Asymptotic multiuser efficiencies for decision-directed multiuserdetectors

The asymptotic multiuser efficiencies (AMEs) are derived for various classes of decision-directed multiuser detectors, including multistage detectors, and decision-feedback detectors. Novel classes of soft-decision multistage detectors are proposed and analyzed. Each class is specified in part by a soft-decision nonlinearity, such as a symmetric quantizer or a linear clipper. Closed-form expressions for two-user AMEs are derived for soft-decision two-stage detectors and can be used as a design criterion to optimize the soft-decision nonlinearities. For a special case of two synchronous users, the soft-decision two-stage detector using an optimized linear clipper with either conventional or decorrelated tentative decisions is shown to achieve optimum AME. Upper and lower bounds on the AME are obtained for decision-feedback detectors using either conventional or decorrelated tentative decisions. It is demonstrated that decision-directed multiuser detectors with conventional tentative decisions have low near-far resistance compared to those with decorrelated tentative decisions     

Small-sample efficiencies of rank tests

Nonparametric tests have been extensively investigated asymptotically for small signals and large numbers of samples. More realistic, though, in many engineering applications is the small-sample large-signal case, which has had little study because of its complexity. The problem of testing the hypothesis of probability density symmetry about a positive versus a negative value is investigated. The efficiency of the optimum rank and the efficiency of the Wilcoxon rank-sum test are found with respect to the optimum parametric test for normally distributed independent samples with large signal-to-noise ratios. Specifically, it is found that for the same signal-to-noise ratio and probability of error the optimum rank test requires at most 4/3 of the number of samples (or equivalently, 4/3 higher signal-to-noise ratio for the same number of samples) of the optimum parametric test; the Wilcoxon nonparametric test requires at most a factor of2/sqrt{2}more. Thus, the efficiency of the Wilcoxon nonparametric test is very close to that of the optimum rank test for normal alternatives, although neither are as close to the efficiency of the optimum parametric test as in the large-sample small-signal problem (where, as is well known, the asymptotic relative efficiencies arepi/3and 1).     

Truncated sequential hypothesis tests

Through a careful examination of the equations by which Wald determines the values of the boundaries for tests of sequential hypotheses, we are able to obtain interesting relationships for the conditional probability distributions of the stage at which the test terminates. These enable us to study sequential tests in which the boundaries are functions of the sample number. We are particularly concerned with tests with convergent boundaries, and investigate a set of boundaries which approach those of a truncated Wald test. Approximate expressions for the expected sample number and probabilities of error are obtained for the tests considered. The obtained approximations apply best for gently tapering slopes. Extensions of our method can be applied to evaluate various ad hoc schemes for truncating tests and to the theory of tests with a varying parameter.     

Performance analysis of sequential tests between Poisson processes

The problem of performance computation for sequential tests between Poisson processes is considered. The average sample numbers and error probabilities of the sequential probability ratio test (SPRT) between two homogeneous Poisson processes are known to solve certain delay-differential equations (DDEs). Exact, numerically stable solutions to these DDEs are developed here, and their asymptotic properties are explored. These solutions are seen to be superior to earlier solutions of Dvoretsky, Kiefer, and Wolfowitz (1953), which suffer from severe numerical instability in some ranges of parameters of interest in applications. The application of these results is illustrated in the problem of performance approximation for the cumulative sum (CUSUM) quickest detection procedure     

A class of sequential tests and its applications

Two iterated algorithms for evaluating the performance of a class of sequential tests are proposed. The goal is equivalent to computing the distribution function of the first passage time for a random walk to cross a one-sided barrier. Limitations on both algorithms are studied, and associated methods for eliminating those limitations when possible are derived. These algorithms are applied to a pseudonoise code acquisition system and a range-sampled radar searching problem. Related computational problems are discussed, and numerical results are given     

Asymptotic optimality of likelihood ratio threshold tests indecentralized detection

Two distributed systems are considered for discriminating between two finite-alphabet bivariate memoryless sources and for detecting a known signal in stationary bivariate additive Gaussian noise. Each system comprises two sensors, M-ary local quantizers and a fusion center which makes decisions based on quantized source observations. The problem of asymptotically optimal quantization is considered in detail for the binary (M=2) case. It is shown that optimality is achieved by quantizing a locally computed likelihood ratio wherein one distribution is in general different from the appropriate source marginal. For the problem of detection in Gaussian noise, it is further demonstrated that the optimal distributed system attains the same asymptotic performance as the optimal centralized system for appropriate choice of M     

Distribution of a random walk with an application to a truncated nonparametric sequential test

Explicit expressions for the probability of reaching a given position at each stage of a random walk are derived for the case of absorbing boundaries. Utilizing these results, exact expressions for the power function and the average sample number function of a truncated nonparametric sequential test are obtained. Some numerical examples are also given.     

