The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation a...The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.展开更多
Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with...Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with different analog-to-information conversion(AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound(CRB)for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio(SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.展开更多
In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close f...In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close form expressions of CRB are obtained through complicated derivation, and then are applied to evaluate the performance of the cyclic estimator.The results are accurate enough and serve well as benchmark for evaluating the performance of parameter estimation method. Numerical simulations illustrate the accuracy and applicability of the derived CRB.展开更多
In this paper,we study the eigenvalue problem of the Markov diffusion operator L^(2),and give generalized inequalities for eigenvalues of the operator L^(2)on a Markov diffusion triple.By applying these inequalities,w...In this paper,we study the eigenvalue problem of the Markov diffusion operator L^(2),and give generalized inequalities for eigenvalues of the operator L^(2)on a Markov diffusion triple.By applying these inequalities,we then get some new universal bounds for eigenvalues of a special Markov diffusion operator L^(2)on bounded domains in an Euclidean space.Moreover,our results can reveal the relationship between the(k+1)-th eigenvalue and the first k eigenvalues in a relatively straightforward manner.展开更多
Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its com...Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.展开更多
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent apert...This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.展开更多
The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multi...The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multiple output （MIMO） radars. To gain some insight into the behavior of the CRB, the CRB with a set of given orthogonal waveforms is studied as a specific case. Second, a maximum likelihood （ML） estimation algorithm is proposed. The mean square error （MSE） of the ML estimation of target location and velocity is obtained by Monte Carlo simulation and it approaches CRB in the high signal-to-noise ratio （SNR） region.展开更多
To achieve a high signal-to-noise ratio(SNR) while maintaining moderate radar antenna, a target-based calibration manner is available to coherently combine multiple radars. The key to this calibration manner is to est...To achieve a high signal-to-noise ratio(SNR) while maintaining moderate radar antenna, a target-based calibration manner is available to coherently combine multiple radars. The key to this calibration manner is to estimate coherence parameters(CPs), i.e., time and phase calibration values in transmission and reception estimation, by separating the target returns into monostatic and bistatic echoes. However, CPs estimations exist uncertainties, which will affect the performance gain after multiradar coherent combination. The principle of coherently combining multiple radars is elaborated and the signal probability model for CPs estimation is established. On this basis, CPs Cramer-Rao bound(CRB) is derived in the closed-form, according to which the non-tight and tight upper bounds for multiple radars coherent combination performance gain are derived in the closed-form and via Monte Carlo(MC) simulations, respectively. Simulations validate the correctness of the derived CRB and gain bounds.展开更多
The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is g...The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.展开更多
For the problem of deterministic parameter estimate, the theoretical lower bound of esti- mate error is the Cramér-Rao bound; while for random parameter, the lower bound of estimate error is generally termed by P...For the problem of deterministic parameter estimate, the theoretical lower bound of esti- mate error is the Cramér-Rao bound; while for random parameter, the lower bound of estimate error is generally termed by Posterior Cramér-Rao Bound (PCRB). Under the background of passive tracking where the target's state can be seen as a time-varying random parameter, PCRB of the state estimate error is analyzed in this paper, and the relation between PCRB and varied condition is also fully in- vestigated using different simulation examples. The presented analytical method provides a theoretical base for performance assessment of all kinds of suboptimal estimate algorithms used in practice.展开更多
The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee ...The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.展开更多
Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn...Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.展开更多
We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface....We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch.展开更多
Let G be a simple graph with n vertices and m edges. In this paper, we present some new upper bounds for the adjacency and the signless Laplacian spectral radius of graphs in which every pair of adjacent vertices has ...Let G be a simple graph with n vertices and m edges. In this paper, we present some new upper bounds for the adjacency and the signless Laplacian spectral radius of graphs in which every pair of adjacent vertices has at least one common adjacent vertex. Our results improve some known upper bounds. The main tool we use here is the Lagrange identity.展开更多
MIMO system can provide higher capacity in independent conditions. When the spatial-temporal fading correlation exists, the capacity may decrease. In this paper, the geometrical MIMO channel model is presented with Ri...MIMO system can provide higher capacity in independent conditions. When the spatial-temporal fading correlation exists, the capacity may decrease. In this paper, the geometrical MIMO channel model is presented with Rician factor. Based on the MIMO ergodic capacity, the capacity bounds are derived with arbitrary finite number of antennas. The bounds are derived in the exact expressions in doubly correlated MIMO R/clan channel. Then a simple expression for the capacity bounds is attained for the high SNR. Finally, the tightness of derived bounds is verified by Monte Carlo simulation.展开更多
A new method for estimating the bounds of eigenvalues ispresented. In order to show that the method proposed is as effectiveas Qiu's an undamping spring-mass system with 5 nodes and 5 degrees ofreedom is given. To...A new method for estimating the bounds of eigenvalues ispresented. In order to show that the method proposed is as effectiveas Qiu's an undamping spring-mass system with 5 nodes and 5 degrees ofreedom is given. To illustrate that the present method can beapplied to structures which cannot be treated by non-negativedecomposition, a plane frame with 202 nodes and 357 beam elements isgiven. The results show that the present method is effective forestimating the bounds of eigenvalues and is more common than Qiu's.展开更多
In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution ...In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.展开更多
We study the relationship between energy consumption and economic growth in the case of USA by using an asymmetric ARDL bounds test approach to achieve the actual model. The quarterly data set covers the period of 197...We study the relationship between energy consumption and economic growth in the case of USA by using an asymmetric ARDL bounds test approach to achieve the actual model. The quarterly data set covers the period of 1973:1- 2013:4. The findings indicate that the effect of energy consumption is asymmetric in the long term but not in the short term. In the long run, the effect of negative component of energy consumption on economic growth is small and statistically insignificant. The coefficient of the positive component of energy consumption is found about 0.9 and statistically significant at 1% level. We conclude that energy saving policies such as technological progress and organizational rearrangements may have the dimmer effect for the impact of a negative component of energy consumption and the booster effect for impact of the positive component of energy consumption. Thus, energy saving policy should be tightly followed by the goal of high economic growth.展开更多
文摘The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.
