Comments on "on Probability of Error in Decision Feedback Equalizer"

The above-mentioned paper [1] derives bounds on the error probability of a decision feedback equalizer (DFE) which are claimed to be significantly tighter than the earlier upper bound of [2]. Unfortunately, [1] makes an unsupportable assumption which reddars the conclusions incorrect. We show that valid bounds can be obtained by the methods of [1], but that for the numerical example of [2] , the resulting upper bound is never tighter than, and sometimes significantly weaker than, that derived in [2]. Similarly, a lower bound derived by the method of [1] is shown for the same numerical example to be very close to the error-free past lower bound previously known.     

Evaluating Radar Detection Probabilities by Steepest Descent Integration

The probability of detection for radars employing noncoherent integration and a fixed threshold or cell-averaging constant false alarm rate (CA-CFAR) processor is computed by numerical contour integration in the complex plane. The technique is applied to both nonfluctuating and chi-squared fluctuating targets. A bound on the truncation error allows for a simple stopping rule for the numerical integration. The method has applicability to many problems in radar detection theory.     

A Bound on Processor Gain

In data transmission systems using electromagnetic propagation there is often interest in the antijam capability of the system and the probability that the transmitted signal can be intercepted. It is shown that, neglecting antenna gain, both of these are adequately described by the processor gain. An information theoretic bound is given for the processor gain and the performance of several conventional signaling systems is indicated. Improvement using forward error correction is also investigated.     

结构系统失效概率的近似分析

提出用一阶简单边界的上、下界来估计结构系统失效概率的近似公式。它考虑了结构系统失效模式之间的相关性但仅包含失效模式的一阶概率。算例表明,通常最大误差在5％以内,精度高而计算简便。     

Degradation of Signal-to-Noise Ratio Due to IF Filtering

A receiver for biphase modulated signals using an integrate-and-dump filter is optimum only if the IF filter bandwidth is infinite. Finite IF filter bandwidth results is a performance degradation. Using the predetection signal-to-noise ratio as the performance criterion, a lower bound on this quantity is determined as a function of the ratio (IF filter bandwidth)/(bit rate). The corresponding upper bound on the error probability is also presented.     

New results in importance sampling [of false alarm statistics]

Importance sampling is a technique which can significantly reduce the number of Monte Carlos necessary to accurately estimate the probability of low-probability of occurrence events (e.g., the probability of false alarm P_F associated with a given detection scheme). A new technique called the Chernoff Importance Sampling Method is introduced. It is shown that the number of required Monte Carlos can be reduced by a factor of a Chernoff-like bound on P _F. In addition, techniques for choosing the multiplying factor of the distorted variance method (the most common method used in importance sampling) are presented     

Detection threshold selection for tracking performance optimization

A technique for the evaluation of the track loss probability and the estimation error during track maintenance in clutter has been developed recently by the authors. This work overcomes the limitation of an earlier technique that does not handle the transient process of tracking divergence. Track loss, being a “runaway” phenomenon, clearly requires transient evaluation capability. The new technique provides, without the need for expensive Monte Carlo simulations, the probability that a hack is maintained in the presence of all sources of uncertainty encountered In a tracking process. This technique is of a hybrid nature; it involves explicit probabilistic accounting of both the continuous and the discrete uncertainties. Here it is demonstrated how this technique can be used for the selection of the detection threshold to optimize the overall performance of a detection-trading system     

A Note on Bounds for Target Tracking with pd>1

Recently several new results for Cramer-Rao lower bounds (CRLBs) in dynamical systems have been developed. Several different approaches and approximations have been presented. For the general case of target tracking with a detection probability smaller than one and possibly in the presence of false measurements, two main approaches have been presented. The first approach is the information reduction factor (IRF) approach. The second approach is the enumeration (ENUM) approach, also referred to as the conditioning approach. It has been found that the ENUM approach leads to a strictly larger covariance matrix than the IRF approach, however, still providing a lower bound on the attainable error covariance. Thus, the ENUM approach provides a strictly tighter bound on the attainable performance. It has been conjectured that these bounds converge to one another in the limit or equivalently after an initial transition stage. We demonstrate, using some recent results from the modified Riccati equation (MRE) and by means of counter examples, that this conjecture does not hold true in general. We also demonstrate that the conjecture does hold true in the special case of deterministic target motion, or equivalently in the absence of process noise. Furthermore, we show that the detection probability has an influence on the limiting behaviors of the bounds. Moreover, we show that the MRE approximation provides a very good and computationally efficient approximation of the ENUM bound. The various results are illustrated by means of representative examples.     

Explicit formulas for two state Kalman, H/sub 2/ and H/sub /spl infin// target tracking filters

The continuous time, two state, target tracking problem is considered from the Kalman, H/sub 2/, and H/sub /spl infin// filter viewpoint. While previous treatments were numerical in nature, analytic transient responses and infinite horizon solutions with analytic performance expressions are presented here. Tracking indices, involving the maneuver and measurement uncertainties, are shown to have a role for both the steady state and transient responses. In addition, the H/sub /spl infin// tracker has a sensor index involving the performance bound and measurement uncertainty, which, along with the tracking index, plays a significant role in the H/sub /spl infin// tracker expressions. Analytical expressions for the probability of target escape, the probability that the target position will be outside the radar beamwidth (BW), are developed not only to compare the performance of various trackers, but also as a design tool to meet tracking specifications. Examples illustrate the performance of the target trackers as a function of the error gain upper bound.     

