Unsupervised learning is applied to solve the acquisition difficulty of original image labels dispensed with clean samples as training set. When a noise of 30 dB is added, the PSNR of the remote sensing test set increases from 20.90 dB to 23.01 dB. SSIM ameliorates from 0.345 to 0.651 by 88.6% and MS-SSIM from 0.781 to 0.883 by 13.1%. The mid-frequency MTF also has a significant improvement.

Effect of mesh refinement on the solution of the inverse uncertainty quantification problem for transient physics

In this paper, effect of mesh refinement on the solution of the IUQ problem for transient physics was studied. Two mathematical formulations, the Maximum Likelihood Estimate (MLE) and the Maximum A Posterior (MAP), were adopted to solve the IUQ problem. Global Sensitivity Analysis (GSA) and Local Sensitivity Analysis (LSA) were performed to provide the necessary data for MLE and MAP implementation. TRACE models with three different mesh numbers based on the transient Flooding Experiment with Blocked Array (FEBA) benchmark were developed. Results of this analysis show that statistical expectation of the physical models (statistical mean) tends to shift towards a certain value with mesh refinement. This shifting behavior can be related to the decrease in the truncation error resulting from numerical discretization due to mesh refinement, consequently, compensating for the mismatch between experimental data and code prediction results that may be falsely credited to the uncertainties inherent in the physical models. Moreover, the results show that the relative absolute error between experimental data and code prediction results was decreased upon incorporating the input parameter uncertainties that were determined based on MLE and MAP formulations. In all cases, the error was smallest for the most refined mesh.

Adaptive fractional‐order unscented Kalman filter with unknown noise statistics

SummaryThis article deals with state estimation of complex nonlinear discrete fractional‐order systems with unknown noise statistics by means of an adaptive fractional‐order Unscented Kalman filter (AFUKF). Firstly, in order to alleviate the communication burden of fractional‐order Unscented Kalman filter, short‐term memory effect is utilized to decide an appropriate memory length. Then aiming at the problem of filtering divergence and accuracy degradation caused by unknown statistical characteristics of noise, based on the maximum a posterior (MAP) principle, a noise statistical estimator is introduced to estimate and correct the statistical characteristics of noise in real‐time. Finally, the unbiasedness of the proposed algorithm is analyzed to verify that the estimated mean and covariance of noise are unbiased. The effectiveness and accuracy of AFUKF are demonstrated via simulation experiments.

A new approach to overcome the inconsistency between SPECT and the anatomical map in maximum A-posterior expectation-maximization reconstruction algorithm

Noise reduction while preserving spatial resolution is one of the most important challenges in the reconstructing of emission tomography images. One of the resolving methods is the Bowsher maximum a-posteriori expectation-maximization reconstruction (MAPEM) algorithm. This method considers a binary selection of the neighbors of each voxel based on the prior anatomical values to use in the regularization function. This method is particularly susceptible to imposing the wrong data into the reconstructed image due to the spatial or functional inconsistencies between the anatomical image and the actual activity distribution. Because of the poor spatial resolution of single-photon emission tomography (SPECT) images and the different nature of emission and anatomical imaging, there is not enough certainty of inconsistency with anatomical images. Therefore, we proposed a new weighted Bowsher method that can overcome this weakness while the image quality indexes, especially the spatial resolution, are almost preserved. In the proposed method, each of the neighbors of a specific voxel takes a constant weight depending on the order of its value and independent of its intensity quantity. The proposed method was evaluated using some different physical phantoms and a patient scan. The results show that the proposed method has superiority in the presence of inconsistency; moreover, the proposed method gives nearly similar results to the regular Bowsher MAPEM in case of consistency. In conclusion, we show that using a suitable constant weighting factor in Bowsher MAPEM, one can operatively reduce the image noise while preserving the image quality parameters where the emission tomography images are either consistent or inconsistent with the prior anatomical map.

Local estimators and Bayesian inverse problems with non-unique solutions

Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solutions, the classical estimators such as the maximum a posterior (MAP) and conditional mean (CM) are not suitable. We introduce two new estimators, the local maximum a posterior (LMAP) and local conditional mean (LCM). A simple algorithm based on clustering to compute LMAP and LCM is proposed. Their applications are demonstrated by three inverse problems: an inverse spectral problem, an inverse source problem, and an inverse medium problem.

