59 results about "Hermitian matrix" patented technology

A method for transmitting/receiving data in a Multiple Input Multiple Output (MIMO) communication system is disclosed. The data transmission method includes determining a precoding matrix to be a part of a phase-shift-based precoding matrix, determining a first diagonal matrix for phase shift to be a part of the phase-shift-based precoding matrix, determining a unitary matrix to be a part of the phase-shift-based precoding matrix, precoding a transmission symbol for each resource using the phase-shift-based precoding matrix to produce precoded data, and transmitting the precoded data, wherein the phase-shift-based precoding matrix is determined by the product of the precoding matrix, a Hermitian matrix of the unitary matrix, the first diagonal matrix, and the unitary matrix.

An antenna system includes a multi-port antenna with an active feeding network coupled thereto. The active feeding network applies complex weights to signals received from and transmitted to each port of the multi-port antenna. The complex weights are applied according to eigenvectors corresponding to a Hermitian matrix representation of the multi-port antenna. The Hermitian matrix may be base on such multi-port antenna parameters such as power dissipation, power radiation, real-power flow, volumetric storage of electromagnetic energy, and/or volumetric dissipation of electromagnetic energy. The multi-port antenna yields orthogonal electromagnetic fields in volumes or surfaces of interest in response to the active feeding network excitation.

Generally, a method and apparatus are provided for computing a matrix inverse square root of a given positive-definite Hermitian matrix, K. The disclosed technique for computing an inverse square root of a matrix may be implemented, for example, by the noise whitener of a MIMO receiver. Conventional noise whitening algorithms whiten a non-white vector, X, by applying a matrix, Q, to X, such that the resulting vector, Y, equal to Q·X, is a white vector. Thus, the noise whitening algorithms attempt to identify a matrix, Q, that when multiplied by the non-white vector, will convert the vector to a white vector. The disclosed iterative algorithm determines the matrix, Q, given the covariance matrix, K. The disclosed matrix inverse square root determination process initially establishes an initial matrix, Q₀, by multiplying an identity matrix by a scalar value and then continues to iterate and compute another value of the matrix, Q_n+1, until a convergence threshold is satisfied. The disclosed iterative algorithm only requires multiplication and addition operations and allows incremental updates when the covariance matrix, K, changes.

The invention discloses a low-complexity precoding method for a downlink multi-user multiple-input multiple-output (MIMO) system. The method is characterized by comprising the following steps of: setting a global channel matrix, calculating a pseudo-inverse matrix of the global channel matrix, performing row decomposition on the global channel matrix, performing column decomposition on the pseudo-inverse matrix, performing orthogonal triangular decomposition on a block pseudo-inverse matrix of a user m, calculating an equivalent channel matrix of the user m, constructing a Hermitian matrix by using the equivalent channel matrix of the user m, performing LDL<H> decomposition on the Hermitian matrix, and calculating a precoding matrix and a receiving matrix of the user m according to L and D. The method has the advantages that by the null-space calculation of the pseudo-inverse matrix of the global channel matrix and the orthogonal triangular decomposition of a block, complex matrix singular value decomposition is avoided, and channel block diagonalization is quickly realized; and in addition, an equivalent channel of each single user is subjected to Hermitian matrix decomposition to finish the design of the precoding matrix, so that a calculation amount is effectively reduced under the condition of no loss of bit error rate performance.

The invention discloses a high-dimensional random matrix-based electronic type transformer error state evaluation method, and aims to perform error state evaluation by means of determining whether statistical distribution of the measurement error of the electronic type transformer has abnormal changes or not based on the high-dimensional random matrix only according to the output of the electronic type transformer, without depending on a standard tool or a physical model. The error state evaluation method specifically comprises the steps of establishing the random matrix through the output data of the electronic type transformer based on a sliding time window; expanding the random matrix based on a Kalman filter; solving a non-Hermitian matrix; performing evaluation on matrix solving; and performing evaluation index calculation on a sample central moment and a sample original moment to carry out the electronic type transformer error state evaluation. Effective evaluation on the error state of the electronic type transformer can be carried out under the premise of not depending on the standard tool or the physical model; and the evaluation result is accurate and visualized, and the evaluation method is universal, effective and can be realized easily.

The invention discloses an SVD (Singular Value Decomposition) method and an SVD device of an MIMO (Multiple Input Multiple Output) pre-coding technology. The SVD method comprises the following steps of converting a channel matrix H into a Hermitian matrix A (A = HH * H), and converting a question for calculating SVD of the channel matrix H into a question for calculating EVD (Eigen Value Decomposition) of the Hermitian matrix A, wherein a diagonalizable matrix of the Hermitian matrix A is just a calculated pre-coding matrix; carrying out EVD iteration on the Hermitian matrix A and calculating a diagonalizable matrix V of the Hermitian matrix A. According to the method and the device, disclosed by the invention, a pre-coding method with a lower calculation complexity can be realized on the premise that the error rate performance of a communication system is ensured, and a pre-coding circuit with high throughput rate and low hardware complexity can be realized at the same time.

