Many classical direction of arrival (DOA) estimation algorithms suffer from sensitivity to sensor coupling. By applying a group of auxiliary sensors in a uniform linear array (ULA), we prove the resiliency of the MUSIC direction finding algorithm against array sensor coupling. We show that the performance of MUSIC algorithm under antenna array with unknown coupling can be very close to the case with known coupling. We can also estimate the mutual coupling coefficients before refining the DOA estimates by utilizing an extended sensor array. Moreover, our analysis on the effect of mutual coupling in direction finding illustrates the existence of some blind angles which should be avoided when the array is designed. Our simulation results corroborate our analysis.

On the Resiliency of MUSIC Direction Finding Against Antenna Sensor Coupling

We present a 2-D direction of arrival (DOA) estimation algorithm in the presence of unknown mutual coupling for the uniform rectangular array (URA) based on the multiple signal classification (MUSIC) algorithm. By setting the sensors on the boundary of the URA as auxiliary sensors, it can accurately estimate the DOAs without any calibration sources or iterative operations. We prove that the effect of mutual coupling can be eliminated by the inherent mechanism of the proposed method. Twice search technique is used to reduce the computation of the 2-D spectrum search. Moreover, we provide a method to estimate the mutual coupling coefficients after getting the DOA estimates. Simulation results confirm the effectiveness of the proposed algorithm.

2-D DOA Estimation in the Presence of Mutual Coupling

We consider a well-defined joint detection and parameter estimation problem. By combining the Bayesian formulation of the estimation subproblem with suitable constraints on the detection subproblem, we develop optimum one- and two-step test for the joint detection/estimation setup. The proposed combined strategies have the very desirable characteristic to allow for the trade-off between detection power and estimation quality. Our theoretical developments are, then, applied to the problems of retrospective changepoint detection and multiple-input multiple-output (MIMO) radar. In the former case, we are interested in detecting a change in the statistics of a set of available data and provide an estimate for the time of change, while in the latter in detecting a target and estimating its location. Intense simulations in the MIMO radar example demonstrate that by using jointly optimum schemes, we can experience significant improvement in estimation quality, as compared to generalized the likelihood ratio test or the test that treats the two subproblems separately, with only small sacrifices in detection power.

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Joint Detection and Estimation: Optimum Tests and Applications

The problem of ambiguities inherent in the manifold of any linear array structure is investigated. Ambiguities, which can be classified into trivial and nontrivial, depending on the ease of their identification, arise when an array cannot distinguish between two different sets of directional sources. Initially, the new concept of an ambiguous generator set is introduced; it represents/generates an infinite number of ambiguous sets of directions. Then, by uniformly/nonuniformly partitioning the array manifold curve of a linear array, different ambiguous generator sets ran be calculated, and as a direct result, a sufficient condition for the presence of ambiguities is obtained. The theoretical aspects of the investigation are followed by the proposal of an innovative approach that calculates not only all such ambiguities existing in a linear array of arbitrary geometry but the rank of ambiguity in each case as well. The main results presented in the paper are supported by a number of representative examples.

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Modeling and estimation of ambiguities in linear arrays

The Statistical Signal and Array Processing Technical Committee (SSAP-TC) deals with signals that are random and processes an array of signals simultaneously. The field of SSAP represents both solid theory and practical applications. Starting with research in spectrum estimation and statistical modeling, study in this field is always full of elegant mathematical tools such as statistical analysis and matrix theory. The area of statistical signal processing expands into estimation and detection algorithms, time-frequency domain analysis, system identification, and channel modeling and equalization. The area of array signal processing also extends into multichannel filtering, source localization and separation, and so on. This article represents an endeavor by the members of the SSAT-TC to review all the significant developments in the field of SSAP. To provide readers with pointers for further study of the field, this article includes a very impressive bibliography-close to 500 references are cited. This is just one of the indications that the field of statistical signals has been an extremely active one in the signal processing community. The article also introduces the recent reorganization of three technical committees of the Signal Processing Society.

