Diagonalization Scheme Research Articles

Hybrid Block Diagonalization for Massive Multiuser MIMO Systems

For a massive multiple-input multiple-output (MIMO) system, restricting the number of RF chains to far less than the number of antenna elements can significantly reduce the implementation cost compared to the full complexity RF chain configuration. In this paper, we consider the downlink communication of a massive multiuser MIMO (MU-MIMO) system and propose a low-complexity hybrid block diagonalization (Hy-BD) scheme to approach the capacity performance of the traditional BD processing method. We aim to harvest the large array gain through the phase-only RF precoding and combining and then digital BD processing is performed on the equivalent baseband channel. The proposed Hy-BD scheme is examined in both the large Rayleigh fading channels and millimeter wave (mmWave) channels. A performance analysis is further conducted for single-path channels and large number of transmit and receive antennas. Finally, simulation results demonstrate that our Hy-BD scheme, with a lower implementation and computational complexity, achieves a capacity performance that is close to (sometimes even higher than) that of the traditional high-dimensional BD processing.

Low-complexity QL-QR decomposition- based beamforming design for two-way MIMO relay networks

In this paper, we investigate the optimization problem of joint source and relay beamforming matrices for a two-way amplify-and-forward (AF) multi-input multi-output (MIMO) relay system. The system, consisting of two source nodes and two relay nodes, is considered, and the linear minimum mean-square-error (MMSE) is employed at both receivers. We assume individual relay power constraints and study an important design problem, a so-called determinant maximization (DM) problem. Since this DM problem is nonconvex, we consider an efficient iterative algorithm by using an MSE balancing result to obtain at least a locally optimal solution. The proposed algorithm is developed based on QL, QR, and Choleskey decompositions which differ in complexity and performance. Analytical and simulation results show that the proposed algorithm can significantly reduce computational complexity compared with their existing two-way relay systems and have equivalent bit-error-rate (BER) performance to the singular value decomposition (SVD) based on a regular block diagonal (RBD) scheme.

MVDR-Based Multicell Cooperative Beamforming Techniques for Unicast/Multicast MIMO Networks With Perfect/Imperfect CSI

In this paper, we consider unicast/multicast multicell cooperative transmission with interference among users/user groups. In this context, we derive the optimal minimum variance distortionless response (MVDR)-based successive minimum variance beamforming (SMVB) scheme that achieves a superior sum-rate performance compared with the block diagonalization scheme. Subsequently, we derive an optimal joint power allocation and broadcast beamforming scheme for multicell cooperative broadcast transmission for a pooled power constraint at the base stations. This scheme is extended to include per base station power constraints by formulating it as a relaxed semi-definite program (SDP). We also consider the multicell cooperative uplink scenario and derive a successive multiuser (MU) uplink beamforming (SMUB) scheme that maximizes the signal-to-interference-plus-noise ratio (SINR) of each user. Next, we consider imperfect channel state information (CSI) and derive a robust beamforming scheme for the downlink, based on minimizing the worst-case interference by formulating it as a second-order cone program. It is demonstrated that the corresponding robust beamformer for the uplink transmission can be derived by employing the multidimensional covariance fitting approach. Simulation results are presented to demonstrate the superior sum-rate performance of the proposed multicell transmission schemes. The performance is also compared with several bounds for cooperative multicell scenarios.

Trust region subproblem with an additional linear inequality constraint

This paper studies an extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with a single linear inequality constraint. We present an efficient algorithm to solve the problem using a diagonalization scheme that requires solving a simple convex minimization problem. Attainment of the global optimality conditions is discussed. Our preliminary numerical experiments on several randomly generated test problems show that, the new approach is much faster in finding the global optimal solution than the known semidefinite relaxation approach, especially when solving large scale problems.

One Bit Feedback Based Diagonal Precoding for Non-Orthogonal Space-Time Block Codes

Quantized feedback about the channel state information (CSI) at the transmitter improves the error performance of MIMO systems. In literature, most of the work is done to improve the error performance of the orthogonal space time block codes (OSTBCs) using feedback of CSI from the receiver to the transmitter. In this letter, we study the performance of non-orthogonal space-time block codes (NOSTBCs) in a 2 $\!\times\!$ 1 multiple-input single-output system with diagonal weighting scheme; this scheme utilizes quantized one bit feedback with no delay from the receiver in a quasi-static Rayleigh fading channel. The considered NOSTBCs are Golden code and Silver code. Error-tolerant diagonal weighting parameter which improves the pair wise error probability (PEP) of the receiver is derived. The PEP performance of the considered set-up is studied for the complex-valued constellation like quadrature amplitude modulation. Simulation results indicate that similar to OSTBCs, the error performance of the NOSTBCs also improves with the proposed diagonal precoding scheme.

