Majorization-minimization Approach Research Articles

Multi-Objective Optimization for IRS-Aidded Multi-user MIMO SWIPT Systems

In this paper, we investigate an intelligent reflecting surface (IRS) assisted simultaneous wireless information and power transfer (SWIPT) system in which users equipped with multiple antennas exploit power-splitting (PS) strategies for simultaneously information decoding (ID) and energy harvesting (EH). Different from the majority of previous studies which focused on single objective optimization problems (SOOPs) and assumed the linearity of EH models, in this paper, we aim at studying the multi-objective optimization problem (MOOP) of the sum rate (SR) and the totalharvested energy (HE) subject to the maximum transmit power (TP) constraint, the user quality of service (QoS), and HE requirements at each user with taking a practical non-linear EH (NLEH) model into consideration. To investigate insightful tradeoffs between the achievable SR and total HE, we adopt the modified weighted Tchebycheff method to transform the MOOP into a SOOP. However, solving the SOOPs and modified SOOP is mathematically difficult due to the non-convexity of the object functions and the constraints of the coupled variables of the base station (BS) transmit precoding matrices (TPMs), the user PS ratios (PSRs), and the IRS phase shift matrix (PSM). To address these challenges, an alternating optimization (AO) framework is used to decompose the formulated design problem into sub-problems. In addition, we apply the majorization-minimization (MM) approach to transform the sub-problems into convex optimization ones. Finally, numerical simulation results are conducted to verify the tradeoffs between the SR and the total amount of HE. The numerical results also indicate that the considered system using the IRS with optimal phase shifts provides considerable performance improvement in terms of the achievable SR and HE as compared to the counterparts without using the IRS or with the IRS of fixed phase shifts.

Robust Transceiver Optimization Against Echo Eclipsing via Majorization-Minimization

The actual target range is unknown during the radar search process, which suggests that an elaborate transceiver synthesis should be concerned, also considering various number of missed target echo samples. This paper focuses on the joint robust synthesis of the radar code and filter bank to improve target detection capability against target echo eclipsing and clutter interference. For several practical considerations, two robust design strategies for transceiver optimization are considered. A majorization-minimization (MM) approach (Section III) is developed to deal with the average signal to interference plus noise ratio (SINR) design problem considering energy and similarity requirements on the waveforms. Then, the MM technique is extended to the max-min case. An accelerated MM-based procedure (Section IV) is presented for solving the worst-case SINR design problem under energy and peak-to-average ratio (PAR) requirements. Both the proposed algorithms can be ensured to converge to a B(oulingand)-stationary point. Finally, simulation results display that two proposed optimization strategies realize better target detection performance and a higher convergence rate compared with the existing approaches.

Multiuser beamforming optimization for IRS‐aided systems with discrete phase shifts

Here, the beamforming design for multiuser multiple-input and multiple-output (MIMO) downlink transmission aided by an intelligent reflecting surface (IRS) with discrete phase shifts is studied. The authors deduce a minimum signal-to-interference-plus-noise-ratio (SINR) maximization fairness problem with the transmit beamformer, the receive beamformer and IRS phase shifts as optimization variables, which is generally NP-hard. Hence, an alternating optimization algorithm based on the gradient extrapolated majorization-minimization (GEMM) approach is employed to solve the above problem. Specifically, when the transmit beamformer and reflective phase shift are fixed, the authors give an optimal closed expression for the receive beamformer. Then, the receive beamformer is fixed, and the minimum SINR maximization problem at the transmitter is transformed into a power minimization problem. Finally, under the zero-forcing (ZF) transmitter beamformer, the GEMM algorithm is used to optimize the reflective phase shift. Simulation results show that by comparing to existing methods, the proposed GEMM algorithm can almost achieve the same performance with lower complexity.

Feature extraction of scraping noise of the car seat electric track based on sparse representation

Abstract With the development of the science and technology, the demanding of convenience and comfort when driving a car are getting higher and higher. As an important part that has a great influence on the comfort of the car driving, the car seat is also developing towards the electric direction. The electric seat is becoming the choice of more and more manufacture of automobile. However, the product quality inspection of the electric track of the car seat is still in a relatively preliminary stage. At present, the detection of the unqualified track product is mainly performed by workers listening in an anechoic room. This will lead to the high cost of construction of the anechoic chamber, low quality inspection efficiency, and instability by different quality inspection personnel. In this paper, we focus on the scraping noise detection of the electric track product, as scraping noise is the main cause of the product disqualification. Since scraping noise often features a higher energy in the high frequency band, we adopt the Short Time Fourier Transform (STFT) to acquire the total energy at different time duration. Then we model the acquired time series as summation of one sparse signal, one low-passing signal, and one noise signal. Based on the property of the three parts, the objective function is established and solved with Majorization-Minimization (MM) approach. The effectiveness of the proposed scraping detection method is verified with the real track vibration signal, and the superiority of the proposed method is verified via the comparison with other impulse detection method.