Highlights of statistical signal and array processing

This paper addresses the problem of finite sample simultaneous detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain. In general, a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance. We develop a multihypothesis testing framework for studying the tradeoffs between detection and parameter estimation (classification) for a finite discrete parameter set. Our multihypothesis testing problem is based on the worst case detection and worst case classification error probabilities of the class of joint detection and classification algorithms which are subject to a false alarm constraint. This framework leads to the evaluation of greatest lower bounds on the worst case decision error probabilities and a construction of decision rules which achieve these lower bounds. For illustration, we apply these methods to signal detection, order selection, and signal classification for a multicomponent signal in noise model. For two or fewer signals, an SNR of 3 dB and signal space dimension of N=10 numerical results are obtained which establish the existence of fundamental tradeoffs between three performance criteria: probability of signal detection, probability of correct order selection, and probability of correct classification. Furthermore, based on numerical performance comparisons between our optimal decision rule and other suboptimal penalty function methods, we observe that Rissanen's (1978) order selection penalty method is nearly min-max optimal in some nonasymptotic regimes. >

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Optimal simultaneous detection and estimation under a false alarm constraint

The performance of the MUSIC (Multiple Signal Classification) algorithm in determining the bearing of a single emitter from the signals of an array of sensors is investigated. The causes and cures of ambiguities in bearing estimation, due to array response duplications, are addressed first. The statistical properties of unambiguous bearing estimates are then considered. In particular, expressions for the first two moments of the error in these estimates are presented. These expressions, being more general than those that have appeared in the literature, are not limited to a line array of isotropic elements; hence they include the effects of antenna pattern and array geometry on estimation accuracy. The numerical examples verify the analytical moment expressions. >

Performance analysis of the MUSIC algorithm in direction finding systems

Min-max simultaneous signal detection and parameter estimation requires the solution to a nonlinear optimization problem. Under certain conditions, the solution can be obtained by equalizing the probabilities of correctly estimating the signal parameter over the parameter range. We present an iterative algorithm based on Newton's root finding method to solve the nonlinear min-max optimization problem through explicit use of the equalization criterion. The proposed iterative algorithm does not require prior proof of whether an equalizer rule exists: convergence of the algorithm implies existence. A theoretical study of algorithm convergence is followed by an amplitude estimation example which shows that decoupling detection from estimation entails a very significant loss in estimation performance even when optimal decoupled decision rules rules are implemented.

An iterative solution to the min-max simultaneous detection and estimation problem

A method for gauging the tradeoff between parameter estimation and order selection estimation performance for discrete parameters is developed The method is based on evaluation of lower bounds on worst-case probability of estimation error and worst-case probability of order selection error subject to a constraint on maximum false alarm probability Since each of the two bounds is derived by evaluating the performance of an optimal order estimator and an optimal parameter estimator, respectively, the bounds are achievable It is shown that it is generally impossible to achieve simultaneously the order selection and parameter estimation lower bounds: there is a necessary compromise between estimation and order selection The authors present numerical studies of these bounds for a common multiple signal model >

Tradeoffs between detection and estimation for multiple signals

For a general discrete parameter signal model and a false alarm constraint, the authors give a general theorem which specifies lower bounds on worst-case probability of miss, worst-case probability of incorrectly specifying the number of parameters (order selection), and worst-case probability of parameter estimation error. These bounds are achievable by constrained min-max decision rules: the constrained min-max detector, the constrained min-max order selector, and the constrained min-max parameter estimator, respectively. As in previous work, the authors use the theory to study fundamental tradeoffs between achievable estimation, order selection, and detection performance for a multiple component signal model. Numerical results indicate that for the example studied, parameter estimation optimality entails very little loss in detection performance, while detection optimality severely sacrifices parameter estimation performance. >

B. Baygun

Papers

Optimal simultaneous detection and estimation under a false alarm constraint

Performance analysis of the MUSIC algorithm in direction finding systems

An iterative solution to the min-max simultaneous detection and estimation problem

Tradeoffs between detection and estimation for multiple signals

Further results on tradeoffs between detection and estimation