The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covarian...The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.展开更多
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise w...The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.展开更多
Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in si...Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (<sup>53</sup>Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (<sup>50</sup>Cr, <sup>52</sup>Cr, <sup>53</sup>Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida展开更多
The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions fo...The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.展开更多
The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representation...The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.展开更多
Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub&...Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is展开更多
To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively...To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.展开更多
Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew...Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.展开更多
Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M m...Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.展开更多
The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a ser...The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix.The computational cost of the algorithm is calculated.Some illustrative examples are given to demonstrate the effectiveness of the proposed method.展开更多
Matrix inversion is a critical part in communication, signal processing and electromagnetic system. A flexible and scalable very long instruction word （VLIW） processor with clustered architecture is proposed for mat...Matrix inversion is a critical part in communication, signal processing and electromagnetic system. A flexible and scalable very long instruction word （VLIW） processor with clustered architecture is proposed for matrix inversion. A global register file （RF） is used to connect al the clusters. Two nearby clusters share a local register file. The instruction sets are also designed for the VLIW processor. Experimental results show that the proposed VLIW architecture takes only 45 latency to invert a 4 × 4 matrix when running at 150 MHz. The proposed design is roughly five times faster than the DSP solution in processing speed.展开更多
In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In ad...In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.展开更多
The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed for...The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed form and an inverse form of the classical Faa di Bruno formula.展开更多
Solving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficie...Solving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficient matrices arises from various engineering and sciences applications [1]-[6]. In this paper, efficient numerical procedures for finding the generalized (or pseudo) inverse of a general (square/rectangle, symmetrical/unsymmetrical, non-singular/singular) matrix and solving systems of Simultaneous Linear Equations (SLE) are formulated and explained. The developed procedures and its associated computer software (under MATLAB [7] computer environment) have been based on “special Cholesky factorization schemes” (for a singular matrix). Test matrices from different fields of applications have been chosen, tested and compared with other existing algorithms. The results of the numerical tests have indicated that the developed procedures are far more efficient than the existing algorithms.展开更多
The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms cond...The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms conducive to the output are sealed and inaccessible. In practice, other than the CPU timing, the applied inversion method is irrelevant. This research-oriented article discusses one such process, the Cayley-Hamilton (C.H.) [1]. Pursuing the process symbolically reveals its unpublished hidden mathematical characteristics even in the original article [1]. This article expands the general vision of the original named method without altering its practical applications. We have used the famous CAS Mathematica [2]. We have briefed the theory behind the method and applied it to different-sized symbolic and numeric matrices. The results are compared to the named CAS’s sealed, packaged library commands. The codes are given, and the algorithms are unsealed.展开更多
Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural net...Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural network. An improved fast algorithm of the BP network was presented, which adopts a singular value decomposition （SVD） and a generalized inverse matrix. It not only increases the speed of network learning but also achieves a satisfying precision. The simulation and experiment results show the effect of improvement of BP algorithm on the classification of the surface defects of steel plate.展开更多
In late December of 1991, observation of three component geomagnetic short period variations was carried out in Chengmai county of Hainan province, along a short measurement profile with small spatial intervals of d...In late December of 1991, observation of three component geomagnetic short period variations was carried out in Chengmai county of Hainan province, along a short measurement profile with small spatial intervals of detection points. Within the period range of 20 s to 500 s, we have discovered that the vertical variations are basically correlated with the horizontal variations in north direction in all measurement points, the real parts of complex transfer functions demonstrate that an asymmetric spatial variation of short wavelength superimposed on regional monotonic tendencious spatial variation. Inversion of the observed data along the small profile was carried out by using the invention method of generalized inverse matrix of finite element forward calculation for the electromagnetic induction of the 2 D conductivity model to investigate the conductivity structure of the profile. We conclude that the anomaly of geomagnetic short periodic variation in the small area originated from the Wangwu Wenjiao fault in the northern part of Hainan island .展开更多
Taking the sectional area and the bending moment of inertia as variables for each beam element, the plane frame will possess a stiffness matrix containing parameters.In terms of the symbolic computation software, the ...Taking the sectional area and the bending moment of inertia as variables for each beam element, the plane frame will possess a stiffness matrix containing parameters.In terms of the symbolic computation software, the inverse matrix is solved to obtain the new analytical solution with respect ic characteristics of elements cross-section.The general program is coded in the microcomputer and corresponding exmpales are computed.展开更多
