We present a powerful solution to the problem of vector set classification, based on a novel goodness-of-fit metric, referred to as signal subspace matching (SSM). Unlike the existing solutions based on principal component analysis (PCA), this solution is eigendecomposition-free and dimension-selection-free, i.e., it does not require PCA nor the election of the subspace dimension, which is done implicitly. More importantly, it copes effectively with the challenging cases wherein the subspaces characterizing the classes are partially or fully overlapping. The SSM metric matches the subspaces characterizing the vector sets of the test and the classes by minimizing the distance between respective soft-projection matrices constructed from the vector sets. We prove the consistency of the solution for the high signal-to-noise-ratio limit, and also for the large-sample limit, conditioned on the noise being white. Experimental results, demonstrating the superiority of the SSM solution over the existing PCA-based solutions, especially in the challenging cases of overlapping subspaces, are included.

We present a novel and computationally simple solution to the problem of determining the number of exponentials in a given time-series, which is applicable to both white and colored noise. The solution is based on a novel and non-asymptotic goodness-of-fit metric, referred to as invariant-signal-subspace matching (ISSM). This metric is aimed at matching pairs of signal-subspaces, created by exploiting the shift-invariance property of the Hankel data-matrix. A pair of such subspaces, together with their corresponding projection matrices, is created for every hypothesized number of exponentials, and the number of exponentials is then determined as that for which the distance between the pair of projection matrices is minimized. We prove the consistency of this criterion for the high signal-to-noise-ratio limit and also prove it for the large-sample limit, conditioned on the noise being white. We also extend this criterion to include multiple pairs of invariant subspace, readily created from the Hankel data-matrix, thus enabling to improve its performance at a slight increase in its computational load. Simulation results, demonstrating the superior performance of the solution over the existing solutions, for both colored and white noise, are included.

We present a novel convex-optimization-based solution to blind linear multiuser detection in direct-sequence code division multiple access systems. The solution is based on a convex low-rank approximation of the linearly constrained constant modulus cost function, thus guaranteeing its global minimization. Further, it can be cast as a semidefinite program, implying that it can be solved using interior-point techniques with polynomial time complexity. The solution is parameter free and is shown to be superior to existing solutions in terms of output signal-to-interference-plus-noise ratio and bit error rate, especially for a small number of samples.

This paper presents an ASIC hardware architecture of a multi-antenna access point (AP), compliant with 802.11a/b/g standard and designed for outdoor metropolitan-area deployment. The AP has a six-antenna array and its PHY layer implements single-user maximum ratio combining (MRC) and transmit beamforming (BF), as well as downlink multi-user fourfold spatial division multiple-access (SDMA). The clients use standard WiFi 802.11a/b/g networks interface cards (NICs).

We present an algorithm for the calibration of sensor arrays in the presence of multipath. The algorithm is based on two sets of calibration data obtained from two angularly separated transmitting points. Simulation results demonstrating the performance of the algorithm are included.

We consider the problem of localizing multiple narrow-band stationary signals using an arbitrary time-varying array such as an array mounted on a moving platform. We assume a Gaussian stochastic model for the received signals and employ the generalized least squares (GLS) estimator to get an asymptotically-efficient estimation of the model parameters. In case the signals are a-priori known to be uncorrelated, this estimator allows one to exploit this prior knowledge to its benefit. For the important case of translational motion of a rigid array, a computationally-efficient spatial-smoothing method is presented. Simulation results confirming the theoretical results are included.

We present an algorithm for direction of arrival tracking that allows operation below the ambiguity threshold of the direction finding system. Using multiple target tracking techniques, the algorithm turns the most likely directions of arrival of each measurement into multiple potential tracks and then selects the true track as that with the maximum cumulative likelihood. The improvement offered by the algorithm, namely the extension of the ambiguity-free domain, is demonstrated by simulated experiments.

We present a new two-step approach to blind beamforming based on the least squares criterion. The first step consists of "whitening" the array received vector, i.e., transforming its response matrix to some unknown unitary matrix. The second step consists of estimating the unitary matrix from the fourth order cumulants by a least squares criterion. In contrast to the corresponding "joint diagonalization" step of the JADE algorithm, our second step exploits all the structural information in the problem and consequently yields better performance. Simulation results demonstrating the improved performance over the JADE algorithm are included.

