Extended Ziv-Zakai lower bound for vector parameter estimation

The Bayesian Ziv-Zakai bound on the mean square error (MSE) in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than MSE. The extended bound is evaluated for some representative problems in time-delay and bearing estimation. The resulting bounds have simple closed-form expressions, and closely predict the simulated performance of the maximum-likelihood estimator in all regions of operation     

Minimax lower bound for time-varying frequency estimation ofharmonic signal

Estimation of the instantaneous frequency and its derivatives is considered for a harmonic complex-valued signal with the time-varying phase and time-invariant amplitude. The asymptotic minimax lower bound is derived for the mean squared error of estimation, provided that the phase is an arbitrary m-times piecewise differentiable function of time. It is shown that this lower bound is different only in a constant factor from the upper bound for the mean squared errors of the local polynomial periodogram with the optimal window size. The time-varying phases “worst” for estimation of the instantaneous frequency and its derivatives are obtained as a solution of the minimax problem     

On the Miller-Chang lower bound for NDA carrier phase estimation

In this letter, we derive a new Miller-Chang lower bound (MCB) for the variance of unbiased non-data-aided (NDA) carrier phase estimates obtained from a block of N samples of a linearly modulated pulse-amplitude modulation or quadrature-amplitude modulation information signal, transmitted through an additive white Gaussian noise channel. This bound is tighter than the corresponding Crame/spl acute/r-Rao lower bound (CRB) for data-aided or continuous-wave carrier phase estimation (CW-CRB), particularly when N is small. For some given N and sufficiently high signal-to-noise ratios, the MCB is tighter than the corresponding true NDA CRB. The main limitation of this new MCB is that its application is restricted to carrier phase estimators which are unbiased for all possible values of the received symbol sequence.     

单观测器无源定位误差下界的仿真分析

单观测器无源定位所能达到的最优定位精度与观测器的运动速度、运动轨迹、测量精度和测量速率密切相关。该文采用仿真方法,分析了观测器运动轨迹、运动速度、测量精度和测量速率等因素对测角无源定位误差Cramer-Rao下界的影响,比较了三种形式观测器轨迹的定位误差下界,得出的结果对确定具体定位与跟踪系统战术指标、以及对滤波算法的选用具有实用价值。     

相位编码信号码元宽度估计的修正克拉美—罗限

推导了相位编码信号码元宽度估计的修正克拉美-罗限(MCRB).采用Parseval定理将单位冲激函数δ(t)平方的积分转换到频域计算,得到脉冲成形函数是矩形脉冲时码元宽度估计的修正克拉美-罗限.当脉冲成形函数是升余弦脉冲时则进行了数值计算.计算表明,当滚降系数为0.5时,升余弦脉冲和矩形脉冲对应的码元宽度估计性能相差1dB左右.     

Cramer‐Rao lower bound and parameter estimation for multibeam satellite links

Data throughput and availability of multibeam satellite links are limited by interference problems, in particular when the design is determined by an aggressive reuse of frequency bands. Usually, this is mitigated by appropriately selected techniques like precoding or multi‐user detection. Before such methods are applicable, however, the most important transmission parameters have to be recovered successfully even under very challenging conditions caused by (full) frequency reuse. The detailed analysis of the log‐likelihood function characterizing the multibeam scenario shows that a beamwise decoupling of the estimation task is possible, if the following three conditions are met: (i) alignment of all frequency offsets; (ii) symbol synchronicity; (iii) orthogonal synchronization sequences. Based on these assumptions, it turns out that the modified Cramer‐Rao lower bound (MCRLB) for carrier frequency and phase, symbol timing and signal amplitude is the same, no matter whether we are dealing with a single or a multiple beam situation. Furthermore, because a maximum likelihood framework for parameter estimation is not available in closed form, we introduce a sub‐optimal concept of low‐complex algorithms. Finally, it is verified by simulation results that the jitter variance of each recovery scheme is close to the related MCRLB, when the decoupling conditions are satisfied. Copyright © 2016 John Wiley & Sons, Ltd.     

