This paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resorting to their hypothesized value. By using estimates of the directional vectors obtained via blind identification i.e. without knowing the arrray manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors, etc ... so that neither array calibration nor physical modeling are necessary. Rather surprisingly, `blind beamformers' may outperform `informed beamformers' in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption blind identification relies on is the statistical independence of the sources, which we exploit using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4th-order cumulant matrices

Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of co-channel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel. In this paper, we show that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices. With this new, analytical approach, it is possible to detect the number of CM signals present in the channel, and to retrieve all of them exactly, rejecting other, non-CM signals. Only a modest amount of samples are required. The algorithm is robust in the presence of noise, and is tested on measured data, collected from an experimental set-up. I. INTRODUCTION A. Blind signal separation An elementary problem in the area of spatial si...

This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.

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...

Direct Sequence (DS) Code Division Multiple Access (CDMA) is a promising technology for wireless environments with multiple simultaneous transmissions because of several features: asynchronous multiple access, robustness to frequency selective fading, and multipath combining. The capacity

Introduction An adaptive filter is defined as a self-designing system that relies for its operation on a recursive algorithm, which makes it possible for the filter to perform satisfactorily in an environment where knowledge of the relevant statistics is not available. Adaptive filters are classified into two main groups: linear, and non linear. Linear adaptive filters compute an estimate of a desired response by using a linear combination of the available set of observables applied to the input of the filter. Otherwise, the adaptive filter is said to be nonlinear. Adaptive filters may also be classified into: (i) Supervised adaptive filters, which require the availability of a training sequence that provides different realizations of a desired response for a specified input signal vector. The desired response is compared against the actual response of the filter due to the input signal vector, and the resulting error signal is

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this paper is to review developments in blind channel identification and estimation within the estimation theoretical framework. We have paid special attention to the issue of identifiability, which is at the center of all blind channel estimation problems. Various existing algorithms are classified into the moment-based and the maximum likelihood (ML) methods. We further divide these algorithms based on the modeling of the input signal. If input is assumed to be random with prescribed statistics (or distributions), the corresponding blind channel estimation schemes are considered to be statistical. On the other hand, if the source does not have a statistical description, or although the source is random but the statistical properties of the source are not exploited, the corresponding estimation algorithms are classified as deterministic. Fig. 2 shows a map for different classes of algorithms and the organization of the paper.

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

Abstract—In this paper, we propose a new precoding method for intersymbol interference (ISI) cancellation by using nonmaximally decimated multirate filterbanks. Unlike the existing precoding methods, such as the TH and trellis precodings, the new precoding i) may be independent of the ISI channel; ii) is linear and does not have to implement any modulo operation; iii) gives the ideal FIR equalization at the receiver for any FIR ISI channel including spectral-null channels; iv) expands the transmission bandwidth in a minimum amount. The precoding is built on nonmaximally decimated multirate filterbanks. Based on multirate filterbank theory, we present a necessary and sufficient condition on an FIR ISI transfer function in terms of its zero set such that there is a linear FIR N 2 K precoder so that an ideal FIR equalizer exists, where the integers K and N are arbitrarily fixed. The condition is easy to check. As a consequence of the condition, for any given FIR ISI transfer function (not identically 0), there always exist such linear FIR precoders. Moreover, for almost all given FIR ISI transfer functions, there exist linear FIR precoders with size N 2 (N 0 1), i.e., the bandwidth is expanded by 1=N. In addition to the conditions on the ISI transfer functions, a method for the design of the linear FIR precoders and the ideal FIR equalizers is also given. Numerical examples are presented to illustrate the theory. I.