This paper proposes a scheme to construct orthogonal channel matrix for full rate quasiorthogonal STBC based on givens rotation with lower bit error rate. The transmission diversity method rotates every single informa...This paper proposes a scheme to construct orthogonal channel matrix for full rate quasiorthogonal STBC based on givens rotation with lower bit error rate. The transmission diversity method rotates every single information symbol. The scheme can suppress channel noise and eliminate the interference term well. Simulation results show that the method can improve performance better than conventional algorithm without increasing decoding complexity.展开更多
For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself ...For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.展开更多
The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 20...The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2 × 2 transforms. The DsiHT is zeroing all components of the input signal while moving or heaping the energy of the signal to one component, for instance the first one. We describe three different types of QR-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, as well as without matrices but using analytical formulas. We also present the mixed QR-decomposition, when different type DsiHTs are used in different stages of the algorithm. The number of such decompositions is greater than 3<sup>(N-1)</sup>, for an N × N complex matrix. Examples of the QR-decomposition are described in detail for the 4 × 4 and 6 × 6 complex matrices and compared with the known method of Householder transforms. The precision of the QR-decompositions of N × N matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for QR-decompositions by the described DsiHTs are given.展开更多
文摘This paper proposes a scheme to construct orthogonal channel matrix for full rate quasiorthogonal STBC based on givens rotation with lower bit error rate. The transmission diversity method rotates every single information symbol. The scheme can suppress channel noise and eliminate the interference term well. Simulation results show that the method can improve performance better than conventional algorithm without increasing decoding complexity.
基金funded by Prince Sultan University,Riyadh,Saudi Arabia。
文摘For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.
文摘The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2 × 2 transforms. The DsiHT is zeroing all components of the input signal while moving or heaping the energy of the signal to one component, for instance the first one. We describe three different types of QR-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, as well as without matrices but using analytical formulas. We also present the mixed QR-decomposition, when different type DsiHTs are used in different stages of the algorithm. The number of such decompositions is greater than 3<sup>(N-1)</sup>, for an N × N complex matrix. Examples of the QR-decomposition are described in detail for the 4 × 4 and 6 × 6 complex matrices and compared with the known method of Householder transforms. The precision of the QR-decompositions of N × N matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for QR-decompositions by the described DsiHTs are given.