Oil Spill Candidate Detection Using a Conditional Random Field Model on Simulated Compact Polarimetric Imagery

Although the compact polarimetric (CP) synthetic aperture radar (SAR) mode of the RADARSAT Constellation Mission (RCM) offers new opportunities for oil spill candidate detection, there has not been an efficient machine learning model explicitly designed to utilize this new CP SAR data for improved detection. This paper presents a conditional random field model based on the Wishart mixture model (CRF-WMM) to detect oil spill candidates in CP SAR imagery. First, a “Wishart mixture model” (WMM) is designed as the unary potential in the CRF-WMM to address the class-dependent information of oil spill candidates and oil free water. Second, we introduce a new similarity measure based on CP statistics designed as a pairwise potential in the CRF-WMM model so that pixels with strong spatial connections have the same class label. Finally, we investigate three different optimization approaches to solve the resulting maximum a posterior (MAP) problem, namely iterated conditional modes (ICM), simulated annealing (SA), and graph cuts (GC). The results show that our proposed CRF-WMM model can delineate oil spill candidates better than the traditional CRF approaches, and that the GC algorithm provides the best optimization.

Evaluation of the effects of stock enhancement on population dynamics using a state-space production model: A case study of Japanese flounder in the Seto Inland Sea

The effect of stock enhancement on increasing biomass is not well understood and is highly controversial because released fish might have a competitive impact on wild stocks. Quantitative assessments exploring the possible impacts of stock enhancement on population dynamics are rare, especially in data-limited fisheries. We developed a state-space production model incorporating stock enhancement to evaluate the impact of stock enhancement at a population scale. Since observation and process errors impair the accuracy of parameter estimation and biomass prediction, we investigated whether prior biomass reference information could improve analytical performance of the state-space production model. We compared the performance of maximum likelihood (ML) and maximum a posterior (MAP) estimation in a special case of a state-space Pella-Tomlinson model or in a state-space Schaefer model, for three simulated levels of process and observation errors. We found that the MAP parameter estimation with valid prior biomass reference data was generally superior to the ML parameter estimation. As a case study, we applied the extended state-space Pella-Tomlinson model to disentangle the impacts of stock enhancement for the Japanese flounder (Paralichthys olivaceus) in the Seto Inland Sea using long-term fishery data. The results showed a limited contribution of stock enhancement to Japanese flounder in the Seto Inland Sea, suggesting that most released flounder replaced the wild fish niche. Given the number of fish released in 2018, future projections for the next ten years under three different fishing pressures showed that stock enhancement was more effective at augmenting biomass when fishing pressure was higher, but that total biomass decreased simultaneously. Catch increase (decrease) in 30% resulted in a 9% decrease (8% increase) in the biomass and a 28% increase (15% decrease) in the net biomass augmentation from stocking. Therefore, a balance between stock enhancement and exploitation is important to obtain sustainable production and efficient stocking, especially facing global climate change which possibly influences the carrying capacity. Our results suggest that a state-space production model can be used to evaluate the impact of stock enhancement and implement better fishery management.

Bearing Fault Diagnosis Under Small Data Set Condition: A Bayesian Network Method With Transfer Learning for Parameter Estimation

Bearings are broadly applied in various types of industrial systems. Fault diagnosis, as a promising way for reliability of modern industrial internet of thing applications, has attracted increasing attention from both academia and industry fields. Being ideal modeling and inference tool in uncertainty situations, Bayesian network (BN) is becoming increasingly popular in many systems. However, in practical uncertain and complicated engineering surroundings, it&#x2019;s difficult or expensive to collect massive labeled fault data for the sake of fault diagnosis model learning. To address the issue of BN parameter learning under small data set conditions, this paper proposes a Varying Coefficient Transfer Learning (VCTL) algorithm based on aggregation and transfer learning, that considers both knowledge from the resource domain and the resource relevance contributions. The balancing weight function is designed to determine whether the learning task in the resource domain is activated. Relevance weight factors are proposed to measure the relevance of resource and target parameters quantitatively, by combing parameter information from resource domains with those obtained from the target domain, using maximum a posterior (MAP) or maximum likelihood estimation (MLE). Finally, the target parameters are aggregated with both the target initial parameters and the parameter knowledge from the resource domain. Based on VCTL, a bearing fault diagnosis approach is proposed and verified. The experimental results show that, under the condition of the small data set, learning accuracy of VCTL algorithm with varying coefficient aggregation is better than MLE algorithm, MAP algorithm or state-of-the-art parameter transfer method, local linear pooling transfer learning (LoLP) algorithm. Under the condition of sufficient data set, learning accuracy of VCTL algorithm approaches the classical MLE or MAP, and the correctness of the proposed algorithm is verified. Moreover, we illustrate the successful application to real-world bearing fault diagnosis case with VCTL, where we had access to expert-provided resource knowledge and real fault diagnosis data.