Current noise as a probe for Wigner molecules

The effects of a Wigner molecule on the current noise and conductance of a one-dimensional quantum dot with two electrons are investigated. Focusing on a lateral transport setup, the sequential regime is considered. Tunnelling rates through the dot are evaluated within an exact diagonalisation scheme. They strongly depend on electron interactions, showing a markedly different behaviour in the presence of a Wigner molecule with respect to the weak interactions case, and thus modify the transport and current noise and the dot. For weak interactions negative differential conductance and super-Poissonian noise are found. As interactions increase, a Wigner molecule develops: it suppresses the negative differential conductance and turns the shot noise to sub-Poissonian values. In particular, the noise is found to be a sensitive probe of the Wigner molecule.

Optimized Finite Difference Method for the Full-Potential XANES Simulations: Application to Molecular Adsorption Geometries in MOFs and Metal-Ligand Intersystem Crossing Transients.

Accurate modeling of the X-ray absorption near-edge spectra (XANES) is required to unravel the local structure of metal sites in complex systems and their structural changes upon chemical or light stimuli. Two relevant examples are reported here concerning the following: (i) the effect of molecular adsorption on 3d metals hosted inside metal-organic frameworks and (ii) light induced dynamics of spin crossover in metal-organic complexes. In both cases, the amount of structural models for simulation can reach a hundred, depending on the number of structural parameters. Thus, the choice of an accurate but computationally demanding finite difference method for the ab initio X-ray absorption simulations severely restricts the range of molecular systems that can be analyzed by personal computers. Employing the FDMNES code [Phys. Rev. B, 2001, 63, 125120] we show that this problem can be handled if a proper diagonalization scheme is applied. Due to the use of dedicated solvers for sparse matrices, the calculation time was reduced by more than 1 order of magnitude compared to the standard Gaussian method, while the amount of required RAM was halved. Ni K-edge XANES simulations performed by the accelerated version of the code allowed analyzing the coordination geometry of CO and NO on the Ni active sites in CPO-27-Ni MOF. The Ni-CO configuration was found to be linear, while Ni-NO was bent by almost 90°. Modeling of the Fe K-edge XANES of photoexcited aqueous [Fe(bpy)3](2+) with a 100 ps delay we identified the Fe-N distance elongation and bipyridine rotation upon transition from the initial low-spin to the final high-spin state. Subsequently, the X-ray absorption spectrum for the intermediate triplet state with expected 100 fs lifetime was theoretically predicted.

The Critical Point Entanglement and Chaos in the Dicke Model

Ground state properties and level statistics of the Dicke model for a finite number of atoms are investigated based on a progressive diagonalization scheme (PDS). Particle number statistics, the entanglement measure and the Shannon information entropy at the resonance point in cases with a finite number of atoms as functions of the coupling parameter are calculated. It is shown that the entanglement measure defined in terms of the normalized von Neumann entropy of the reduced density matrix of the atoms reaches its maximum value at the critical point of the quantum phase transition where the system is most chaotic. Noticeable change in the Shannon information entropy near or at the critical point of the quantum phase transition is also observed. In addition, the quantum phase transition may be observed not only in the ground state mean photon number and the ground state atomic inversion as shown previously, but also in fluctuations of these two quantities in the ground state, especially in the atomic inversion fluctuation.

The progressive solutions for the Dicke Hamiltonian

A progressive diagonalization scheme for the Dicke Hamiltonian, which describes the interaction of N two-level atoms with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the ground state of the Dicke Hamiltonian with a finite number of atoms can be solved almost exactly by using a progressive diagonalization scheme that involves a one-variable equation at each step. The scheme is efficient for the lower part of the spectrum. Calculated results for ground-state energies, photon numbers, atomic inversions, fluctuations in the latter two quantities, entanglement measures, and Shanon information entropies at resonance points for some finite j cases as functions of the coupling parameter are given. These outcomes show significant changes in the photon number, atomic inversion, and their fluctuations near the critical point where the entanglement measure reaches its maximum value.