Off-Grid DOA Estimation With Mutual Coupling via Block Log-Sum Minimization and Iterative Gradient Descent

Mutual coupling (MC) effect between antennas can deteriorate the direction of arrival (DOA) estimation performance. Block sparse signal representation (BSSR) is an effective solution to mitigate the MC effect. Nevertheless, continuous angle space has to be discretized into a finite set of grid points, which lead to the grid mismatch. In this paper, we present an iterative block sparsity reconstruction algorithm for off-grid DOA estimation with MC. First, by exploiting the banded symmetric Toeplitz structure of MC matrix, a reduced BSSR model is formulated to preferably mitigate the MC effect. Then, an iterative block sparsity reconstruction algorithm with multiple measurement vectors (MMV) is proposed. Due to the NP-hard property of block l0 norm minimization, a block log-sum minimization method is developed to encourage sparsity for such a block sparse recovery problem, and a surrogate objective function is derived via the majorization-minimization approach. Finally, an iterative gradient descent algorithm is explored to refine the DOAs. Simulations verify that the proposed off-grid algorithm has robustness under limited snapshots and coherent sources.

A Majorization-Minimization Approach for Image Smoothing with the Edge-Stopping Functions

A Majorization-Minimization Approach for Image Smoothing with the Edge-Stopping Functions

Effective Resource Allocation and Load Balancing in Hierarchical HetNets: Toward QoS-Aware Multi-Access Edge Computing

AbstractMobile edge computing (MEC) is a key feature of next-generation heterogeneous networks aimed at providing a variety of services for different applications by performing related processing tasks closer to the user equipment. In this research, we investigated on connection management approaches in multi-access edge computing systems. This paper presents joint radio resource allocation and MEC optimization in a multi-layer NOMA HetNet in order to maximize system’s energy efficiency. The continues carrier allocation and handoff decision variables, in addition to the interference incorporated in the goal function, modifies the primary optimization problem to a mixed integer nonlinear programming. Network selection is done statically based on the Analytic Hierarchy Process, and station selection is done dynamically based on the Data Envelope Analysis method. Also, an effective feedback mechanism has been designed in collaboration with the server resource manager to solve a global optimization problem in order to load balancing and meet the users quality of service constraints simultaneously. To reduce the computational complexity and to achieve a locally optimal solution, we applied variable relaxation and majorization minimization approach in which offloading decision and multi-part Markov noise analysis have been developed to model users’ preferences without the need for explicit information from the users. Based on the simulations, the proposed approach not only results in a significant increase of system’s energy efficiency but also enhances the system throughput in multiple-source scenarios.

Millimeter-wave massive MIMO channel estimation based on majorization–minimization approach

Millimeter-wave massive MIMO systems acquire a high dimensional distorted channel matrix to perform channel estimation. The captured channel matrix is sparse and rank deficient due to low scattering at millimeter-wave bands. The reduced number of RF chains enable the indirect access of signal at each antenna. This makes it difficult to estimate the channel accurately. To address this issue, researchers have focussed on compressive sensing and convex regularization methods. The first one performs well in noiseless scenario and while the latter suffers from over shrinking of all eigenvalues equally and is not suitable for large dimensional matrices. In this paper, a majorization minimization based fast non-convex (MM-FNC) algorithm is proposed to solve non-convex regularization based channel estimation. The proposed algorithm estimates the low-rank channel with fast convergence properties for large dimensional arrays. Simulation results show that the proposed approach exhibits superior performance over the CS-based orthogonal matching pursuit (CS-OMP) method, nuclear norm minimization methods (NNM) and matrix factorization (MF) methods in terms of normalized mean square error and achievable spectral efficiency with respect to different signal-to-noise ratio level.