Cramer-Rao lower bound and EM algorithm for envelope-based SNR estimation of nonconstant modulus constellations

Signal-to-noise ratio (SNR) estimation for linearly modulated signals is addressed in this letter, focusing on envelopebased estimators, which are robust to carrier offsets and phase jitter, and on the challenging case of nonconstant modulus constellations. For comparison purposes, the true Cramér-Rao lower bound is numerically evaluated, obtaining an analytical expression in closed form for the asymptotic case of high SNR values, which quantifies the performance loss with respect to coherent estimation. As the maximum-likelihood algorithm is too complex for practical implementation, an expectationmaximization (EM) approach is proposed, achieving a good tradeoff between complexity and performance for mediumto- high SNRs. Finally, a hybrid scheme based on EM and moments-based estimates is suggested, which performs close to the theoretical limit over a wide SNR range.     

On the true Cramer-Rao lower bound for data-aided carrier-phase-independent frequency offset and symbol timing estimation

In this letter we present new and simple closed form expressions for the true Cramer-Rao lower bound (CRB) for data-aided (DA) joint and individual carrier frequency offset and symbol timing estimation from a linearly modulated waveform transmitted over an AWGN channel. The bounds are derived under a carrier-phase-independent (CPI) estimation strategy wherein the carrier phase is viewed as a nuisance parameter and assumed to have a worst-case noninformative uniform distribution over [-ππ]. The computation of these CRBs requires only a single numerical integration. In addition, computationally simpler yet highly accurate asymptotic lower bounds are presented. As particularizations, new bounds for individual CPI frequency estimation with known symbol timing from M-PSK and continuous wave (CW) signals are also reported.     

A cooperative Bayesian and lower bound estimation in dynamic framed slotted ALOHA algorithm for RFID systems

A novel estimation scheme that combines Bayesian and lower bound estimating radio frequency identification tag population size is proposed. The developed methodology is based on the fusion between the Bayesian and lower bound estimating techniques. It turns out that the fusion rule is built up thanks to an existing linear relationship between the cited techniques. Simulation results show that the developed technique significantly improves the accuracy of the estimating tag quantity and presents less estimation error. Also, the resulting advanced dynamic framed slotted ALOHA protocol considerably improves the performance and efficiency of the radio frequency identification anti‐collision compared with the most recent protocols using others estimating methods.     

The Cramer-Rao lower bound for bilinear systems

Estimation of the unknown parameters that characterize a bilinear system is of primary importance in many applications. The Cramer-Rao lower bound (CRLB) provides a lower bound on the covariance matrix of any unbiased estimator of unknown parameters. It is widely applied to investigate the limit of the accuracy with which parameters can be estimated from noisy data. Here it is shown that the CRLB for a data set generated by a bilinear system with additive Gaussian measurement noise can be expressed explicitly in terms of the outputs of its derivative system which is also bilinear. A connection between the nonsingularity of the Fisher information matrix and the local identifiability of the unknown parameters is exploited to derive local identifiability conditions of bilinear systems using the concept of the derivative system. It is shown that for bilinear systems with piecewise constant inputs, the CRLB for uniformly sampled data can be efficiently computed through solving a Lyapunov equation. In addition, a novel method is proposed to derive the asymptotic CRLB when the number of acquired data samples approaches infinity. These theoretical results are illustrated through the simulation of surface plasmon resonance experiments for the determination of the kinetic parameters of protein-protein interactions.     

Sensor location calibration for bearing estimation

New calibration methods are presented for bearing estimation with sensor location uncertainties, which are based on eigenvalue decomposition of the sample covariance matrix and three or more nondisjoint sources in known bearings. The methods can be applied to arbitrary arrays, including linear arrays, require fewer computations, and are suitable for low signal-to-noise ratio (SNR) cases. Computer simulations are given to illustrate the performance of the proposed methods.Supported by National Science and Technology Board of Singapore.On leave from the Department of Electronic Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China.     

A lower bound on the estimation error for an unknown parameter with discontinuous observations (Corresp.)

A lower bound on the mean square error for an estimate of unknown parameter is derived for the case where the observation noise is a martingale with jump discontinuities.     

A lower bound on the mean-square error in random parameter estimation (Corresp.)