In order to decrease the probability of missing some data points or noises being added in the inverse truncated mixing matrix （ITMM） algorithm, a two-stage frequency- domain method is proposed for blind source separ...In order to decrease the probability of missing some data points or noises being added in the inverse truncated mixing matrix （ITMM） algorithm, a two-stage frequency- domain method is proposed for blind source separation of underdetermined instantaneous mixtures. The separation process is decomposed into two steps of ITMM and matrix completion in the view that there are many soft-sparse （not very sparse） sources. First, the mixing matrix is estimated and the sources are recovered by the traditional ITMM algorithm in the frequency domain. Then, in order to retrieve the missing data and remove noises, the matrix completion technique is applied to each preliminary estimated source by the traditional ITMM algorithm in the frequency domain. Simulations show that, compared with the traditional ITMM algorithms, the proposed two-stage algorithm has better separation performances. In addition, the time consumption problem is considered. The proposed algorithm outperforms the traditional ITMM algorithm at a cost of no more than one- fourth extra time consumption.展开更多
Massive multiple-input multiple-output provides improved energy efficiency and spectral efficiency in 5 G. However it requires large-scale matrix computation with tremendous complexity, especially for data detection a...Massive multiple-input multiple-output provides improved energy efficiency and spectral efficiency in 5 G. However it requires large-scale matrix computation with tremendous complexity, especially for data detection and precoding. Recently, many detection and precoding methods were proposed using approximate iteration methods, which meet the demand of precision with low complexity. In this paper, we compare these approximate iteration methods in precision and complexity, and then improve these methods with iteration refinement at the cost of little complexity and no extra hardware resource. By derivation, our proposal is a combination of three approximate iteration methods in essence and provides remarkable precision improvement on desired vectors. The results show that our proposal provides 27%-83% normalized mean-squared error improvement of the detection symbol vector and precoding symbol vector. Moreover, we find the bit-error rate is mainly controlled by soft-input soft-output Viterbi decoding when using approximate iteration methods. Further, only considering the effect on soft-input soft-output Viterbi decoding, the simulation results show that using a rough estimation for the filter matrix of minimum mean square error detection to calculating log-likelihood ratio could provideenough good bit-error rate performance, especially when the ratio of base station antennas number and the users number is not too large.展开更多
文摘The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.
文摘The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.
文摘Clinical assessment of fluid volume status in children during malaria can be taxing and often inaccurate. During malaria, changes in fluid volume are rather multifarious and estimating this parameter, especially in sick children is very challenging for clinicians who frequently rely on indices such as long capillary refill times, tachycardia, central venous pressure and decreased urine volume as guides. Here, we present the UHAS-MIDA, an open-source software tool that calculates the red blood cell (RBC) concentration and blood volume during malaria in children determined using a stable isotope of chromium (<sup>53</sup>Cr as the label) by gas chromatography-mass spectrometry in selective ion monitoring (GC/MS-SIM) analysis. A key component involves the determination of the compositions of the most abundant naturally occurring isotopes of Cr (<sup>50</sup>Cr, <sup>52</sup>Cr, <sup>53</sup>Cr), and converting the proportions into a 3 × 3 matrix. To estimate unknown proportions of chromium isotopic mixtures from the measured abundances of three ions, an inverse matrix was calculated. The inverse together with several inputs is then used to calculate the corrected MS ion abundances. Thus, we constructed the software tool UHAS- MIDA using HTML, CSS/Bootstrap, JavaScript, and PHP scripting languages. The tool enables the user to efficiently determine RBC concentration and fluid volume. The source code, binary packages and associated materials for UHAS-MIDA are freely available at https://github.com/bentil078/Abaye-et-al_UHASmida
文摘The symmetric,positive semidefinite,and positive definite real solutions of the matrix equation XA=YAD from an inverse problem of vibration theory are considered.When D=T the necessary and sufficient conditions for the existence of such solutions and their general forms are derived.
基金Supported by the National Natural Science Foundation of China (12261066, 11661059)the Natural Science Foundation of Inner Mongolia (2021MS01020)。
文摘The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is
文摘To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.
基金Supported by the National Natural Science Foundation of China(10471085)
文摘Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.
文摘Let P be a property referring to a real matrix. For a sign pattern A, if there exists a real matrix B in the qualitative class of A such that B has property P, then we say A allows P. Three cases that A allows an M matrix, an inverse M matrix and a P 0 matrix are considered. The complete characterizations are obtained.
文摘The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix.The computational cost of the algorithm is calculated.Some illustrative examples are given to demonstrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(6110015561227004+4 种基金613720716137213161201289)the Fundamental Research Funds of the Central Universities of China(K5051302096JB140207)
文摘Matrix inversion is a critical part in communication, signal processing and electromagnetic system. A flexible and scalable very long instruction word （VLIW） processor with clustered architecture is proposed for matrix inversion. A global register file （RF） is used to connect al the clusters. Two nearby clusters share a local register file. The instruction sets are also designed for the VLIW processor. Experimental results show that the proposed VLIW architecture takes only 45 latency to invert a 4 × 4 matrix when running at 150 MHz. The proposed design is roughly five times faster than the DSP solution in processing speed.
基金Project supported by the National Natural Science Foundation of China （Grant No.60672160）
文摘In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.
基金Supported by the National Natural Science Foundation of China(Grant No.11401237)
文摘The present paper gives a new Bell matrix inversion which arises from the classical Lagrange inversion formula. Some new relations for the Bell polynomials are obtained, including a Bell matrix inversion in closed form and an inverse form of the classical Faa di Bruno formula.
