Unmanned underwater vehicles (UUVs) are increasingly being used in a diverse range of applications. In one particular application, we analyze UUV operations for location, detection and classification of mines. The mission objective is to search the area of interest, using underwater imaging sensors such as side scan sonars, until either the first mine is located, or it is verified that none can be found. Communication constraints require that the vehicle be connected with physically for downloads. In such as scenario, the search area can be considered as a line, and prior probabilities of finding a mine on the line can be related to external considerations such as the bottom characteristics, etc. The optimization problem is the determination of a sequence of points on the line where the UUV should be configured to return for a data download, so as to minimize the expected mission time. Operational models are defined and analytical expressions and numerical results describe the optimal strategies for searching with several distributions and return point specifications

A common model for sonar clutter is of the transmitted signal convolved with a colored Gaussian process relating to the sea-bottom profile. This environment becomes strongly non-Gaussian if there are multiple realizations - the univariate statistics remain Gaussian, but the joint probability density function (PDF) is not. It turns out that the gains versus a Gaussian-assumption can be substantial.

A common model for sonar clutter is that of the transmitted signal convolved with a colored Gaussian process relating to the sea-bottom profile. Rather surprisingly, this noise becomes strongly non-Gaussian if there are multiple realizations and if a realistic random phase is introduced - the univariate statistics remain Gaussian, but the joint probability density function is not. In this letter, we explore this behavior and we develop optimal detection statistics for a "two-look" situation. It turns out that the gains over a naive assumption of Gaussianity can be substantial.

Importance sampling (IS) is developed as a variance reduction technique for Monte Carlo simulation of data communications over random phase additive white Gaussian noise channels. The binary problem (with known performance) is examined initially to determine parameter values and estimate the performance gain of IS. These results can then be applied to intractable m-ary signaling problems through composite IS. An example compares the performance of linear, square-law, and optimum receivers for binary block coded data.

The problem of decoding binary linear block codes has received much attention; the two extremes are optimal, high-complexity soft-decision (or maximum-likelihood) decoding and lower performance, much lower complexity hard-decision (or algebraic) decoding. This article considers a class of decoders which first implements hard-decision decoding; second, tests to see if that is enough, that its result matches the result of soft-decision decoding; and third, continues to search if a match is not found. The advantage of such a testing procedure is that if the hard-decision decoding result is found to be enough (called a success for the test), then the computational effort expended by the decoder is low. The performance, as measured by the probability of a success, of a variety of simple tests of the hard-decision codeword are analyzed.

For the problem of weak signal detection, the locally optimum test statistic for a known signal in independent and identically distributed (i.i.d.) noise of probability density function f(/spl middot/) is given. We show that the logistic distribution is the only example for which the locally-optimal nonlinearity has a uniform distribution.

A one-pass vector quantizer design algorithm is presented. The algorithm sequentially selects a subset of the training vectors (in a high density area of the training data space) and computes a VQ code vector. Next, a sphere is constructed about the code vector whose radius is determined such that the encoding error for points within the sphere is acceptable. Finally, the data within the sphere is then pruned (deleted) from the training data set. This procedure continues on the remainder of the training set until the desired number of code vectors are located. This one-pass VQ design algorithm is compared with several benchmark results for uncorrelated Gaussian, correlated Gaussian, and Laplace sources; its performance is seen to be as good or better than the benchmark results. Further, the one-pass algorithm needs only slightly more computation than a single iteration of the LBG algorithm.

The performance of specific signal constellations in digital communications problems is often described through use of the union bound, an upper bound which is asymptotically tight with respect to the signal-to-noise ratio. It is not unnatural to ask how tight this result is for small to medium values of signal-to-noise ratio; one way to answer this question is to develop an asymptotically tight lower bound. Such is the goal of the present paper.>

Variable-length codes (e.g. Huffman codes) are commonly employed to minimize the average codeword length for noiseless encoding of discrete sources. Upon transmission over noisy channels, conflicting views note that such codes "tend to be self-synchronizing" and suffer from the "catastrophic effect of the error's propagation". Maxted and Robinson (1985) used a state model to describe the error recovery of the decoder. The present paper extends their results in several ways.

It is common signal detection practice to base tests on quantized data and frequently, as in decentralized detection, this quantization is extreme: to a single bit. As to the accompanying degradation in performance, certain cases (such as that of an additive signal model and an efficacy measure) are well-understood. However, there has been little treatment of more general cases. In this correspondence we explore the possible performance loss from two perspectives. We examine the Chernoff exponent and discover a nontrivial lower bound on the relative efficiency of an optimized one-bit quantized detector as compared to unquantized. We then examine the case of finite sample size and discover a family of nontrivial bounds. These are upper bounds on the probability of detection for an unquantized system given a specified quantized performance, given that both systems operate at the same false-alarm rate.

