A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feed-forward memory connections, wideband array processing, and in problems with a multi-input, multi-output network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...

Application of subspace-based algorithms to narrowband direction-of-arrival (DOA) estimation requires that certain modeling assumptions be made. Most importantly, both the array response in all directions of interest and the spatial covariance of the noise must be known. In practice, however, neither of these quantities is known precisely. Depending on the degree...

Since Tong, Xu and Kailath [1] demonstrated the feasibility of identifying possibly nonminimum phase channels using second-order statistics, considerable research activ-ity, both in algorithm development and fundamental analysis, has been seen in the area of blind identification of multiple FIR channels. Many of the recently developed approaches invoke, either explicitly or implicitly, the algebraic structure of the data model, while some others resort to the use of cyclic correlation/spectral fitting tech-niques. The objective of this paper is to establish insightful connections among these studies and present recent developments of blind channel equalization. We also unify various representative algorithms into a common theoretical framework. 1 1

In this paper we study a technique for using decision direction to extract digital signals from antenna array data. The algorithm alternates between (1) estimating and demodulating the received signals, and (2) using the resulting bit decisions to regenerate the signal waveforms and recompute the beamformer weights. An analysis of the (asymptotic) symbol error rate performance of the algorithm for the case of M-ary PSK signals is included, along with several representative simulation examples. This work was supported in part by a contract from E-Systems, Inc., Greenville Division (Dr. William A. Gardner, Principal Investigator), and by the National Science Foundation under grant MIP-9110112. 1. Introduction The problem of extracting communication signals using an array of sensors is one of increasing importance to modern communications. For example, as the demand for bandwidth and time slots in mobile cellular radio systems increases, thought has been given to the use of multiple an...

This thesis summarizes several contributions to the areas of signal processing and auditory source separation. The philosophy of Frequency-Warped Signal Processing is introduced as a means for separating the AM and FM contributions to the bandwidth of a complex-valued, frequency-varying sinusoid p[n], transforming it into a signal with slowly-varying parameters. This transformation facilitates the removal of p[n] from an additive mixture while minimizing the amount of damage done to other signal components. The average winding rate of a complex-valued phasor is explored as an estimate of the instantaneous frequency. Theorems are provided showing the robustness of this measure. To implement frequency tracking, a Frequency-Locked Loop algorithm is introduced which uses the complex winding error to update its frequency estimate. The input signal is dynamically demodulated and filtered to extract the envelope. This envelope may then be remodulated to reconstruct the target partial, which ...

This paper studies the effect of array calibration errors on the performance of various DF (direction finding) based signal copy algorithms. Unlike blind copy methods, this class of algorithms requires an estimate of the directions of arrival (DOAs) of the signals in order to compute the copy weight vectors. Under the assumption that the observation time is sufficiently long, the following algorithms are studied: classical beamforming, least squares, total least squares, linearly constrained minimum variance beamforming, and structured stochastic estimation. Expressions for the mean-square error of the signal estimates are derived as a function of the calibration errors for both the case where the DOAs are known precisely and for the case where the DOAs must be estimated. This work was supported by a contract from E-Systems, Inc., Greenville Division (Dr. William A. Gardner, Principal Investigator), and by the National Science Foundation under grant MIP-9110112. 1. Introduction An im...

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This paper analyzes the performance of methods for estimating the parameters of narrowband signals arriving at an array of sensors. The so-called deterministic and stochastic maximum likelihood (ML) methods are considered. A performance analysis is carried out for finite number of snapshots but assuming that the array is composed of a sufficiently large number, m, of sensors. Strong consistency of the parameter estimates is proved and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large (time) sample case, the present analysis shows that the accuracy is the same for the two ML methods. The covariance matrix of the estimation error attains the Cram'er-Rao bound (CRB). For many array geometries of practical interest, the array propagation vectors become orthogonal as m is increased. It is shown that also the traditional beamforming method provides consistent (but not necessarily efficient) estimates under this assumption. This is true a...

This paper presents an approach to using a large team of UAVs to find radio frequency (RF) emitting targets in a large area. Small, inexpensive UAVs that can collectively and rapidly determine the approximate location of intermittently broadcasting and mobile RF emitters have a range of applications in both military, e.g., for finding SAM batteries, and civilian, e.g., for finding lost hikers, domains. Received Signal Strength Indicator (RSSI) sensors on board the UAVs measure the strength of RF signals across a range of frequencies. The signals, although noisy and ambiguous due to structural noise, e.g., multipath effects, overlapping signals and sensor noise, allow estimates to be made of emitter locations. Generating a probability distribution over emitter locations requires integrating multiple signals from different UAVs into a Bayesian filter, hence requiring cooperation between the UAVs. Once likely target locations are identified, EO-camera equipped UAVs must be tasked to provide a video stream of the area to allow a user to identify the emitter. I.

Asymptotic analysis methods for performance prediction of so-called subspace directionof -arrival estimation methods has been developed earlier, assuming that a large-enough number of array measurements, or snapshots, is collected. This paper also addresses the problem of making performance predictions, but for beamspace-based subspace methods. The novel approach in this paper assumes the number of array elements to be large, while the number of snapshots is arbitrary. The perturbation effect, due to additive sensor noise, on a certain subspace is used for establishing the asymptotic behavior of direction-of-arrival estimates. The asymptotic estimation errors for the estimators resulting from Signal Subspace Fitting methods, such as WSF, and Noise Subspace Fitting (NSF) methods, such as MUSIC and a multi-dimensional counterpart to WSF, are shown to be asymptotically unbiased and normally distributed. Provided that the array response vectors become orthogonal when the number of array el...