文摘Solving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficient matrices arises from various engineering and sciences applications [1]-[6]. In this paper, efficient numerical procedures for finding the generalized (or pseudo) inverse of a general (square/rectangle, symmetrical/unsymmetrical, non-singular/singular) matrix and solving systems of Simultaneous Linear Equations (SLE) are formulated and explained. The developed procedures and its associated computer software (under MATLAB [7] computer environment) have been based on “special Cholesky factorization schemes” (for a singular matrix). Test matrices from different fields of applications have been chosen, tested and compared with other existing algorithms. The results of the numerical tests have indicated that the developed procedures are far more efficient than the existing algorithms.
文摘The inversion of a non-singular square matrix applying a Computer Algebra System (CAS) is straightforward. The CASs make the numeric computation efficient but mock the mathematical characteristics. The algorithms conducive to the output are sealed and inaccessible. In practice, other than the CPU timing, the applied inversion method is irrelevant. This research-oriented article discusses one such process, the Cayley-Hamilton (C.H.) [1]. Pursuing the process symbolically reveals its unpublished hidden mathematical characteristics even in the original article [1]. This article expands the general vision of the original named method without altering its practical applications. We have used the famous CAS Mathematica [2]. We have briefed the theory behind the method and applied it to different-sized symbolic and numeric matrices. The results are compared to the named CAS’s sealed, packaged library commands. The codes are given, and the algorithms are unsealed.
基金Item Sponsored by National Natural Science Foundation of China (60277029)
文摘Artificial neural network is a new approach to pattern recognition and classification. The model of multilayer perceptron （MLP） and back-propagation （BP） is used to train the algorithm in the artificial neural network. An improved fast algorithm of the BP network was presented, which adopts a singular value decomposition （SVD） and a generalized inverse matrix. It not only increases the speed of network learning but also achieves a satisfying precision. The simulation and experiment results show the effect of improvement of BP algorithm on the classification of the surface defects of steel plate.
文摘In late December of 1991, observation of three component geomagnetic short period variations was carried out in Chengmai county of Hainan province, along a short measurement profile with small spatial intervals of detection points. Within the period range of 20 s to 500 s, we have discovered that the vertical variations are basically correlated with the horizontal variations in north direction in all measurement points, the real parts of complex transfer functions demonstrate that an asymmetric spatial variation of short wavelength superimposed on regional monotonic tendencious spatial variation. Inversion of the observed data along the small profile was carried out by using the invention method of generalized inverse matrix of finite element forward calculation for the electromagnetic induction of the 2 D conductivity model to investigate the conductivity structure of the profile. We conclude that the anomaly of geomagnetic short periodic variation in the small area originated from the Wangwu Wenjiao fault in the northern part of Hainan island .
文摘Taking the sectional area and the bending moment of inertia as variables for each beam element, the plane frame will possess a stiffness matrix containing parameters.In terms of the symbolic computation software, the inverse matrix is solved to obtain the new analytical solution with respect ic characteristics of elements cross-section.The general program is coded in the microcomputer and corresponding exmpales are computed.
基金The National Natural Science Foundation of China(No.60872074)
文摘In order to decrease the probability of missing some data points or noises being added in the inverse truncated mixing matrix （ITMM） algorithm, a two-stage frequency- domain method is proposed for blind source separation of underdetermined instantaneous mixtures. The separation process is decomposed into two steps of ITMM and matrix completion in the view that there are many soft-sparse （not very sparse） sources. First, the mixing matrix is estimated and the sources are recovered by the traditional ITMM algorithm in the frequency domain. Then, in order to retrieve the missing data and remove noises, the matrix completion technique is applied to each preliminary estimated source by the traditional ITMM algorithm in the frequency domain. Simulations show that, compared with the traditional ITMM algorithms, the proposed two-stage algorithm has better separation performances. In addition, the time consumption problem is considered. The proposed algorithm outperforms the traditional ITMM algorithm at a cost of no more than one- fourth extra time consumption.
文摘Massive multiple-input multiple-output provides improved energy efficiency and spectral efficiency in 5 G. However it requires large-scale matrix computation with tremendous complexity, especially for data detection and precoding. Recently, many detection and precoding methods were proposed using approximate iteration methods, which meet the demand of precision with low complexity. In this paper, we compare these approximate iteration methods in precision and complexity, and then improve these methods with iteration refinement at the cost of little complexity and no extra hardware resource. By derivation, our proposal is a combination of three approximate iteration methods in essence and provides remarkable precision improvement on desired vectors. The results show that our proposal provides 27%-83% normalized mean-squared error improvement of the detection symbol vector and precoding symbol vector. Moreover, we find the bit-error rate is mainly controlled by soft-input soft-output Viterbi decoding when using approximate iteration methods. Further, only considering the effect on soft-input soft-output Viterbi decoding, the simulation results show that using a rough estimation for the filter matrix of minimum mean square error detection to calculating log-likelihood ratio could provideenough good bit-error rate performance, especially when the ratio of base station antennas number and the users number is not too large.