A new lower bound on mean-square error in parameter estimation is presented. The bound is tighter than the Cramér-Rao and Bobrovsky-Zakai lower bounds. It requires no bias or regularity assumptions, it is computationally simple, and it can be applied to estimates of vector parameters or functions of the parameters.     

The true Crame/spl acute/r-Rao lower bound for data-aided carrier-phase-independent time-delay estimation from linearly Modulated waveforms

In this paper, we present the derivation and analysis of the true Crame/spl acute/r-Rao lower bound (CRB) for the variance of unbiased, data-aided (DA) symbol-timing estimates, obtained from a block of K samples of a linearly modulated information signal, transmitted through an additive white Gaussian noise channel with random carrier phase. We consider a carrier-phase-independent time-delay estimation scenario wherein the carrier phase is viewed as an unwanted or nuisance parameter. The new bounds require only a moderate computational effort and are tighter than the CRB for the variance of unbiased time-delay estimates obtained under the assumption that the carrier phase is known. These bounds are particularly useful to assess the ultimate accuracy that can be achieved by pilot-assisted symbol synchronizers. Conversely, they may be used to evaluate data sequence suitability for the purpose of time-delay estimation. Comparison of the actual variance of a DA feedforward timing estimator with the new bounds show that these are attainable by practical synchronizers.     

A new lower bound for the frequency assignment problem

We propose a new lower bound on the number of frequencies required to meet the frequency demands in a cellular network. It extends Gamst's (1986) work by devising a procedure of frequency insertion, which makes the best of unexploited frequency spaces between the assigned frequencies. Our lower bound is claimed to have much wider and easier real-world applicability due to its relaxed prerequisite condition. Furthermore, it is shown via an illustrative example to be much tighter than its previous counterpart     

A new lower bound for the channel assignment problem

The strength of lower bounds for the span in channel assignment problems is discussed with reference to standard benchmark problems. It is shown that in some circumstances current bounds are capable of very significant improvement. The use of methods from mathematical programming is outlined and a new lower bound applicable to cellular problems is presented     

A distribution-free lower bound for availability of quantile-basedinspection schemes

This paper develops a lower bound for the availability of quantile-based inspection schemes when device lifetimes are assumed to have an increasing failure rate. The lower bound is useful in designing inspection schemes when lifetime distributions are not explicitly known, but must be estimated from limited failure data     

Improved general lower bound for spatially-correlated Rician MIMO capacity

In this letter we derive a new closed-form lower bound on the ergodic capacity of single-sided correlated Rician MIMO channels with arbitrary-rank mean matrices. The new bound is significantly tighter than previously reported bounds, and matches almost exactly with empirically-generated (exact) capacity results for all signal to noise ratios. The new closed-form bound is also more computationally efficient than the previous bounds in the literature.     

Realizable lower bounds for time delay estimation

The accuracy of time delay estimates obtainable in active localization systems is studied, focusing on the effect of ambiguities in the time delay estimates. Such ambiguities occur when the transmitted signal has small relative bandwidth. Then, for signal to noise ratios below a certain threshold, the commonly used Cramer-Rao lower bound is not realizable. The study concentrates on the region of intermediate SNR values, where the Cramer-Rao bound is no longer achievable, but useful information on time delays can still be obtained from the measurement. Realizable bounds for the single and two echo cases are obtained by deriving a new form of the Barankin (1949) bound for active time delay estimation. This form maintains the realizability property of the most general form, but is of reasonable complexity. New bounds are derived for the multiple echo case. Examples are presented to illustrate the dependence of the bound on parameters such as SNR, relative bandwidth, and echo separation     

On the method-independent lower bound (MILB) to the variance of attenuation estimation in random reflection

Based on the Cramer-Rao inequality, the MILB is calculated for the problem of estimating the frequency slope of the attenuation coefficient of tissue from random reflections of ultrasonic waves. Under typical signal conditions, this bound for a 1-cm x 1-cm region was found to be about 0.08 db/(MHz-cm), rather close to the clinical requirement of 0.1 dB/(MHz-cm). Comparison to existing methods (including an autoregressive deconvolution method) shows room for further improvement.