Multihypothesis sequential probability ratio tests .I. Asymptoticoptimality

The problem of sequential testing of multiple hypotheses is considered, and two candidate sequential test procedures are studied. Both tests are multihypothesis versions of the binary sequential probability ratio test (SPRT), and are referred to as MSPRTs. The first test is motivated by Bayesian optimality arguments, while the second corresponds to a generalized likelihood ratio test. It is shown that both MSPRTs are asymptotically optimal relative not only to the expected sample size but also to any positive moment of the stopping time distribution, when the error probabilities or, more generally, risks associated with incorrect decisions are small. The results are first derived for the discrete-time case of independent and identically distributed (i.i.d.) observations and simple hypotheses. They are then extended to general, possibly continuous-time, statistical models that may include correlated and nonhomogeneous observation processes. It also demonstrated that the results can be extended to hypothesis testing problems with nuisance parameters, where the composite hypotheses, due to nuisance parameters, can be reduced to simple ones by using the principle of invariance. These results provide a complete generalization of the results given by Veeravalli and Baum (see ibid., vol.41, p.1994-97, 1995), where it was shown that the quasi-Bayesian MSPRT is asymptotically efficient with respect to the expected sample size for i.i.d. observations     

Generation and evaluation of current and logic tests for switch-level sequential circuits

This article presents an approach to developing high quality tests for switch-level circuits using both current and logic test generation algorithms. Faults that are aborted or undetectable by logic tests may be detected by current tests, or vice versa. An efficient switch level test generation algorithm for generating current and logic tests is introduced. Clear definitions for analyzing the effectiveness of the joint test generation approach are derived. Experimental results are presented for demonstrating high coverage of stuck-at, stuck-on, and stuck-open faults for switch level circuits when both current and logic tests are used.This is expanded version of the work originally presented at the 1991 International Test Conference.     

Polymer efficiencies

Researchers at Cambridge University's Cavendish Laboratory have developed a technique for making photovoltaic polymer thin films with external quantum efficiencies 10 times greater than previously achieved.     

Asymptotic computation of certain sequential algorithms for source coding with a fidelity criterion (Corresp.)

Speeds of computation divergence as distortion tends to the rate-distortion limit are determined for three recent sequential source coding algorithms. The speeds follow from analysis and simulation; they remain unchanged for several sources and rates. The stack algorithm is most efficient in terms of nodes extended per encoder output digit.     

A lower bound for the detection/isolation delay in a class of sequential tests

We address the problem of minimax detecting and isolating abrupt changes in random signals. The criterion of optimality consists in minimizing the maximum mean detection/isolation delay for a given maximum probability of false isolation and mean time before a false alarm. It seems that such a criterion has many practical applications, especially for safety-critical applications, in monitoring dangerous industrial processes and also when the decision should be made in a hostile environment. The redundant strapdown inertial reference unit integrity monitoring problem is discussed. An asymptotic lower bound for the mean detection/isolation delay is given.     

Multihypothesis sequential probability ratio tests. II. Accurateasymptotic expansions for the expected sample size

For pt. I see ibid. vol.45, p.2448-61, 1999. We proved in pt.I that two specific constructions of multihypothesis sequential tests, which we refer to as multihypothesis sequential probability ratio tests (MSPRTs), are asymptotically optimal as the decision risks (or error probabilities) go to zero. The MSPRTs asymptotically minimize not only the expected sample size but also any positive moment of the stopping time distribution, under very general statistical models for the observations. In this paper, based on nonlinear renewal theory we find accurate asymptotic approximations (up to a vanishing term) for the expected sample size that take into account the “overshoot” over the boundaries of decision statistics. The approximations are derived for the scenario where the hypotheses are simple, the observations are independent and identically distributed (i.i.d.) according to one of the underlying distributions, and the decision risks go to zero. Simulation results for practical examples show that these approximations are fairly accurate not only for large but also for moderate sample sizes. The asymptotic results given here complete the analysis initiated by Baum and Veeravalli (1994), where first-order asymptotics were obtained for the expected sample size under a specific restriction on the Kullback-Leibler distances between the hypotheses     