The invention discloses a rapid adaptive iteration method for achieving Doppler wave beam sharpening imaging. According to the invention, by use of covariance matrix rapid calculation and covariance matrix rapid inversion, super-resolution Doppler wave beam sharpening imaging of angles in forward squint regions of aircrafts like airplanes, missiles and the like is achieved, and a problem of high complexity of covariance matrix solving and covariance matrix inversion operation in the traditional direct iteration adaptive method is solved. The method is characterized in that, based on the problems of covariance matrix calculation and covariance matrix inversion in the iteration adaption, by use of properties of a Toeplitz matrix and a Hermitian matrix, the matrix is rapidly obtained by solving a row of elements; by use of the Gohberg Semencul (GS) type decomposition method, rapid solving of inverse matrix of the covariance matrix is achieved; and it is achieved that the Doppler wave beam sharpening imaging of the iteration adaptive method occupies fewer operation resources in engineering application and is quite highly efficient.

The invention discloses a method and device for realizing importance sorting of network nodes, and the method comprises the steps: obtaining to-be-sorted network nodes of which the number is not greater than N, generating an N * N-dimensional adjacent matrix L containing the weight W and connection edge information among the sorted network nodes, and calculating a static length M for realizing importance sorting of the network nodes according to the adjacent matrix L, and according to the adjacent matrix L and the static length M, calculating an Hermitian matrix A, and according to the value of the sum of the Hermitian matrixes A, outputting a quantum state S containing the importance sorting result of the to-be-sorted network nodes by using a quantum circuit corresponding to an HHL algorithm, the sum of A and S satisfying a linear relationship. By using the embodiment of the invention, index value difference of the to-be-sorted network nodes can be reflected, and the quantum superposition characteristic in the quantum field can be utilized to improve the calculation efficiency.

The invention provides an iterative computation method for self-adaptive weight number in space time adaptive processing (STAP), aiming at solving the problem that the real-time requirement is hardly met by STAP technology due to the fact that great computation quantity and equipment quantity of a system are consumed as the STAP arithmetic self-adaptive weight value computation needs to directly inverse a space-time covariance matrix. The iterative computation method comprises the following steps of: firstly, obtaining an inverse matrix of a first impulse covariance matrix in a recursion way according to the Hermitian matrix properties, and obtaining the inversion of the final space-time covariance matrix step by step by means of nestification and recursion according to the impulse order, so that the computation quantity for computing the STAP self-adaptive weight value can be greatly reduced. According to the iterative computation method, the clutter suppression performance which is as same as that of the covariance matrix direct inversion STAP algorithm can be obtained, and the computation quantity for solving the self-adaptive weight value is only about 50% of the computation quantity of the covariance matrix direct inversion since the computation of the covariance matrix direct inversion is avoided, so that the engineering realization can be preferably carried out.

The invention discloses a large-scale power grid abnormal load identification method based on a power method and a parallel computing technology. The large-scale power grid abnormal load identification method comprises the following steps that step 1, data source matrixes Xs and z of all partitions are synchronously constructed; Step 2, the time window width T of each partition is determined and asampling starting moment t < 1 > is set; Step 3, a sliding window matrix X < z > of each partition is synchronously obtained ; 4, the sliding window matrixes X < z > of all the partitions are subjected to standardization processing synchronously, and non-Hermitian matrixes X < n > and X < z > of all the partition standards are obtained; 5, a sample covariance matrix S < z > of each partition is synchronously obtained ; 6, the maximum characteristic values max (th) and z (th) of the sample covariance matrix of each partition are quickly estimated by using a power method; 7, each partition estimates the signal-to-noise ratio z at the current moment, so that the dynamic threshold z of the maximum characteristic value of the sample covariance matrix of the corresponding partition is obtained;And 8, power grid state abnormity out-of-limit judgment is carried out. The method has the characteristics that the calculation efficiency can be remarkably improved, and the applicability to large-scale power grid application is enhanced.

The invention discloses a complex field blind source separation method. A complex filed target matrix system is built, and real symmetrization is carried out to obtain a reconstructed target matrix system formed by a real-value target matrix, the complex field combined diagonalization problem is converted into the real field combined diagonalization problem to solve the complex field blind source separation problem; compared with other algorithms that are also suitable for the complex filed, the method doesn't restrain a diagonalization target matrix to be combined into a hermitian symmetric matrix or a positive definite hermitian matrix and is wide in application; an alternative least square iterative algorithm based on combined diagonalization least square cost functions is adopted, and the structural characteristics of the target matrix system formed by the real-value target matrix are fully used to realize the combined diagonalization of a new target matrix system; The cost functions are solved by the alternative least square iterative algorithm, the estimate values of a mixed matrix are obtained, the blind source separation is realized, and the simulation results verify that the method provided is high in convergence precision.