Online Inference for Mixture Model of Streaming Graph Signals With Sparse Excitation

This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with excitation driven by a sparse matrix. While the mixture model is motivated from practical scenarios, it presents significant challenges to prior graph learning methods. As a remedy, we consider an inference problem focusing on the node centrality of graphs. We design an expectation-maximization (EM) algorithm with a unique low-rank plus sparse prior derived from low pass signal property. We propose a novel online EM algorithm for inference from streaming data. As an example, we extend the online algorithm to detect if the signals are generated from an abnormal graph. We show that the proposed algorithms converge to a stationary point of the maximum-a-posterior (MAP) problem. Numerical experiments support our analysis.

Noisy multimodal brain image registration using markov random field model

In this paper, a new scheme is proposed to register brain Magnetic Resonance (MR) and Computed Tomography (CT) images under a noisy environment. The scheme is developed based on the notion of mutual information and this is extended to the feature space-based registration. The 2D joint histogram of the noisy MR and CT images has been computed and this is assumed to be the degraded version of the true 2D joint histogram that corresponds to the CT and MR images. The true 2D joint histogram is modeled as Markov Random Field (MRF) model and is estimated from the degraded one by formulating the problem in Maximum A Posterior (MAP) estimation framework. The MAP estimates are obtained by the combination of Simulated Annealing (SA) and Iterated Conditioned Mode (ICM) algorithms. The Mutual Information (MI) at different values of the parameter vector θ are computed from the estimated joint histogram and is maximized to determine the optimal registration parameter. The MI curve is modeled as multivariate Gaussian distribution and the registration parameter vector is obtained with a confidence interval. The scheme has been tested with the slices of patients from the Retrospective Image Registration Evaluation (RIRE) database. The efficacy of the scheme on MR and CT volumes is demonstrated by rendering the registered slices. The proposed algorithm is successfully tested with different degrees of Gaussian, Rician and Rayleigh noise conditions. Performance measures such as parameter estimation errors, error statistics and landmark based validation are used to demonstrate the efficacy of the proposed algorithm. The scheme is found to exhibit improved performance, especially at high noisy conditions as compared to the existing schemes.

Deep convolutional neural network with random field model for lake ice mapping from Sentinel-1 imagery

ABSTRACT Timely information on lake ice cover conditions is critical in support of commercial shipping, winter-road transportation, and winter leisure activities such as snowmobiling and ice fishing. Monitoring of lake ice extent and ice phenology (i.e. dates associated with freeze-up/break-up and ice duration) is also valuable for improving numerical weather prediction (NWP) and for climate monitoring. The availability of free synthetic aperture radar (SAR) data from the European Space Agency’s Sentinel-1 A/B constellation provides an unprecedented opportunity to develop operational algorithms for lake ice cover mapping at a temporal frequency not available until now from SAR missions (ca. every 1–5 days depending on latitude). For NWP, rapid and accurate mapping of ice cover and open water areas in lake-rich regions is required. However, the classification of SAR imagery using traditional machine learning (ML) approaches is challenging due to the large data volume generated by imaging systems such as Sentinel-1 SAR as well as the complexity of radar signatures as a function of sensor and target characteristics. For lakes specifically, radar backscatter can vary greatly with incidence angle, polarization and surface properties (e.g. calm and wind-roughed open water, new thin ice, surface roughness due to the presence of pressure ridges, ice type, melting of ice and on-ice snow). To address the challenge of large-scale lake ice mapping, we investigate the GPU-boosted deep neural network approach that is efficient at handling big complex data. In this paper, we design a novel maximum a posterior (MAP) approach combining a convolutional neural network (CNN) and conditional random field (CRF) for better addressing the challenges of operational lake ice mapping. The proposed approach is tested on 17 Sentinel-1 dual-polarization (VV and VH) SAR images, where eight are used for training and validation and nine used for out-of-sample testing. To identify the optimal network architecture, an independent validation set is used to evaluate the performance of a series of six CNNs with increasing model complexity. The best model overcomes the noise effect in Sentinel-1 SAR imagery and the lake ice signature ambiguity issue; it achieves average classification accuracies of 97.10% and 97.14% for open water and ice, respectively, on the validation set. Moreover, the best model outperforms the last-ranked model by about 2% in terms of mean overall accuracy (OA), demonstrating the improvement and importance of model selection. The use of CRF can consistently improve the CNN by reducing the artefacts and noise effect in ice maps, outperforming the CNN model when used alone by about 3% in terms of mean OA on the validation set. The proposed CNN-CRF approach also achieves high accuracy on the nine test scenes, achieving a mean OA of 93.10%, demonstrating strong generalization capability that is important for SAR lake ice mapping.