Performance measure for Markovian switching systems using best-fitting Gaussian distributions

This paper considers the theoretical posterior Cramer-Rao lower bound (PCRLB) for the case of tracking a manoeuvring target with Markovian switching dynamics. In a recent article [2] it was proposed to calculate the PCRLB conditional on the manoeuvre sequence and then determine the bound as a weighted average, giving an unconditional PCRLB. However, we demonstrate that this approach can produce an overly optimistic lower bound, because the sequence of manoeuvres is implicitly assumed known. Motivated by this, we develop a general approach and derive a closed-form estimate of the PCRLB in the case of Markovian switching systems. The basis of the approach is to, at each time step, replace the multi-modal prior target probability density function (pdf) with a best-fitting Gaussian (BFG) approximation. We present a recursive formula for calculating the mean and covariance of this Gaussian distribution, and demonstrate how the covariance increases as a result of the potential manoeuvres. We are then able to calculate the PCRLB for this BFG model using an existing Riccati-like recursion. Because of the BFG approximation, we are no longer guaranteed a bound and so we refer to our estimate as an "error performance measure" rather than a bound. The presented approach is applied both to filtering and smoothing cases. The simulation results indicate a very close agreement between the proposed performance measure and the error performance of an interacting multiple model estimator.     

Composite Bound on Arrival Time Estimation Errors

Time of arrival (TOA) estimation of narrowband signals is a problem of considerable practical interest in radar and sonar applications. A new technique is presented to analyze the mean square error (MSE) performance of TOA estimation schemes, based on recently developed lower bound. We obtain a complete characterization of the MSE as a function of the signal and noise parameters. The results are given in a simple closed-form analytical expression.     

PCM/FM aeronautical telemetry in frequency selective multipath interference

The performance of PCM/FM using a delay-line detector in multipath interference is analyzed. In aeronautical telemetry applications, the multipath interference causes a in the signal spectrum which is web modeled by a channel composed of a line-of-sight signal and a strong specular reflection with magnitude /spl Gamma/ and excess delay less than a bit time. Analysis shows that the bit error probability is strongly dependent on the location of the within the spectrum. The bit error probability averaged over the location is also analyzed. For the case of no predetection filtering, the average bit error probability is dependent on the depth of the but not on the width. The loss in performance (relative to the AWGN environment) is bounded by (1-/spl Gamma/)/sup -2/ which is the depth of the . For the case of predetection filtering, the average bit error probability is dependent on both the width and depth of the . The performance loss is bounded by (1-/spl Gamma/)/sup -2/spl Gamma// which is less than that for the case of no predetection filtering.     

分组码在有记忆删除信道上的性能计算

 本文首先描述了一种有记忆删除信道模型,然后提出了分组码在该信道上的性能的迭代算法。最后以Golay(23,12,7)码为例给出了多种信道参数之下的性能曲线。     

Crosstalk Resistant Receiver for M-ary Multiplexed Communications

Attention is directed to the problem of M-ary signal transmission from a multiplicity of synchronized information sources. A receiver processor is derived which suppresses the effect of crosstalk between nonorthogonal signals. The processor is valid for a general zero mean, noise environment. A probability of error bound is derived for the processor. Several examples illustrate the processor.     

Comments on "The Psi-Angle Error Equation in Straplown Inertial Navigation Systems"

The negative sign on the psi-angle differential equation for strapdow inertial navigation error analysis discussed by Weinreb and Bar-ltzhack is not due to differences in error propagation between gimbaled and strapdown systems, but to the definition of strapdown gyro drift rate given by them. If a consistent definition of gyro drift rate for gimbaled and strapdown systems error analysis is used, the sign change does not occur.     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

Mutual and conditional mutual informations for optimizingdistributed Bayes detectors

This paper considers optimization of distributed detectors under the Bayes criterion. A distributed detector consists of multiple local detectors and a fusion center that combines the local decision results to obtain a final decision. Introduced first are distributional distance measures, the mutual information (MI) and the conditional mutual information (CMI), that are obtained by applying information theoretic concepts to detection problems. Error bound analyses show that these distance measures approximate the Bayesian probability of error better than the conventional ones regardless of the operational environments. Then, a new optimization technique is proposed for distributed Bayes detectors. The method uses the distributional distances instead of the original Bayes criterion to avoid the complexity barrier of the optimization problem. Numerical examples show that the proposed distance measures yield solutions far better than the existing ones     

Bounds on Probability of Error in Decision Feedback Equalizers

Evaluation of the probability of error in decision feedback equalizers is difficult due to the presence of a hard limiter in the feedback path. This paper derives the upper and lower bounds on the probability of a single error and multiple error patterns. The bounds are fairly tight. The bounds can also be used to select proper tap gains of the equalizer.     

线性分组码不可检错误概率新的下限

线性分组码的不可检错误概率是评价自动请求重传(ARQ)系统的重要参数。不可检错误概率的计算涉及码的重量分布,而大部分码的重量分布还不知道,因此,研究不可检错误概率的限显得非常重要。本文得到了GF()上(n,k)线性分组码不可检错误概率的两个新的下限,在一定程度上,改进了Wolf等人的结果。由于新的限与码的重量结构无关,因此可以方便地估计任何线性分组码的不可检错误概率。