Limiting efficiencies of burst-correcting array codes

The author evaluates the limiting efficiencies e(-S ) of burst-correcting array codes A(n₁,n₂, -s) for all negative readouts -s as n₂ tends to infinity and n₁ is properly chosen to maximize the efficiency. Specializing the result to the products of the first i primes donated by s_i (1⩽i<∞), which are optimal choices for readouts, gives the expression e(-s_i)=(2p_i+1 -2)/(2p_i+1-1) where p_i+1 is the next prime. Previously, it was known only that e(-2)⩾4/5 and e(-1)⩾2/3. This result reveals the existence of burst-correcting array codes with efficiencies arbitrarily close to 1 and with rates also arbitrarily close to 1     

Discretized Gabor-based beam algorithm for time-harmonic radiation from two-dimensional truncated planar aperture distributions .II. Asymptotics and numerical tests

For pt.I see ibid., vol.50, no.12, p.1751-59 (2002). In this second part of the two-part sequence dealing with Gabor-based Gaussian beam (GB) representations for the excitation of time-harmonic three-dimensional (3-D) vector electromagnetic fields excited by two-dimensional (2-D) arbitrarily polarized truncated planar aperture distributions (set in a discretized [configuration (space)]-[spectrum (wavenumber)] phase space), we employ high-frequency asymptotic approximations to reduce the formal solutions developed in part I to efficient algorithms for implementation. The resulting explicit expressions for the 3-D GB propagators are applied to the species of narrow-waisted GBs, which possess ray-like features without the failures of ray fields in ray-optical transition regions. The potential utility of such GBs in the synthesis of wave interactions with complex environments has been discussed previously. The narrow-waisted GB algorithms for the aperture and radiated near-to-far zone fields are calibrated for robustness, accuracy and efficiency by comparison with numerically generated reference solutions in a series of tests involving coordinate-separable rectangular aperture distributions with cosine amplitude tapers.     

A truncated best-path algorithm

A variant of the best-path (BP) algorithm that can be used for deducing a posteriori symbol probabilities for input sequences of unlimited length is proposed. Decoders using the proposed algorithm have fixed memory requirements and fixed decoding delays regardless of the length of the transmitted sequence. This is made possible by utilizing the Viterbi algorithm's ability to self-initialize itself and by segmenting the decoding process     

Radiative efficiencies of radio frequency sulfur discharges

The radiative efficiencies of RF sulfur discharges under various conditions of power loading, sulfur vapor pressure, and argon buffer pressure have been determined. The highest CW efficiency was 11 percent for a sulfur density of6.3 times 10^{16}cm^-3and 20 torr argon buffer. The results of pulsed operation show that the efficiency increases slightly to 13 percent for a sulfur density of8.8 times 10^{16}cm^-3.     

On the asymptotic efficiencies of robust detectors

Two methods are considered for comparing the asymptotic efficiencies of robust detectors in the problem of detecting coherent signals in additive noise. The first of these methods considers the relative detector sample sizes for a fixed value of the detector power, while the second method considers the relative detector sample sizes for a fixed value of the local detector power, as measured by the local values of the slopes or curvatures of the detector power functions. These measures of efficiency are variations of the asymptotic relative efficiencies (AREs) of Pitman and Blomqvist, respectively, adapted to the robust detection problem. These two approaches are used to compare the performance of robust nonlinear correlators to that of robust M -detectors in both one-sided and two-sided detection problems, under an ε-contaminated mixture model for uncertainty in the noise statistics. Both measures of ARE, fixed-power and fixed-local-power, indicate that the robust nonlinear correlator outperforms the robust M-detector for this type of model. However, the fixed-local-power ARE is shown to be more useful in measuring the degree to which the robust nonlinear correlator is more efficient