K-distribution

About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.

Radar detection of signals with unknown parameters in K-distributed clutter

Abstract: The detection of signals with unknown parameters in correlated K-distributed noise, using the generalised Neyman-Pearson strategy is considered. The a priori uncertainty on the signal is removed by performing a maximum likelihood estimate of the unknown parameters. The resulting receivers can be regarded as a generalisation of the conventional detector, but for a zero-memory nonlinearity depending on the amplitude probability density function of the noise as well as on the number of integrated pulses. It is shown that the performance for uncorrelated observations is unaffected by the specific signal pattern, but depends only on the signal-to-noise ratio; moreover, the effect of the clutter correlation on the performance can be accounted for simply by a detection gain. A performance assessment, carried out by computer simulation, shows that the proposed receivers significantly outperform conventional ones as the noise amplitude probability density function markedly deviates from the Rayleigh law. It also shows that the generalised Neyman-Pearson strategy is a suitable means of circumventing the uncertainty on wanted target echos since the operating characteristics of the receivers for the case of signals with unknown parameters closely follow those of the receiver for a completely known signal.

On a selection and ranking procedure for gamma populations

Abstract: The problem of selecting a subset of k gamma populations which includes the “best” population, i.e. the one with the largest value of the scale parameter, is studied as a multiple decision problem. The shape parameters of the gamma distributions are assumed to be known and equal for all the k populations. Based on a common number of observations from each population, a procedure R is defined which selects a subset which is never empty, small in size and yet large enough to guarantee with preassigned probability that it includes the best population regardless of the true unknown values of the scale parameters θi. Expression for the probability of a correct selection using R are derived and it is shown that for the case of a common number of observations the infimum of this probability is identical with the probability integral of the ratio of the maximum of k-1 independent gamma chance variables to another independent gamma chance variable, all with the same value of the other parameter. Formulas are obtained for the expected number of populations retained in the selected subset and it is shown that this function attains its maximum when the parameters θi are equal. Some other properties of the procedure are proved. Tables of constants b which are necessary to carry out the procedure are appended. These constants are reciprocals of the upper percentage points of Fmax, the largest of several correlated F statistics. The distribution of this statistic is obtained.

A metric space of discrete probability distributions

Abstract: A functional defined by means of entropy is considered. It is shown that it is a distance in the set of discrete probability distributions.