Known Signals In Additive Noise Research Articles

Optimum Quantization for Binary Hypothesis Testing

In this letter, optimum quantization of samples for use in ultra-wideband (UWB) ranging and communication systems is considered. The necessary conditions which the optimal quantization parameters, i.e. the quantization levels and thresholds, should satisfy are derived based on two optimality criteria of maximizing the detection probability and minimizing the error probability respectively. In particular, the design of optimal quantizers for weak signals is specially explored. To give a concrete example, applications to the case of detecting known signals in additive noise are investigated. Numerical results on four-level quantization demonstrate that the optimal quantizers perform better than suboptimal quantizers thanks to the extra information contained in the optimal parameters.

Adaptive detection of known signals in additive noise by means of kernel density estimators

We consider the problem of detecting known signals contaminated by additive noise with a completely unknown probability density function f. To this end, we propose a new adaptive detection rule. It is defined by plugging a kernel density estimator f/spl circ/ of f into the maximum a posteriori (MAP) detector. The estimate f/spl circ/ can either be computed off-line from a training sequence or on-line simultaneously with the detection. For the off-line detector, we prove that the (asymptotic) error probability for weak signals converges to the minimal error probability of the MAP detector as the number of training data tends to infinity, and we also establish rates of convergence and the optimal choice of bandwidth order for a certain class of noise densities. In a Monte Carlo study, the off-line plug-in MAP detectors are compared with the L/sup 1/- and L/sup 2/-detectors for various noise distributions. When the training sequence is long enough, the plug-in detectors have excellent performance for a wide range of distributions, whereas the L/sup 2/-detector breaks down for heavy-tailed distributions and the L/sup 1/-detector for distributions with little mass around the origin.

Importance sampling for detection of scale problems

The application of importance sampling (E)to the problem of detecting random signals is considered. It is well known that conventional importance sampling (CIS) which uses a scaled IS density suffers from a dimensionality effect when it is used to simulate systems that detect a known signal in additive noise. Our fundamental result shows that CIS is guaranteed to give an IS gain when used to simulate the detection-of-scale problem. Further, a numerical example for the generalized Gaussian family is provided where the IS gain from CIS actually increases with the dimensionality of the problem.

Approximate analysis of the convergence of relative efficiency to ARE for known signal detection

The limitations of the asymptotic relative efficiency (ARE) in predicting finite sample size detector performance have been noted in several previous studies. It has been observed that the finite-sample-size relative efficiency (RE) may converge very slowly to its asymptotic limit. In addition, in some cases the RE approaches the ARE from below, while in other cases the RE either starts above or overshoots the ARE and approaches it from above. Results indicate that both of these effects can be predicted for a useful class of detectors for known signals in additive noise. The prediction formula is developed for the generalized correlation detector structure. The result is then used to analyze some specific detectors. Among these are the sign detector, the dead-zone detector, the soft-limiter and the noise blanker. Calculations and simulations giving the relative efficiency as a function of sample size have been used to verify predictions. >

A comparison of parametric and nonparametric detector performance levels in underwater noise

The aim of the work is to determine and clarify the effects of some typical problems that arise when working with a real‐noise source. To this end, stationarity, time correlation between data samples, and parametric and nonparametric detection for a large segment of Arctic under‐ice noise are examined. In particular, the effect that correlation between samples has on the ability to detect a known signal in additive noise using several different parametric detectors is analyzed. Since most underwater environments are both nonstationary and non‐Gaussian, nonparametric detectors are of interest also. Thus a comparison of the performance levels of several different nonparametric detectors is performed for four common underwater environments.

Robust detection of known signals

The problem of detection of known signals in additive noise is solved under the assumption that the unknown noise density is a member of some known family of symmetric densities. A general approach to the design of receivers that are asymptotically most robust is established. As an example, a detector is derived by applying the procedure to the special case obtained when the noise density family is defined by F=\left\{f \left| \int^{a}_{-a} f(x) dx = p, f \mbox{symmetric} \right}. Simulation results showing the detector's performance for small sample sizes are provided.