Max-Min Fair Energy-Efficient Beamforming Design for Intelligent Reflecting Surface-Aided SWIPT Systems With Non-Linear Energy Harvesting Model

This paper considers an intelligent reflecting surface (IRS)-aided simultaneous wireless information and power transfer (SWIPT) network, where multiple users decode data and harvest energy from the transmitted signal of a transmitter. The proposed design framework exploits the cost-effective IRS to establish favorable communication environment to improve the fair energy efficient. In particular, we study the max-min energy efficiency (EE) of the system by jointly designing the transmit information and energy beamforming at the base station (BS), phase shifts at the IRS, as well as the power splitting (PS) ratio at all users subject to the minimum rate, minimum harvested energy, and transmit power constraints. The formulated problem is non-convex and thus challenging to be solved. We propose two algorithms namely penalty-based and inner approximation (IA)-based to handle the non-convexity of the optimization problem. As such, we divide the original problem into two sub-problems and apply the alternating optimization (AO) algorithm for both proposed algorithms to handle it iteratively. In particular, in the penalty-based algorithm for the first sub-problem, the semi-definite relaxation (SDR) technique, difference of convex functions (DC) programming, majorization-minimization (MM) approach, and fractional programming theory are exploited to transform the non-convex optimization problem into a convex form that can be addressed efficiently. For the second sub-problem, a penalty-based approach is proposed to handle the optimization on the phase shifts introduced by the IRS with the proposed algorithms. For the IA-based method, we jointly optimize beamforming vectors and phase shifts while the PS ratio is solved optimally in the first sub-problem. Simulation results verify the effectiveness of the IRS, which can significantly improve the system EE as compared to conventional benchmark schemes and also unveil a trade-off between convergence and performance gain for the two proposed algorithms.

A majorization-minimization scheme for L 2 support vector regression

In a support vector regression (SVR) model, using the squared ϵ-insensitive loss function makes the optimization problem strictly convex and yields a more concise solution. However, the formulation of -SVR leads to a quadratic programming which is expensive to solve. This paper reformulates the optimization problem of -SVR by absorbing the constraints in the objective function, which can be solved efficiently by a majorization-minimization approach, in which an upper bound for the objective function is derived in each iteration which is easier to be minimized. The proposed approach is easy to implement, without requiring any additional computing package other than basic linear algebra operations. Numerical studies on real-world datasets show that, compared to the alternatives, the proposed approach can achieve similar prediction accuracy with substantially higher time efficiency in training.

Majorization–Minimization approach for real-time enhancement of sparsity-driven SAR imaging

The earlier works in the context of sparsity-driven SAR imaging have shown significant improvement in the reconstruction process due to admitting sparsity as a prior. In spite of the importance of real-time processing requirement in the remote sensing (RS) applications, most of the works have not focused on real-time procedures and reducing the computational burden, but rather enhancing the quality of formed image. To address this weakness, this paper presents a problem-driven algorithm, which relies on Majorization–Minimization (MM) procedure. Using MM in our solutions, a simpler surrogate optimization problem is solved instead of the difficult original form. To show the efficacy of MM algorithm in real-time applications experimental results based on simulated and real data along with a performance analysis are presented. All results validate the superiority of the proposed MM-based method in terms of computational load and processing time as compared with previous works.

Expectation Maximization-Based Target Localization From Range Measurements in Multiplicative Noise Environments

In this letter, target localization from range measurements corrupted by both additive and multiplicative noises is studied. First, the maximum likelihood estimator (MLE) is proposed. Then, the novel expectation maximization (EM) algorithm with guaranteed convergence is proposed to find the MLE. It is shown that the expectation step can be calculated componentwisely, and the maximization step can be solved via the Majorization-Minimization (MM) approach. The algorithm is termed as R-EM-MM. To provide a benchmark performance of R-EM-MM, the theoretical performance of unbiased estimator, i.e., Cramèr Rao bound (CRB) is derived. In addition, the enhanced R-EM-MM (E-R-EM-MM) is proposed to jointly learn the noise statistics and perform target localization. Finally, numerical simulations are conducted to demonstrate the near optimal performance, compared with CRB and other state-of-art method.