A Novel Bayesian Super-Resolution Method for Radar Forward-Looking Imaging Based on Markov Random Field Model

Super-resolution technology is considered as an efficient approach to promote the image quality of forward-looking imaging radar. However, super-resolution technology is inherently an ill-conditioned issue, whose solution is quite susceptible to noise. Bayesian method can efficiently alleviate this issue through utilizing prior knowledge of the imaging process, in which the scene prior information plays a pretty significant role in ensuring the imaging accuracy. In this paper, we proposed a novel Bayesian super-resolution method on the basis of Markov random field (MRF) model. Compared with the traditional super-resolution method which is focused on one-dimensional (1-D) echo processing, the MRF model adopted in this study strives to exploit the two-dimensional (2-D) prior information of the scene. By using the MRF model, the 2-D spatial structural characteristics of the imaging scene can be well described and utilized by the nth-order neighborhood system. Then, the imaging objective function can be constructed through the maximum a posterior (MAP) framework. Finally, an accelerated iterative threshold/shrinkage method is utilized to cope with the objective function. Validation experiments using both synthetic echo and measured data are designed, and results demonstrate that the new MAP-MRF method exceeds other benchmarking approaches in terms of artifacts suppression and contour recovery.

A new framework for utilizing side information in sparse representation

An underdetermined system of linear equation has infinitely number of answers. To find a specific solution, regularization method is used. For this propose, we define a cost function based on desired features of the solution and that answer with the best matches to these function is selected as the desired solution. In case of sparse solution, zero-norm function is selected as the cost function. In many engineering cases, there is side information which are omitted because of the zero-norm function. Finding a way to conquer zero-norm function limitation, will help to improve estimation of the desired parameter. In this regard, we utilize maximum a posterior (MAP) estimation and modify the prior information such that both sparsity and side information are utilized. As a consequence, a framework to utilize side information into sparse representation algorithms is proposed. We also test our proposed framework in orthogonal frequency division multiplexing (OFDM) sparse channel estimation problem which indicates, by utilizing our proposed system, the performance of the system improves and fewer resources are required for estimating the channel.

MRI reconstruction based on Bayesian piecewise sparsity constraint and adaptive 3D transform

Sparse representation of image is crucial to a promising reconstruction in compressed sensing magnetic resonance imaging (CS-MRI), which significantly accelerates imaging process by highly undersampling k-space data. However, realizing high sparsity and estimation accuracy of image coefficients directly affects the visual quality of the reconstructed image. In this work, an adaptive 3D transform learning method is developed to efficiently enhance the sparsity of coefficients produced by 3D transform on similar patches. In addition, we also consider the statistical characteristics of 3D coefficients, and build a probabilistic model that employs Gaussian scale mixture (GSM) prior for the grouped 3D coefficients with close magnitude levels. Based on Bayesian inference, a piecewise sparsity constraint is derived from maximum a posterior (MAP) estimation of 3D coefficients. Furthermore, the combination of piecewise sparsity constraint and adaptive 3D transform allows one to establish a novel CS-MRI reconstruction model and the corresponding numerical algorithms are deduced under the framework of alternating direction method of multipliers (ADMM). Compared to several advanced CS-MRI methods, the proposed approach better suppresses artifacts and preserves more image features with superior performance metrics.

Amplify-and-forward relaying in mobile multi-hop molecular communication via diffusion

In this paper, we investigate amplify-and-forward (AF) relaying scheme for mobile three-dimensional (3D) multi-hop molecular communication via diffusion (MCvD) in the stochastic channel by using different type of molecules (DTM) and same type of molecules (STM) in each hop, respectively. Under the DTM scheme, both the inter-symbol interference (ISI) and the noise of each link are taken into account Compared with the DTM scheme, an additional factor should be considered for the STM scheme, which is the self-interference (SI) effect. Under DTM and STM, we derive the mathematical expressions of optimal detection thresholds at receiver node in mobile two-hop MCvD system by using the maximum-a-posterior (MAP) decision method. Then we extend the analysis to mobile multi-hop MCvD system. Furthermore, the performances of bit error probability and mutual information are evaluated via particle-based simulation of the Brownian motion. The numerical and simulation results reveal that the performance under DTM outperforms that under STM, which indicates the potential of AF relaying scheme under DTM to improve the overall performance of this system. Besides, the comparison results between mobile and static multi-hop link under DTM and STM are given. The obtained results are expected to provide guidance significance for designing mobile multi-hop MCvD system with lower bit error probability and higher mutual information.