Mati Wax

Detection of signals by information theoretic criteria

A new approach is presented to the problem of detecting the number of signals in a multichannel time-series, based on the application of the information theoretic criteria for model selection introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). Unlike the conventional hypothesis testing based approach, the new approach does not requite any subjective threshold settings; the number of signals is obtained merely by minimizing the AIC or the MDL criteria. Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.

Maximum likelihood localization of multiple sources by alternating projection

An algorithm, referred to as APM, for computing the maximum-likelihood estimator of the locations of simple sources in passive sensor arrays is presented. The algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot. The algorithm is iterative; the maximum of the likelihood function is computed by successive approximations. The convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios. The key to this global convergence is the initialization scheme. >

Spatio-temporal spectral analysis by eigenstructure methods

This paper presents new algorithms for estimating the spatio-temporal spectrum of the signals received by a passive array. The algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals. They allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems. Simulation results that illustrate the performance of the new algorithms are presented.

Detection of the number of coherent signals by the MDL principle

An approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on J. Rissanens (1983) minimum description length (MDL) principle. The approach is applicable to any type of sources, including the case of sources which are fully correlated, referred to as the coherent signals case. Two slightly different detection criteria are derived, both requiring the estimation of the locations of the sources. The first is tailored to the detection problem per se, whereas the second is tailored to the combined detection/estimation problem. Consistency of the two criteria is proved and their performance is demonstrated by computer simulations. >

On unique localization of multiple sources by passive sensor arrays

Necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays. The conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints. The conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources. Two different conditions are presented. The first guarantees uniqueness for every batch of sampled data. The second, which is weaker, guarantees uniqueness for almost every batch of sampled data, with the exception of a set of batches of measure zero. It is shown that a condition that is slightly weaker than the second one is also necessary. >

Optimum localization of multiple sources by passive arrays

The maximum likelihood (ML) estimator of the location of multiple sources and the corresponding Cramer-Rao lower bound on the error covariance matrix are derived. The derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case. It is shown that the ML processor consists of a bank of beam-formers, each focused to a different source, followed by a variable matrix-filter that is controlled by the assumed location of the sources. In the special case of uncorrelated sources and very low signal-to-noise ratio this processor reduces to an aggregate of ML processors for a single source with each processor matched to a different source. Iterative algorithms for the actual computation of the ML estimator are also presented.

Joint estimation of time delays and directions of arrival of multiple reflections of a known signal

We present an efficient algorithm for estimating the time delays and the directions-of-arrival (DOAs) of multiple reflections of a known signal. The algorithm is based on an iterative scheme that transforms the multidimensional maximum likelihood criterion into two sets of simple one-dimensional (1-D) maximization problems. Simulation results illustrating the performance of the algorithm in comparison with the Cramer-Rao bound are included.

Detection and localization of multiple sources via the stochastic signals model

A method for the detection of coherent and noncoherent signals based on the application of J. Rissanens (1978) minimum-description-length principle for model selection to the stochastic signals model is presented. The detection and localization are done simultaneously with the location estimator coinciding with the maximum-likelihood estimator derived by J.F. Bohme (1986). The proposed method outperforms the method of M. Wax and I. Ziskind (1989), especially in the threshold region. Simulation results demonstrating the improved performance are included. >

Direction finding of coherent signals via spatial smoothing for uniform circular arrays

We present a preprocessing technique that in conjunction with spatial smoothing circumvents the difficulty of direction-of-arrival estimation of coherent signals in the case of uniform circular arrays. Special consideration is given to problems arising in practice, such as mutual coupling and array geometry imperfections. Simulation results illustrating the performance of this scheme in conjunction with the MUSIC method are included. >

Decentralized processing in sensor arrays

We present a new scheme for decentralized processing in passive sensor arrays based on communicating the sample-covariance matrices of the subarrays. The new scheme offers improved accuracy over the conventional triangulation scheme with only a modest increase in the communication load.