Pinyuen Chen

Wireless tomography, Part I: A novel approach to remote sensing

Wireless tomography, a novel approach to remote sensing, is proposed in Part I of this series. The methodology, literature review, related work, and system engineering are presented. Concrete algorithms and hardware platforms are implemented to demonstrate this concept. Self-cohering tomography is studied in depth. More research will be reported, following this initiative.

A selection procedure for estimating the number of signal components

This paper proposes a selection procedure to estimate the multiplicity of the smallest eigenvalue of the covariance matrix. The unknown number of signals present in a radar data can be formulated as the difference between the total number of components in the observed multivariate data vector and the multiplicity of the smallest eigenvalue. In the observed multivariate data, the smallest eigenvalues of the sample covariance matrix may in fact be grouped about some nominal value, as opposed to being identically equal. We propose a selection procedure to estimate the multiplicity of the common smallest eigenvalue, which is significantly smaller than the other eigenvalues. We derive the probability of a correct selection, P(CS), and the least favorable configuration (LFC) for our procedures. Under the LFC, the P(CS) attains its minimum over the preference zone of all eigenvalues. Therefore, a minimum sample size can be determined from the P(CS) under the LFC, P(CS|LFC), in order to implement our new procedure with a guaranteed probability requirement. Numerical examples are presented in order to illustrate our proposed procedure.

On Selecting Among Treatments with Binomial Outcomes

ABSTRACT Most of the procedures for selecting one of the best among several experimental treatments under the binomial setting are based on applying the normal theory to the discrete data. Consequently, they may not be safely applied when dealing with small sample sizes. This article considers exact derivations and the applications of the LFCs for certain binomial procedures.

Development of a lower confidence limit for the number of signals

We propose a multistep procedure for constructing a lower confidence limit for computing the number of signals present in a vector measurement. We derive the probability of correct estimation P(CE) and the least favorable configuration (LFC) for our procedure. Under the LFC, P(CE) attains its minimum over the parameter space of all eigenvalues. Therefore, to implement our technique, procedure parameters are determined for the LFC for each sample size n so that the probability requirement is reached.

Subset selection for the least probable multinomial cell

SummaryAn inverse sampling procedureR is proposed for selecting a randomsize subset which contains the least probable cell (i.e., the cell with the smallest cell probabilities) from a multinomial distribution withk cells. Type 2-Dirichlet integrals are used (i) to express the probability of a correct selection in terms of integrals with parameters only in the limits of integration, (ii) to prove that the least favorable configuration underR is the so-called slippage configuration withk equal cell probabilities, and (iii) to express exactly the expectation of the total number of observations required and the expectation of the subset size under the procedureR.

A procedure for detecting the number of signal components in a radar measurement

This paper uses statistical selection theory to detect the multiplicity of the smallest eigenvalue of the covariance matrix, computed using measured multichannel multipulse radar data. We propose a selection procedure to estimate the multiplicity and value of the smallest eigenvalue(s). We derive the probability of a correct selection, P(CS), and the least favorable configuration (LFC) for our procedures. Under the LFC, the P(CS) attains its minimum over the vector space of all eigenstructures. Therefore a minimum sample size can be determined from the probability of CS under the LFC, P(CS/LFC), in order to implement our new procedure with a guaranteed probability requirement. The techniques described can be applied to the analysis of measured data collected from any multichannel radar. As such, a new solution to the adaptive beamforming problem arises out of the application of ranking and selection theory to the radar problem. First, the number of interfering signals present in a data vector is estimated using our new procedure. Then, optimal rank reduction can be achieved given this knowledge. And finally, adaptive processing for interference rejection and target detection can be performed using any of the standard techniques. The techniques discussed may be generalized.

Truncated selection procedures for the most probable event and the least probable event

This paper proposes two sequential procedures for selecting respectively the multinomial cell with the largest cell probability and the multinomial cell with the smallest cell probability. The stopping rule for both procedures uses truncation of the procedure studied by Ramey and Alam (1979, Biometrika, 66, 171–173). A property of the least favorable configuration of the proposed procedures is proved, which partially solves a conjecture given in Ramey and Alam (1979). The proposed procedures are compared with other procedures which have been considered in the literature and are found to be better in certain respects.

An interval estimation for the number of signals

We propose a multi-step procedure for constructing a confidence interval for the number of signals present. The proposed procedure uses the ratios of a sample eigenvalue and the sum of different sample eigenvalues sequentially to determine the upper and lower limits for the confidence interval. A preference zone in the parameter space of the population eigenvalues is defined to separate the signals and the noise. We derive the probability of a correct estimation, P(CE), and the least favorable configuration (LFC) asymptotically under the preference zone. Some important procedure properties are shown. Under the asymptotic LFC, the P(CE) attains its minimum over the preference zone in the parameter space of all eigenvalues. Therefore a minimum sample size can be determined in order to implement our procedure with a guaranteed probability requirement.

AN INTEGRATED FORMULATION FOR SELECTING THE MOST PROBABLE MULTINOMIAL CELL

We refer to the two classical approaches to multinomial selection as the indifference zone approach and the subset selection approach. This paper integrates these two approaches by separating the parameter space into two disjoint subspaces: the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best (most probable) cell for a correct selection (CS1) but in the IZ we define any selected subset to be correct (CS2) if it contains the best cell. We then propose a single stage procedure R to achieve the selection goals CS1 and CS2 simultaneously with certain probability requirements. It is shown that both the probability of a correct selection under IZ, P(CS2|PZ), and the probability of a correct selection under IZ, P(CS2|IZ), satisfy some monotonicity properties and the least favorable configuration in PZ and the worst configuration in IZ can be found by these properties.

A Note on a Curtailed Sequential Procedure for Subset Selection of Multinomial Cells

SYNOPTIC ABSTRACTThis paper deals with a curtailed sequential procedure for selecting a random size subset that contains the multinomial cell which has the largest cell probability. The proposed procedure R always selects the same subset as does the corresponding fixed-sample-size procedure, and thus achieves the same probability of a correct selection. However procedure R is sequential and accomplishes this with a smaller expected number of vector-observations than required by the fixed-sample-size procedure. Exact formulas for the savings are given as well as numerical calculations based on these formulas.