The authors consider the robust detection of a known constant signal in additive, mutually independent and identically distributed noise which is nominally Laplace. Employing the classical saddlepoint methodology of Huber (1951), they specify the form of the robust detector and obtain closed form results which allow for the analysis of the performance of the robust detector. They show via examples that the robustness can entail a considerable cost in detector performance. In addition, they compare the performance of the robust detector to that of the Neyman-Pearson detector for examples where the noise is Laplace and also where the noise is least favorable for the given detector.>

A new approach toward robust parameter estimation is presented. As opposed to schemes based on classical saddlepoint techniques, the methods apply quite naturally to dependent and/or nonstationary data and also have the advantage of providing a quantitative measure of the degree of robustness offered by a particular estimator. It is shown why censoring observations of large magnitude does indeed impart robustness, and it also shown how nontraditional schemes have certain advantages, particularly when trading off performance and robustness. The application of the results is further demonstrated by including several illustrative examples.>

Memoryless discrete-time detection of a known time-varying signal in dependent non-Gaussian noise is considered. Optimal detectors are specified for cases where the detector nonlinearity is time-invariant and time-varying. A performance comparison is provided by way of examples.

The discrete-time detection of a constant signal in corrupting noise is considered. First the case where the noise is independent and identically distributed is considered, and the criterion of asymptotic relative efficiency is employed to investigate the effect on the detector's performance induced by altering the form of the detector nonlinearity from that of the locally optimal nonlinearity. The results show that the resultant degradation in performance can be bounded in terms of theL_{2}distance between the locally optimal nonlinearity and the nonlinearity of interest. We then extend our results to the case of weakly dependent\phi-mixing noise and see that, in particular, asymptotic relative efficiency can be viewed as a mapping between metric spaces that is continuous at the point of interest.

It is shown how a modified sign detector may be designed for the nonparametric detection of a constant signal in strong mixing noise. An upper bound on the asymptotic performance of the detector is established, and the form of a detector whose performance achieves this bound is specified. The optimal design of the detector under a finite sample criterion is also considered, and it is shown that there is a marked difference in the detector designs resulting from the two different criteria.

The role of weak dependence between observed samples is investigated in the detection of time varying signals in noise, with the goal of establishing quantitative conditions for when the dependency can be ignored. A result is presented that allows bounding the variation in false-alarm rate and detection probability induced by ignoring the dependency. This result is applied to the case of stationary Gaussian noise, and it is shown that the dependency can be ignored if the noise autocorrelation decreases sufficiently fast. In fact, a bound on the variation in false-alarm rate and detection probability is linked to the rate of descent of the noise autocorrelation through an expression that can be easily evaluated.

In this correspondence we consider the design of memoryless discrete-time detectors for a\phi-mixing signal in\phi-mixing noise, where a large degree of dependency may exist between the signal and the noise. The fidelity criterion is taken to be the asymptotic relative efficiency, and it is shown that with this fidelity criterion the nonlinearity in the optimal detector can be found as the solution of an integral equation in which knowledge of only the second-order statistics of the random processes involved is required.

We consider discrete time memoryless detection of random signals in dependent non-Gaussian noise, where both the signal and noise belong to a large class of strong mixing processes, and where a large amount of dependency may occur between the signal and noise. The problem of approximating the optimal nonlinearity under the criterion of asymptotic relative efficiency is considered, and sufficient conditions are presented to insure that the loss in performance of the approximation can be made arbitrarily small. Particular applications are then made to extensions of existing results where the approximating nonlinearity is a quantizer or a polynomial.

We consider some aspects of a data compression scheme called block truncation coding which are necessarily encountered when the scheme is implemented in practice. We derive an expression used to compute an essential quantity of the algorithm and analyze the effect of perturbing this quantity. Furthermore, we discuss how best to account for the perturbation in the overall scheme.

We show that the width of the center spectral lobe for a wide class of MSK-type signals is lower bounded by that for conventional PSK, and we also provide an expression that can be used to determine the width of the center spectral lobe for MSK.

A nonparametric scheme for detecting a constant signal embedded in m-dependent noise is cousidered, aud the performance of the detector in both the asymptotic case and the case of a finite number of samples is investigated. It is shown that the design of the detector with a finite amount of data can be radically different from the design based upon the asymptotic limit.

The design of detectors for known signals in non-Gaussian\phi-mixing noise is considered. The class of\phi-mixing processes considered is seen to be quite general and allows flexible modeling of a variety of dependent noises. Applying the criterion of asymptotic relative efficiency, the design of the optimal memoryless detector is specified and is seen to depend only on second-order statistical knowledge of the noise. It is then shown that in many cases this design reduces to approximating the noise process with anm-dependent process, finding the corresponding nonlinearity as a solution to a Fredholm integral equation of the second kind, and obtaining the optimal nonlinearity through a limiting process. In addition, conditions are given for the existence of a unique optimal nonlinearity. A bound on the performance of the optimal\phi-mixing detector relative to that of the detector designed under anm-dependent assumption is given. Extensions to the ease of detectors with memory are considered.