基金supported by the National Natural Science Foundation of China(6140121061571228)
文摘Time-delay and Doppler shift estimation is a basic task for pulse-Doppler radar processing. For low-rate sampling of echo signals, several kinds of compressive sampling(CS) pulse-Doppler(CSPD) radar are developed with different analog-to-information conversion(AIC) systems. However, a unified metric is absent to evaluate their parameter estimation performance. Towards this end, this paper derives the deterministic Cramer-Rao bound(CRB)for the joint delay-Doppler estimation of CSPD radar to quantitatively analyze the estimate performance. Theoretical results reveal that the CRBs of both time-delays and Doppler shifts are inversely proportional to the received target signal-to-noise ratio(SNR), the number of transmitted pulses and the sampling rate of AIC systems. The main difference is that the CRB of Doppler shifts also lies on the coherent processing interval. Numerical experiments validate these theoretical results. They also show that the structure of the AIC systems has weak influence on the CRBs, which implies that the AIC structures can be flexibly selected for the implementation of CSPD radar.
文摘In this paper, Cramer-Rao Bound (CRB) is derived from phase-coding signal with additive white noise, where three important parameters are focused on: carrier frequency, chip width and amplitude. Simplified and close form expressions of CRB are obtained through complicated derivation, and then are applied to evaluate the performance of the cyclic estimator.The results are accurate enough and serve well as benchmark for evaluating the performance of parameter estimation method. Numerical simulations illustrate the accuracy and applicability of the derived CRB.
基金Supported by the Open Research Fund of Key Laboratory of Nonlinear Analysis and Applications(Central China Normal University),Ministry of Education,P.R.China(Grant No.NAA2025ORG011)Science and Technology Plan Project of Jingmen(Grant No.2024YFZD076)+3 种基金Research Team Project of Jingchu University of Technology(Grant No.TD202006)Research Project of Jingchu University of Technology(Grant Nos.HX20240049HX20240200)the Teaching Reform Research Project of Hubei Province(Grant No.2024496)。
文摘In this paper,we study the eigenvalue problem of the Markov diffusion operator L^(2),and give generalized inequalities for eigenvalues of the operator L^(2)on a Markov diffusion triple.By applying these inequalities,we then get some new universal bounds for eigenvalues of a special Markov diffusion operator L^(2)on bounded domains in an Euclidean space.Moreover,our results can reveal the relationship between the(k+1)-th eigenvalue and the first k eigenvalues in a relatively straightforward manner.
文摘Usually, only the Cramer-Rao lower bound （CRLB） of single target is taken into consideration in the state estimate of passive tracking systems. As for the case of multitarget, there are few works done due to its complexity. The recursion formula of the posterior Cramer-Rao lower bound （PCRLB） in multitarget bearings-only tracking with the three kinds of data association is presented. Meanwhile, computer simulation is carried out for data association. The final result shows that the accuracy probability of data association has an important impact on the PCRLB.
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
基金supported by the National Natural Science Foundation of China(61171120)the Key National Ministry Foundation of China(9140A07020212JW0101)+2 种基金the Foundation of Tsinghua University(20101081772)the Foundation of National Laboratory of Information Control Technology for Communication System of Chinathe Foundation of National Information Control Laboratory
文摘This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.
基金supported by the National Natural Science Foundation of China(61171120)the Key National Ministry Foundation of China(9140A07020212JW0101)the Foundation of Tsinghua University(20101081772)
文摘The optimal estimation performance of target parameters is studied. First, the general form of Cramer-Rao bound （CRB） for joint estimation of target location and velocity is derived for coherent multiple input multiple output （MIMO） radars. To gain some insight into the behavior of the CRB, the CRB with a set of given orthogonal waveforms is studied as a specific case. Second, a maximum likelihood （ML） estimation algorithm is proposed. The mean square error （MSE） of the ML estimation of target location and velocity is obtained by Monte Carlo simulation and it approaches CRB in the high signal-to-noise ratio （SNR） region.