A low-complexity, high-performance vector quantization technique for medium-to-high-bit-rate encoding based on multistage (residual) VQ is introduced. The design, a variable-rate version of multistage VQ, is the vector extension of the piecewise uniform scalar quantizers of P.F. Swaszek and J.B. Thomas (1984), and is related to the piecewise uniform VQs of F. Kuhlmann and J.A. Buckview (1988). Examples for the independent Gaussian and Laplacian sources are included.>

The low complexity, nearly optimal vector quantizer (VQ) is a generalization of T. R. Fischer's (1986) pyramid VQ and is similar in structure to the unrestricted polar quantizers previously presented for the independent Gaussian source. An analysis of performance is presented with results for both the product code pyramid VQ and the unrestricted version. This analysis, although asymptotic in nature, helps to demonstrate the performance advantages of the VQ. Implementation issues of the VQ are discussed. Nonasymptotic results are considered. In particular, the author presents an approximate design algorithm for finite bit rate and demonstrates the usefulness of this VQ through several example designs with Monte Carlo simulations of performance. For the restricted form (the pyramid VQ), the author provides further implementational information and low dimension analytical results.>

Unrestricted polar quantizers (UPQ's) were previously introduced to overcome the weak mean-squared error performance of polar coordinate quantizers for the independent bivariate Gaussian source when the number of levels was small (< 3bits /dimension). An asymptotic ntean-squared error analysis of the UPQ's with a general circularly symmetric source is presented. The performance of the UPQ's is shown to be asymptotically within0.17dB of that of the optimum bivariate quantizer. The results are extended to dimensions greater than two. Examples for the independent Gaussian source are included.

The detection of a constant signal in additive noise is considered for independent and correlated impulsive noise environments. Suboptimum detector structures which estimate the occurrences of impulses and eliminate those data points are shown, through example, to yield performance close to that of systems which are given the indices of the data contaminated by the impulses.

For signal quantization with the minimum mean square error criterion, optimum spherical coordinate quantizers have been shown to outperform optimum rectangular coordinate qnantizers for many spherically symmetric sources. In this paper, spherical coordinate quantizers are designed and analyzed under the added constraint that each scalar quantizer is a uniform (equal step-size) quantizer. It is shown that for small block length, uniform spherical coordinate quantizers outperform the uniform rectangular coordinate quantizer as well as the uniform qnantizer consisting of a tesselation of the minimum inertia, space filling polytope.

An upper bound to the asymptotic mean-square error performance of optimized rotated polar quantizers is presented for a circularly symmetric random input. This form of quantizer is of interest because it has a scalar implementation and has been shown, for a small number of levels with a Gaussian source, to have much better performance than either the rectangular or polar schemes previously documented.

The design of signal quantizers when the statistical description of the source is a histogram on a finite domain is considered. Minimum mean and minimax error criteria are discussed, both leading to the design of piecewise linear compressor functions. The problem of allocating the histogram intervals in the symmetric source density case is addressed through the use of Chebyshev probability inequalities. Finally, an adaptive implementation of the proposed system is described.

The detection of a vanishingly small, known signal in multi-variate noise is considered. Efficacy is used as a criterion of detector performance, and the locally optimal detector (LOD) for multivariate noise is derived. It is shown that this is a generalization of the well-known LOD for independent, identically distributed (i.i.d.) noise. Several characterizations of multivariate noise are used as examples; these include specific examples and some general methods of density generation. In particular, the class of multivariate densities generated by a zero-memory nonlinear transformation of a correlated Gaussian source is discussed in some detail. The detector structure is derived and practical aspects of obtaining detector subsystems are considered. Through the use of Monte Carlo simulations, the performance of this system if compared to that of the matched filter and of the i.i.d. LOD. Finally, the class of multivariate densities generated by a linear transformation of an i.i.d, noise source is described, and its LOD is shown to be a form frequently suggested to deal with multivariate, non-Gaussian noise: a linear filter followed by a memoryless nonlinearity and a correlator.

Several investigators have considered polar coordinates quantization of a circularly symmetric source; in particular, the independent bivariate Gaussian source. Their schemes quantize the polar coordinates independently in an attempt to reduce the mean-square error below that of an analogous rectangular coordinates quantizer yet retain an implementation simpler than that of the optimal bivariate quantizer. The design of a spherical coordinates quantizer inkdimensions withk>2(k=2matches published results) is considered. Examples are presented along with comparisons to the rectangular (one-dimensional) and optimal schemes.