We present a new least-squares-based approach for the joint diagonalization problem arising in blind beamforming. The resulting estimation criterion turns out to coincide with that proposed by Cardoso and Souloumaic (see IEE Proc. F, Radar Signal Process., vol.140, no.6, p.362-70, Dec. 1993) on intuitive grounds, thus establishing the optimality of their criterion in the least-squares (LS) sense.

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

We present an analysis of the signal-to-interfere-plus-noise ratio (SINR) at the output of the minimum variance beamformer. The analysis yields an explicit expression for the SINR in terms of the different parameters affecting the performance, including the signal-to-noise ratio (SNR), the interference-to-noise ratio (INR), the signal-to-interference ratio (SIR), the angular separation between the desired signal and the interference, the array size and shape, the correlation between the desired signal and the interference, and the finite sample size.

A new technique for localisation of multiple signals is presented. Unlike existing techniques which require that the whole array be sampled simultaneously and consequently require many receivers, our technique allows us to sample arbitrary subarrays sequentially and consequently significantly reduces the required number of receivers. The estimation method we use in conjunction with this sampling scheme is based on approximating the corresponding maximum likelihood estimator by a computationally simpler generalized least squares (GLS) estimator that is proved to be both consistent and efficient.

A new method for localizing multiple signals in spatially-colored background noise using an arbitrary passive sensor array is presented. The method enables also to exploit prior knowledge that the signals are uncorrelated, in case such information is available, so as to improve the performance and allow localization even if the number of signals exceeds the number of sensors. The estimation is based on the generalized least squares criterion, and is both consistent and efficient. Simulation results confirming the theoretical results are included.

A method of determining the constraint length and generating polynomials of rate 1/L convolutional coded data using only the encoded data is presented.>

Conditions for unique localization of radiating sources by passive sensor arrays are presented. Unlike previous analyses, the case wherein the signals are constrained to certain loci in the complex plane is addressed. The conditions specify the maximum number of sources that can be uniquely localized by a general array satisfying some mild geometrical constraints. This number exceeds substantially the corresponding number for the unconstrained-signals case.>

A technique for detection and localization of multiple sources in the presence of noise with unknown and arbitrary covariance is presented. The technique is applicable to coherent and noncoherent signals and to arbitrary array geometry. It is based on Rissanen's (1983) MDL minimum description length principle for model selection. Its computational load is comparable to that of analogous techniques for white noise. Simulation results demonstrating the performance of this technique are included.>

A novel method for detection of coherent and noncoherent signals, based on the application of Rissanen's minimum description length principle for model selection to the stochastic signals model, is presented. In this method, the detection and localization are done simultaneously, with the location estimator coinciding with the maximum likelihood estimator derived by Bohme. The proposed method outperforms the recently proposed method of Wax and Ziskind (1989), especially in the threshold region. Another important factor in the improved performance is the maximum likelihood estimator for the stochastic signals model which, unlike the maximum likelihood estimator of the deterministic signals used in the solution of Wax and Ziskind, is efficient. Simulation results demonstrating the improved performance are included.>

An approach to the problem of constructing tree structured classifiers that is based on Rissanen's (1983) minimum description length (MDL) principle is presented. Simple and efficient rules for sequential growing and pruning of the tree are derived using this approach. The two rules are derived from a single MDL-based criterion. These splitting and pruning rules are intuitively pleasing and computationally simple. The computational load of the pruning rule is substantially smaller than the alternative pruning schemes of A. Mabbet et al. (1980) and L. Breiman et al. (1984). The extension of these splitting and pruning criteria to the case of multiple classes is straightforward. Experimental results illustrating the performance of this technique in automatic character recognition are provided.>

The authors present a novel approach to the problem of detecting the number of sources impinging on a passive sensor array. The approach is applicable also to the case of fully correlated sources appearing, for example, in specular multipath propagation. Two slightly different detection criteria, both based on the minimum description length (MDL) principle and both requiring the estimation of the locations of the sources, are presented. The first is tailored to the detection problem per se, while the other is tailored to the combined detection-estimation problem. The authors prove the consistency of the two criteria and demonstrate their performance by simulation results.>

We present a new criterion for selecting the order of AR models which, unlike the existing criteria, is amenable to on-line or adaptive operation. It is based on the Predictive Least-Squares principle and is implemented in a computationally efficient way by predictive lattice filters. We prove the consistency of the criterion and demonstrate its performance by computer simulations.