Energy Efficiency Maximization via Joint Active and Passive Beamforming Design for Multiuser MISO IRS-Aided SWIPT

This letter studies a multiuser multiple-input single-output (MISO) intelligent reflecting surface (IRS)-aided simultaneous wireless information and power transfer (SWIPT) system. Specifically, a multi-antenna base station (BS) transmits data along with energy to a set of users to decode data and harvest energy by adopting the power splitting (PS) simultaneously. The energy efficiency indicator (EEI) is introduced to trade off between data rate and harvested energy, which is maximized by jointly optimizing beamforming vectors at the BS, PS ratio at each user, and phase shifts at the IRS. To solve this non-convex optimization problem, we first adopt the majorization-minimization (MM) approach to construct a concave-convex fractional function which can be handled via the Dinkelbach algorithm and then propose an efficient algorithm for solving two subproblems based on the alternating optimization (AO). For the first subproblem, semi-definite relaxation (SDR), MM approach, and Dinkelbach algorithm are adopted, while for the second sub-problem, a new manifold approach is proposed to handle the unit-modulus constraints due to IRS passive reflection. Simulation results demonstrate the superior performance of our proposed algorithm compared to other baseline schemes.

Laplace ℓ1 robust Student’s T-filter for attitude estimation of satellites

A Laplace ℓ1 robust student’s T-filter is presented for satellites to estimate their attitude state despite severe measurement noise and modeling error. Although the student’s T-filter (STF) has the capability of handling measurement noise, it cannot address the unknown modeling error. It is further sensitive to the degree of freedom (DOF). Hence, the measurement covariance is updated by using the maximum correntropy criterion to accommodate the covariance of unknown modeling error in robust filtering design. Moreover, the Laplace distribution is derived to reduce the influence of the DOF parameter by forming a surrogate function of an optimization problem. Then, the majorization minimization approach is formulated to solve such an optimization problem and present the proposed filtering algorithm in the STF framework. Numerical simulation of applying the proposed attitude estimation scheme is performed by comparing it with the third/fifth-order cubature Kalman filters.

Nonstationary Modeling With Sparsity for Spatial Data via the Basis Graphical Lasso

Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential equations, and empirical orthogonal functions all fall within this basic framework. Given a particular basis, stochastic dependence relies on flexible modeling of the coefficients. Under a Gaussianity assumption, we propose a graphical model family for the stochastic coefficients by parameterizing the precision matrix. Sparsity in the precision matrix is encouraged using a penalized likelihood framework—we term this approach the basis graphical lasso. Computations follow from a majorization-minimization (MM) approach, a byproduct of which is a connection to the standard graphical lasso. The result is a flexible nonstationary spatial model that is adaptable to very large datasets with multiple realizations. We apply the model to two large and heterogeneous spatial datasets in statistical climatology and recover physically sensible graphical structures. Moreover, the model performs competitively against the popular LatticeKrig model in predictive cross-validation but improves the Akaike information criterion score and a log score for the quality of the joint predictive distribution.

Variable metric techniques for forward–backward methods in imaging

Variable metric techniques are a crucial ingredient in many first order optimization algorithms. In practice, they consist in a rule for computing, at each iteration, a suitable symmetric, positive definite scaling matrix to be multiplied to the gradient vector. Besides quasi-Newton BFGS techniques, which represented the state-of-the-art since the 70’s, new approaches have been proposed in the last decade in the framework of imaging problems expressed in variational form. Such recent approaches are appealing since they can be applied to large scale problems without adding significant computational costs and they produce an impressive improvement in the practical performances of first order methods. These scaling strategies are strictly connected to the shape of the specific objective function and constraints of the optimization problem they are applied to; therefore, they are able to effectively capture the problem features. On the other side, this strict problem dependence makes difficult extending the existing techniques to more general problems. Moreover, in spite of the experimental evidence of their practical effectiveness, their theoretical properties are not well understood. The aim of this paper is to investigate these issues; in particular, we develop a unified framework for scaling techniques, multiplicative algorithms and the Majorization–Minimization approach. With this inspiration, we propose a scaling matrix rule for variable metric first order methods applied to nonnegatively constrained problems exploiting a suitable structure of the objective function. Finally, we evaluate the effectiveness of the proposed approach on some image restoration problems.

Multi-Objective Energy Efficient Resource Allocation and User Association for In-Band Full Duplex Small-Cells

In this paper, we develop a framework to maximize the network energy efficiency (EE) by optimizing joint user-base station (BS) association, subchannel assignment, and power control considering an in-band full-duplex (IBFD)-enabled small-cell network. We maximize EE (ratio of network aggregate throughput and power consumption) while guaranteeing a minimum data rate requirement in both the uplink and downlink. The considered problem belongs to the category of mixed-integer non-linear programming problem (MINLP), and thus is NP-hard. To cope up with this complexity and to derive a trade-off between system throughput and energy utilization, we first restate the considered problem as a multi-objective optimization problem (MOOP) aiming at maximizing system’s throughput and minimizing system’s energy consumption, simultaneously. This MOOP is then tackled by using $\epsilon $ -constraint method. To do so, we first transform the binary subchannel and BS assignment variables into continuous ones without altering the feasible region of the problem and then approximate the non-convex rate functions through majorization-minimization (MM) approach. Simulation results are presented to demonstrate the effectiveness of our proposed algorithm in improving network’s EE compared to the existing literature. Furthermore, simulation results unveil that by employing the IBFD capability in OFDMA networks, our proposed resource allocation algorithm achieves a 69% improvement in the EE as compared to the half-duplex system for practical values of residual self-interference.