Interference Alignment Based Transceiver Design in OSG mode of HetNets

This paper focuses on solving co-channel interference (CCI) issues arising in the open subscriber group (OSG) mode of heterogeneous networks (HetNets). Considering a general framework consisting of arbitrary number of picocells within a macro cell, where the inter-user interference (IUI) is the main CCI to macro user equipments (UEs), while the the inter-cell interference (ICI) is the major CCI to pico UEs. In this paper, three IA based transceiver design schemes are proposed. For macro cell, we uniformly use block diagonalization (BD) scheme to eliminate the IUI. And for picocells, three IA schemes are proposed to mitigate the ICI. The first scheme, named as zero forcing IA (ZF-IA) scheme, aligns the inter picocell interference onto an arbitrary sub-space of the cross-tier interference using ZF scheme. Considering the channel state information (CSI) of the desired channel of pico UEs, the second scheme, named as optimal desired sub-channel selected IA (ODC-IA) scheme, aligns the inter picocell interference onto a certain sub-space of the cross-tier interference, which guarantees the largest channel gain of the desired signal of pico UEs. The third IA scheme, named as maximum cross-tier interference selected IA (MI-IA) scheme, is designed for the system with less receive antennas. The inter picocell interference is aligned onto the space of the strongest cross-tier interference and only the interference on this space is nullified. The complexity analysis and simulations show that the proposed transceiver design schemes outperform the existing IA schemes in the OSG mode of HetNets, and the MI-IA scheme reduces the requirement of the receive antennas number with lower complexity.

Hybrid density matrix approach as a factorization scheme for many-body systems: Illustrated by a quantum dot–continuum system

We present a theoretical factorization scheme for interactions between many-body systems with localized discrete and delocalized quasicontinuous states. The projection operator technique combines a conventional correlation expansion with an exact diagonalization scheme. Our approach is capable of treating the continuum dynamically and to apply non-Markovian treatments beyond the Markovian approximation typically used in Lindblad formalism. Therefore it can be an important tool to describe a variety of systems as well as interaction mechanisms.

Shallow‐impurity‐related binding energy and linear optical absorption in ring‐shaped quantum dots and quantum‐well wires under applied electric field

The electronic states of two‐dimensional (2D) semiconductor quantum wells and quantum wires of disk‐ and ring‐like geometries, under the application of lateral static electric fields, are investigated. The effects of a shallow hydrogenic impurity on the energy levels of both the electron and hole states are reported and the respective binding energies are calculated. The eigenfunctions and eigenvalues of the Hamiltonian are retrieved under the effective mass approximation applying a direct matrix diagonalization scheme in conjunction with a 2D finite element method. A finite confinement potential is chosen for the structures, which are embedded in a 2D‐box bounded by a hard‐wall potential. It is shown that the first order optical absorption coefficient strongly depends on the geometrical parameters and external perturbations of the systems allowing for an optimization of the opto‐electronic properties through control of the latter.

Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions

We study the stochastic Allen-Cahn equation driven by a noise term with intensity $\sqrt{\varepsilon}$ and correlation length $\delta$ in two and three spatial dimensions. We study diagonal limits $\delta, \varepsilon \to 0$ and describe fully the large deviation behaviour depending on the relationship between $\delta$ and $\varepsilon$. The recently developed theory of regularity structures allows to fully analyse the behaviour of solutions for vanishing correlation length $\delta$ and fixed noise intensity $\varepsilon$. One key fact is that in order to get non-trivial limits as $\delta \to 0$, it is necessary to introduce diverging counterterms. The theory of regularity structures allows to rigorously analyse this renormalisation procedure for a number of interesting equations. Our main result is a large deviation principle for these renormalised solutions. One interesting feature of this result is that the diverging renormalisation constants disappear at the level of the large deviations rate function. We apply this result to derive a sharp condition on $\delta, \varepsilon$ that guarantees a large deviation principle for diagonal schemes $\varepsilon, \delta \to 0$ for the equation without renormalisation.

A Fractional Inpainting Model Based on the Vector-Valued Cahn--Hilliard Equation

The Cahn--Hilliard equation provides a simple and fast tool for binary image inpainting. By now, two generalizations to gray value images exist: bitwise binary inpainting and TV-H$^{-1}$ inpainting. This paper outlines a model based on the vector-valued Cahn--Hilliard equation. Additionally, we generalize our approach to a fractional-in-space version. Fourier spectral methods provide efficient solvers since they yield a fully diagonal scheme. Furthermore, their application to three spatial dimensions is straightforward. Numerical examples show the superiority of the proposed fractional Cahn--Hilliard inpainting approach over its nonfractional version. It improves the peak signal-to-noise ratio and structural similarity index. Likewise, the experiments confirm that the proposed model competes with previous inpainting methods, such as the total variation inpainting approach and its fourth-order variant.

Tuning of exciton states in a magnetic quantum ring

The exciton states in a CdTe quantum ring subjected to an external magnetic field containing a single magnetic impurity are investigated. We have used the multiband approximation which includes the heavy hole–light hole coupling effects. The electron–hole spin interactions and the s, p–d interactions between the electron, the hole and the magnetic impurity are also included. The exciton energy levels and optical transitions are evaluated using the exact diagonalization scheme. We show that due to the spin interactions it is possible to change the bright exciton state into the dark state and vice versa with the help of a magnetic field. We propose a new route to experimentally estimate the s, p–d spin interaction constants.