We present a novel and efficient algorithm for computing the maximum likelihood estimator of the locations of multiple sources in passive sensor arrays. The algorithm is equally well applicable to the case of fully correlated signals appearing, for example, in multipath propagation problems. Simulation results that demonstrate the performance of the algorithm and a detailed analysis of the uniqueness of the solution are included.

New measures are proposed for mutual and causal dependence between two time series, based on information theoretical ideas. The measure of mutual dependence is shown to be the sum of the measure of unidirectional causal dependence from the first time series to the second, the measure of unidirectional causal dependence from the second to the first, and the measure of instantaneous causal dependence. The measures are applicable to any kind of time series: continuous, discrete, or categorical.

We present new eigenstructure based methods for spatial-temporal processing in passive sensor arrays. Unlike the existing methods of Schmidt and Bienvenu and Kopp, the new estimators are not based only on the underlying orthogonality relation between the "noise" subspace and the "signal" subspace, but also on statistical considerations stemming from the structure of the maximum likelihood estimator. As such, these estimators make better use of the available data and therefore have superior performance, especially in the threshold region, where efficient utilization of the data is most rewarding.

This paper considers some asymptotic statistical properties of covarianee eigenstructure spectral analysis techniques. It is shown that when the signal model is of the appropriate form, and the observations are Gaussian, the signal parameter estimates, obtained by locating the nulls in the eigen-spectrum, are asymptotically zero mean normal random variables. Based on this observation, the paper then considers the formation of confidence regions for the signal parameters. The paper presents the general case of a multi-dimensional eigenstructure algorithm, which estimates one or more parameters of each signal in the observed data.

The determination of the number of signals in a wide class of problems, including array processing, harmonic retrieval and pole retrieval, is addressed. A new approach, based on the application of the information theoretic criteria for model identification introduced by Akaike, Schwartz and Rissanen, is presented. It is shown that the criterion introduced by Schwartz and Rissanen yields a consistent estimate of the number of signals, while the criterion introduced by Akaike yields an inconsistent estimate that tends, in the large-sample limit, to overestimate the number of signals.

The problem of of decentralizing the processing in a passive array composed of subarrays at geographically dispersed sites is addressed. A new scheme, based on obtaining estimates of the covariance matrices from each subarray is presented, and its performance is compared to the conventional triangulation method. It is shown that the new scheme offers improved accuracy with only a modest increase in the communication load. Moreover, unlike the conventional triangulation scheme, it does not require any data association step; the data association is done automaticly in the proposed algorithm.

An iterative algorithm for the inversion of a doubly block Toeplitz matrix consisting of m × m blocks of size p × p is described. The algorithm presented exploits the structure of the doubly block Toeplitz matrix and outperforms Akaike's algorithm by a factor of\max {2 \frac{p}{m},2}. The use of this algorithm for an iterative solution of a doubly block Toeplitz set of linear equations is also presented.

A new approach is presented to the problem of estimating the directions-of-arrival and the frequencies of multiple narrowband sources--the so-called 2-D harmonic retrieval problem. The approach presented applies to the general case of correlated sources and includes multipath propagation as a special case. The estimators presented yield high resolution and asymptotically unbiased estimates of the directions-of-arrival and frequencies of the impinging sources and enable trade-offs between resolution and accuracy.

In radio and sonar applications it sometimes happens that narrow-band signals, originated from a remote source and observed at a pair of receivers, differ by unknown differential phase and Doppler shift in addition to the differential delay corresponding to the range difference. The correspondence presents the joint maximum likelihood (ML) estimate of the differential delay, Doppler, and phase and examines their accuracy by deriving the Cramér-Rao bound. It is shown that the joint ML estimators are the values of the delay and Doppler that maximize the magnitude of a generalized ambiguity function analogous to the one used in radar. It is also shown that for long observation time and high enough signal-to-noise ratio there is no degradation in the accuracy of the time-delay estimator due to the additional phase and Doppler uncertainty and that the differential Doppler is uncorrelated with the differential delay and phase estimators.

This paper presents the maximum likelihood estimate of the time delay between two signals with random relative phase shift. The analysis applies for both broad-band and narrowband signals and incorporates a parametric representation of the spread of the phase variation which allows the examination of all cases ranging from uniformly distributed phase shift to known phase shift. A realization of the ML estimator is presented which illustrated the difference between optimum processing for random phase shift and no phase shift. The Cramer-Rao bound is also derived and the performance degradation is discussed.

An improved lower bound on the local mean-square error and upper and lower bounds on the bias which are tighter than previously known bounds are derived.