Construction of unimodular tight frames for compressed sensing using majorization-minimization

In this paper, we propose a method to construct uni-modular tight frames (UMTFs), which are tight frames with the additional constraint that every entry of the matrix has the same magnitude. UMTFs are useful in many applications, since multiplication of a UMTF by a vector can be implemented in polar coordinates using very low computational cost. Since normalized UMTFs are unit norm tight frames (UNTFs), and since a UNTF is a minimizer of the frame potential, we propose an algorithm to find UMTFs by minimizing the frame potential. We show that minimizing the frame potential is equivalent to minimizing the total coherence when the frame is unimodular. We use the majorization-minimization approach to propose a low complexity, iterative, fast-converging algorithm for minimizing the frame potential. We also extend our algorithm to the cases where the phase angles of the sensing matrix are required to belong to a given finite set of feasible angles, and to the case where the signal being sampled is sparse in an arbitrary, possibly non-canonical basis. We illustrate the utility of our proposed construction in the context of sparse signal recovery. Partial DFT matrices, obtained by randomly selected rows from the full DFT matrix, are UMTFs. However, they perform poorly when dealing with signals that admit a sparse representation in the wavelet, Fourier and discrete cosine transform domains. In such scenarios, we illustrate the superior performance of our construction compared to the partial DFT, complex Gaussian and Bernoulli random matrices through simulations. The proposed algorithm offers the same performance as the partial DFT matrix, and outperforms the complex Gaussian and Bernoulli random matrices, when the signal is sparse in the canonical basis.

SOLVIT: A Reference-Free Source Localization Technique Using Majorization Minimization

We consider the problem of localizing the source using range, and range-difference measurements. Both the problems are non-convex, and non-smooth, and are challenging to solve. In this article, we develop an iterative algorithm - So urce L ocalization V ia an It erative technique (SOLVIT) to localize the source using all the distinct range-difference measurements, i.e., without choosing a reference sensor. SOLVIT is based on the Majorization Minimization approach - in which a novel upper bound is formulated, and minimized to get a closed-form solution at every iteration. We also solve the source localization problem based on range measurements, and rederive the Standard Fixed Point algorithm using the Majorization Minimization approach. By doing so, we show a less intricate way to prove the convergence of the Standard Fixed Point algorithm. Numerical simulations, and experiments in an anechoic chamber confirm that SOLVIT performs better than existing reference-based, and reference-free methods in terms of source positioning accuracy.

Multi-exponential Transverse Relaxation Times Estimation from Magnetic Resonance Images under Rician Noise and Spatial Regularization.

Relaxation signal inside each voxel of magnetic resonance images (MRI) is commonly fitted by a multi-exponential decay curve. The estimation of a discrete multi-component relaxation model parameters from magnitude MRI data is a challenging nonlinear inverse problem since it should be conducted on the entire image voxels under non-Gaussian noise statistics. This paper proposes an efficient algorithm allowing the joint estimation of relaxation time values and their amplitudes using different criteria taking into account a Rician noise model, combined with a spatial regularization accounting for low spatial variability of relaxation time constants and amplitudes between neighboring voxels. The Rician noise hypothesis is accounted for either by an adapted nonlinear least squares algorithm applied to a corrected least squares criterion or by a majorization-minimization approach applied to the maximum likelihood criterion. In order to solve the resulting large-scale non-negativity constrained optimization problem with a reduced numerical complexity and computing time, an optimization algorithm based on a majorization approach ensuring separability of variables between voxels is proposed. The minimization is carried out iteratively using an adapted Levenberg-Marquardt algorithm that ensures convergence by imposing a sufficient decrease of the objective function and the non-negativity of the parameters. The importance of the regularization alongside the Rician noise incorporation is shown both visually and numerically on a simulated phantom and on magnitude MRI images acquired on fruit samples.