Estimation of Population Mean in the Presence of Linear Trend

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.

Solute-Solvent Charge-Transfer Excitations and Optical Absorption of Hydrated Hydroxide from Time-Dependent Density-Functional Theory.

The electronic structure of simple hydrated ions represents one of the most challenging problems in electronic-structure theory. Spectroscopic experiments identified the lowest excited state of the solvated hydroxide as a charge-transfer-to-solvent (CTTS) state. In the present work we report computations of the absorption spectrum of the solvated hydroxide ion, treating both solvent and solute strictly at the same level of theory. The average absorption spectrum up to 25 eV has been computed for samples taken from periodic ab initio molecular dynamics simulations. The experimentally observed CTTS state near the onset of the absorption threshold has been analyzed at the generalized-gradient approximation (GGA) and with a hybrid density-functional. Based on results for the lowest excitation energies computed with the HSE hybrid functional and a Davidson diagonalization scheme, the CTTS transition has been found 0.6 eV below the first absorption band of liquid water. The transfer of an electron to the solvent can be assigned to an excitation from the solute 2pπ orbitals, which are subject to a small energetic splitting due to the asymmetric solvent environment, to the significantly delocalized lowest unoccupied orbital of the solvent. The distribution of the centers of the excited state shows that CTTS along the OH(-) axis of the hydroxide ion is avoided. Furthermore, our simulations indicate that the systematic error arising in the calculated spectrum at the GGA originates from a poor description of the valence band energies in the solution.

Quaternion-valued robust adaptive beamformer for electromagnetic vector-sensor arrays with worst-case constraint

A robust adaptive beamforming scheme based on two-component electromagnetic (EM) vector-sensor arrays is proposed by extending the well-known worst-case constraint into the quaternion domain. After defining the uncertainty set of the desired signal׳s quaternionic steering vector, two quaternion-valued constrained minimization problems are derived. We then reformulate them into two real-valued convex quadratic problems, which can be easily solved via the so-called second-order cone (SOC) programming method. It is also demonstrated that the proposed algorithms can be classified as a specific type of the diagonal loading scheme, in which the optimal loading factor is a function of the known level of uncertainty of the desired steering vector. Numerical simulations show that our new method can cope with the steering vector mismatch problem well, and alleviate the finite sample size effect to some extent. Besides, the proposed beamformer significantly outperforms the sample matrix inversion minimum variance distortionless response (SMI-MVDR) and the quaternion Capon (Q-Capon) beamformers in all the scenarios studied, and achieves a better performance than the traditional diagonal loading scheme, in the case of smaller sample sizes and higher SNRs.

An improved block diagonal precoding scheme for MIMO multicast channel with two users

Matrix theory plays an important role in precoding methodology for multiple input multiple output (MIMO) systems. In this paper, an improved block diagonal (BD) precoding scheme is proposed for a MIMO multicast channel with two users, where the unitary precoding matrix is constructed in a block-wise form by joint triangularization decomposition. In order to reduce large signal-to-noise ratios (SNRs) spread across different transmitted data streams and users, the combination of joint equi-diagonal triangularization (JET) and joint geometric mean decomposition (JGMD) is applied to submatrix construction in the inner process of this precoding scheme. An elaborate implementation is presented, and the existence condition of JGMD is also investigated for two complex-valued matrices with two columns, where the analytical result reveals the connection with the particular channel realization and essentially determines when to consider JGMD for submatrix construction. In addition, the properties of the diagonal elements generated by joint triangularization decomposition are discussed as well as the computational complexity of the proposed scheme. Simulation results indicate that in general, JGMD is employed with high probability in the hybrid model, and the proposed scheme readily outperforms the JET scheme in terms of bit error rate (BER) performance in the moderate to high SNR regimes.

Feedback control of flow alignment in sheared liquid crystals

Based on a continuum theory, we investigate the manipulation of the nonequilibrium behavior of a sheared liquid crystal via closed-loop feedback control. Our goal is to stabilize a specific dynamical state, that is, the stationary "flow alignment," under conditions where the uncontrolled system displays oscillatory director dynamics with in-plane symmetry. To this end we employ time-delayed feedback control (TDFC), where the equation of motion for the ith component q(i)(t) of the order parameter tensor is supplemented by a control term involving the difference q(i)(t)-q(i)(t-τ). In this diagonal scheme, τ is the delay time. We demonstrate that the TDFC method successfully stabilizes flow alignment for suitable values of the control strength K and τ; these values are determined by solving an exact eigenvalue equation. Moreover, our results show that only small values of K are needed when the system is sheared from an isotropic equilibrium state, contrary to the case where the equilibrium state is nematic.