The invention relates to a Hartley transform-based visible light communication space modulation method and an implementation system therefor. In the Hartley transform-based visible light communication space modulation method and the implementation system therefor, discrete Hartley transform is adopted for replacing discrete Fourier transform in OFDM; a real number output signal is obtained while that an IDHT input signal is real number is ensured; an output signal is still bipolar at this time, space modulation is introduced, a positive value real number signal is added on one lamp while an inverse value of a negative value real number signal is added on another lamp; while no Hermitian matrix is used and no direct current bias needs to be added, a problem that complex number bipolar signals cannot be directly applied to visible light signal transmission can be solved.

The invention discloses a method and a device for realizing network node sorting. The method comprises the following steps: obtaining to-be-sorted network nodes of which the number is not greater thanN, wherein N = 2<n>, and n is a positive integer; generating an N * N-dimensional adjacency matrix A according to the interaction relationship among the to-be-sorted network nodes; determining an out-degree Dout and an in-degree Din of the adjacent matrix according to the adjacent matrix A; according to the adjacent matrix A, the out-degree D<out> and the in-degree D, calculating an Hermitian matrix E and b<arrow>, wherein the Hermitian matrix E = [D<out> + D - (A + A<T>)], and b<arrow> = [D<out> - D]1<arrow>; and according to the value of the Hermitian matrix E and the value of the b<arrow>,outputting a quantum state S<*> containing a sorting result of the to-be-sorted network nodes by utilizing a quantum circuit corresponding to an HHL algorithm, wherein E, S<*> and b<arrow> meet a relationship that ES<*> = b<arrow>. The large-scale network node sorting efficiency can be improved, quick sorting of large-scale network nodes is achieved, the calculation amount of quantum circuits corresponding to the HHL algorithm is reduced, and the calculation efficiency of the quantum circuit is improved.

A system and method for designing photonic band gap structures. The system and method provide a user with the capability to produce a model of a two-dimensional array of conductors corresponding to a unit cell. The model involves a linear equation. Boundary conditions representative of conditions at the boundary of the unit cell are applied to a solution of the Helmholtz equation defined for the unit cell. The linear equation can be approximated by a Hermitian matrix. An eigenvalue of the Helmholtz equation is calculated. One computation approach involves calculating finite differences. The model can include a symmetry element, such as a center of inversion, a rotation axis, and a mirror plane. A graphical user interface is provided for the user's convenience. A display is provided to display to a user the calculated eigenvalue, corresponding to a photonic energy level in the Brilloin zone of the unit cell.

The invention discloses a method for implementing Hermitian matrix decomposition by using FPGA (field programmable gate array) and provides a method for implementing a Jacobi algorithm by using the FPGA. A complex Hermitian matrix received by an array antenna is decomposed by adopting the Jacobi algorithm, the Jacobi algorithm is implemented by using the FPGA on hardware implementation, complex multiplication and division operations in the Jacobi algorithm are all replaced by CORDIC cores according to certain rules, and finally feature values and feature vectors of the Hermitian matrix are acquired. The feature values and the feature vectors of the Hermitian matrix are calculated by using the FPGA, almost all the CORDIC cores are used on the related matrix operations, the CORDIC cores arereused, multiplication and division operations are saved greatly, FPGA resources are saved, and the method is fast in processing time, good in parallelism and broad in application prospect in array signal processing.

The invention relates to a low-complexity efficient channel estimation algorithm comprising the following steps of: (1) executing diagonalization of matrix on a signal X at a channel estimation part, solving a Hermitian matrix P and a diagonal matrix Lambda X according to the formula of X=P Lambda XP<-1>; (2) executing channel estimation by an MMSE (Minimum Mean Square Error) algorithm to get a channel estimation matrix which is described in the specification, wherein the noise variance is described in the specification, the LS (Least Squares) channel estimation is described in the specification, RH=E(HHH) is a channel correlative matrix, and H is a channel frequency domain response; and (3) executing channel estimation based on the channel estimation matrix. In the algorithm, the amount of calculation of the algorithm is further reduced without reduction of the performance of the original MMSE algorithm.

The present invention provides a method and apparatus for determining an effective channel and feedback information. The method for determining an effective channel comprises: selecting more than one basic column vectors for determining a precoding matrix; calculating products of channel row vectors and the basic column vectors; and determining the effective channel or a Hermitian matrix of the effective channel by using the products. It can be seen from above that with the calculation of products of channel row vectors and more than one basic column vectors determining a precoding matrix and determination of an effective channel or Hermitian matrixes of the effective channel by using the products, the equipment is enabled to lower the amount of calculation and the complexity of calculation, lower the power consumption of the equipment and reduce the circuit size needed in performing corresponding processing in determining an effective channel or Hermitian matrixes of the effective channel and in determining channel feedback information.