The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is propose...The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.展开更多
考虑双平行线阵中非圆信号二维波达方向(Direction of arrival,DOA)估计问题,提出了一种基于Euler变换传播算子(Propagator method,PM)的二维DOA估计算法。该算法利用非圆信号的特性,扩展了接收数据矩阵,使得角度估计性能优于二维PM算...考虑双平行线阵中非圆信号二维波达方向(Direction of arrival,DOA)估计问题,提出了一种基于Euler变换传播算子(Propagator method,PM)的二维DOA估计算法。该算法利用非圆信号的特性,扩展了接收数据矩阵,使得角度估计性能优于二维PM算法。同时采用Euler变换把非圆PM算法中的复数运算转换为实数运算,降低计算复杂度,角度估计性能逼近非圆PM算法。该算法可以实现二维角度的自动配对,与传统PM算法相比,可同时估计出更多的信源。该算法的优越性均可在文中得到验证。展开更多
In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relati...In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.展开更多
The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel functio...The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel function is of the form Ke(ξ,t)=exp(−iξt). Joseph Fourier, the famous French Mathematician and Engineer, was the pioneer and he studied the properties in his seminal works. This important tool created an avenue of research later and it is very important in tackling problems in strong differential form and studying spectral properties of various ordinary and partial differential operators. In our article, we will obtain explicit bounds for the modified Fourier transform and derive some corollaries using in the Kernel function a multiple of the Euler-Mascheroni constant γ. The bounds obtained involve the Riemann zeta function for positive integers at the right-hand side.展开更多
基金supported by the National Science Foundation of China (No.61371169)the Aeronautical Science Foundation of China(No.20120152001)
文摘The problem of two-dimensional(2 D)direction of arrival(DOA)estimation for double parallel uniform linear arrays is investigated in this paper.A real-valued DOA estimation algorithm of noncircular(NC)signal is proposed,which combines the Euler transformation and rotational invariance(RI)property between subarrays.In this work,the effective array aperture is doubled by exploiting the noncircularity of signals.The complex arithmetic is converted to real arithmetic via Euler transformation.The main contribution of this work is not only extending the NC-Euler-ESPRIT algorithm from uniform linear array to double parallel uniform linear arrays,but also constructing a new 2 Drotational invariance property between subarrays,which is more complex than that in NCEuler-ESPRIT algorithm.The proposed 2 DNC-Euler-RI algorithm has much lower computational complexity than2 DNC-ESPRIT algorithm.The proposed algorithm has better angle estimation performance than 2 DESPRIT algorithm and 2 D NC-PM algorithm for double parallel uniform linear arrays,and is very close to that of 2 D NC-ESPRIT algorithm.The elevation angles and azimuth angles can be obtained with automatically pairing.The proposed algorithm can estimate up to 2(M-1)sources,which is two times that of 2 D ESPRIT algorithm.Cramer-Rao bound(CRB)of noncircular signal is derived for the proposed algorithm.Computational complexity comparison is also analyzed.Finally,simulation results are presented to illustrate the effectiveness and usefulness of the proposed algorithm.
文摘考虑双平行线阵中非圆信号二维波达方向(Direction of arrival,DOA)估计问题,提出了一种基于Euler变换传播算子(Propagator method,PM)的二维DOA估计算法。该算法利用非圆信号的特性,扩展了接收数据矩阵,使得角度估计性能优于二维PM算法。同时采用Euler变换把非圆PM算法中的复数运算转换为实数运算,降低计算复杂度,角度估计性能逼近非圆PM算法。该算法可以实现二维角度的自动配对,与传统PM算法相比,可同时估计出更多的信源。该算法的优越性均可在文中得到验证。
基金Project supported by the National Natural Science Foundation of China (Grant No.10671120)
文摘In this paper, using the characteristic analysis method, we study the relativistic Euler equations of conservation laws in energy and momentum in special relativity. The interactions of elementary waves for the relativistic Euler equations are shown. The collision of two shocks, two centered rarefaction waves, a shock and a rarefaction wave yield corresponding ransmitted waves. The overtaking of two shocks appears a transmitted shock wave, together with a reflected centered rarefaction wave.
文摘The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel function is of the form Ke(ξ,t)=exp(−iξt). Joseph Fourier, the famous French Mathematician and Engineer, was the pioneer and he studied the properties in his seminal works. This important tool created an avenue of research later and it is very important in tackling problems in strong differential form and studying spectral properties of various ordinary and partial differential operators. In our article, we will obtain explicit bounds for the modified Fourier transform and derive some corollaries using in the Kernel function a multiple of the Euler-Mascheroni constant γ. The bounds obtained involve the Riemann zeta function for positive integers at the right-hand side.