基金supported by the National Natural Science Foundation of China(61471372)
文摘To achieve a high signal-to-noise ratio(SNR) while maintaining moderate radar antenna, a target-based calibration manner is available to coherently combine multiple radars. The key to this calibration manner is to estimate coherence parameters(CPs), i.e., time and phase calibration values in transmission and reception estimation, by separating the target returns into monostatic and bistatic echoes. However, CPs estimations exist uncertainties, which will affect the performance gain after multiradar coherent combination. The principle of coherently combining multiple radars is elaborated and the signal probability model for CPs estimation is established. On this basis, CPs Cramer-Rao bound(CRB) is derived in the closed-form, according to which the non-tight and tight upper bounds for multiple radars coherent combination performance gain are derived in the closed-form and via Monte Carlo(MC) simulations, respectively. Simulations validate the correctness of the derived CRB and gain bounds.
基金supported by the Fundamental Research Funds for the Central Universities (CDJXS 11 10 00 19)Mu Chunlai is supported by NSF of China(11071266)
文摘The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.
文摘For the problem of deterministic parameter estimate, the theoretical lower bound of esti- mate error is the Cramér-Rao bound; while for random parameter, the lower bound of estimate error is generally termed by Posterior Cramér-Rao Bound (PCRB). Under the background of passive tracking where the target's state can be seen as a time-varying random parameter, PCRB of the state estimate error is analyzed in this paper, and the relation between PCRB and varied condition is also fully in- vestigated using different simulation examples. The presented analytical method provides a theoretical base for performance assessment of all kinds of suboptimal estimate algorithms used in practice.
基金supported by the National Natural Science Foundation of China(11301546).supported by the National Natural Science Foundation of China(11271147,11471136)
文摘The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.
文摘Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
文摘Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.
基金Supported by the National Natural Science Foundation of China (61170324 and 61100105)
文摘We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch.
基金Supported by the National Natural Science Foundation of China(11471077)the Open Research Fund of Key Laboratory of Spatial Data Mining and Information Sharing of MOE(2018LSDMIS09)Foundation of Key Laboratory of Intelligent Metro of Universities in Fujian Province(53001703)
文摘Let G be a simple graph with n vertices and m edges. In this paper, we present some new upper bounds for the adjacency and the signless Laplacian spectral radius of graphs in which every pair of adjacent vertices has at least one common adjacent vertex. Our results improve some known upper bounds. The main tool we use here is the Lagrange identity.
基金Acknowledgements This work was supported by National 13asie Research Program of China （2009CB320401）, National Natural Science Foundation of China （60972075, 61072055）, Key Scientific and Technologi- cal Project of China 2010ZX03003-003-01, and Fundamental Research Funds for the Central Universities （2009RC0116）.
文摘MIMO system can provide higher capacity in independent conditions. When the spatial-temporal fading correlation exists, the capacity may decrease. In this paper, the geometrical MIMO channel model is presented with Rician factor. Based on the MIMO ergodic capacity, the capacity bounds are derived with arbitrary finite number of antennas. The bounds are derived in the exact expressions in doubly correlated MIMO R/clan channel. Then a simple expression for the capacity bounds is attained for the high SNR. Finally, the tightness of derived bounds is verified by Monte Carlo simulation.
基金the National Natural Science Foundation (No.19872028)the Mechanical Technology Development Foundation of China
文摘A new method for estimating the bounds of eigenvalues ispresented. In order to show that the method proposed is as effectiveas Qiu's an undamping spring-mass system with 5 nodes and 5 degrees ofreedom is given. To illustrate that the present method can beapplied to structures which cannot be treated by non-negativedecomposition, a plane frame with 202 nodes and 357 beam elements isgiven. The results show that the present method is effective forestimating the bounds of eigenvalues and is more common than Qiu's.
基金Supported by the National Natural Science Foundation of China(10671177)
文摘In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.
文摘We study the relationship between energy consumption and economic growth in the case of USA by using an asymmetric ARDL bounds test approach to achieve the actual model. The quarterly data set covers the period of 1973:1- 2013:4. The findings indicate that the effect of energy consumption is asymmetric in the long term but not in the short term. In the long run, the effect of negative component of energy consumption on economic growth is small and statistically insignificant. The coefficient of the positive component of energy consumption is found about 0.9 and statistically significant at 1% level. We conclude that energy saving policies such as technological progress and organizational rearrangements may have the dimmer effect for the impact of a negative component of energy consumption and the booster effect for impact of the positive component of energy consumption. Thus, energy saving policy should be tightly followed by the goal of high economic growth.
