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234
Blind Beamforming for Non Gaussian Signals
 IEE ProceedingsF
, 1993
"... 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 mani ..."
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Cited by 494 (31 self)
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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 fourthorder cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalization of 4thorder cumulant matrices
An Analytical Constant Modulus Algorithm
, 1996
"... Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of cochannel 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 ..."
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Cited by 121 (31 self)
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Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of cochannel 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, nonCM 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 setup. I. INTRODUCTION A. Blind signal separation An elementary problem in the area of spatial si...
Equalization Using the Constant Modulus Criterion: A
 Review,” Proccedings of the IEEE, Invited
, 1997
"... 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 cata ..."
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Cited by 101 (21 self)
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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.
Basis Expansion Models and Diversity Techniques for Blind Identification and Equalization of TimeVarying Channels
 PROC. IEEE
, 1998
"... ..."
Multichannel Blind Identification: From Subspace to Maximum Likelihood Methods
 Proc. IEEE
, 1998
"... 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 ..."
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Cited by 80 (2 self)
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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 momentbased 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.
Adaptive Filters
"... Introduction An adaptive filter is defined as a selfdesigning 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 classif ..."
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Cited by 80 (1 self)
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Introduction An adaptive filter is defined as a selfdesigning 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
Multichannel Blind Deconvolution: Fir Matrix Algebra And Separation Of Multipath Mixtures
, 1996
"... 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 mat ..."
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Cited by 73 (0 self)
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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 feedforward memory connections, wideband array processing, and in problems with a multiinput, multioutput network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...
Blind Adaptive Interference Suppression For DirectSequence CDMA
 IEEE TRANS. COMMUN
, 1994
"... 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 ..."
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Cited by 65 (7 self)
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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
Recent Developments in Blind Channel Equalization: From Cyclostationarity to Subspaces
 Signal Processing
, 1996
"... Since Tong, Xu and Kailath [1] demonstrated the feasibility of identifying possibly nonminimum phase channels using secondorder statistics, considerable research activity, both in algorithm development and fundamental analysis, has been seen in the area of blind identification of multiple FIR chan ..."
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Cited by 37 (1 self)
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Since Tong, Xu and Kailath [1] demonstrated the feasibility of identifying possibly nonminimum phase channels using secondorder statistics, considerable research activity, 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 techniques. 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
Fractionally spaced equalization using CMA: Robustness to channel noise and lack of disparity
 IEEE Trans. Signal Processing
, 1997
"... Abstract—In the noisefree case, the fractionally spaced equalization using constant modulus (FSECM) criterion has been studied previously. Its minima were shown to achieve perfect equalization when zeroforcing (ZF) conditions are satisfied and to be able to still achieve fair equalization when th ..."
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Cited by 31 (2 self)
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Abstract—In the noisefree case, the fractionally spaced equalization using constant modulus (FSECM) criterion has been studied previously. Its minima were shown to achieve perfect equalization when zeroforcing (ZF) conditions are satisfied and to be able to still achieve fair equalization when there is lack of disparity. However, to our best knowledge, the effect of additive channel noise on the FSECM costfunction minima has not been studied. In this paper, we show that the noisy FSECM cost function is subject to a smoothing effect with respect to the noisefree cost function, the result of which is a tradeoff between achieving zero forcing and noise enhancement. Furthermore, we give an analytical closedform expression for the loss of performance due to the noise in terms of inputoutput mean square error (MSE). Under the ZF conditions, the FSECM MSE is shown to be mostly due to output noise enhancement and not to residual intersymbol interference (ISI). When there is lack of disparity, an irreducible amount of ISI appears independently of the algorithm. It is the lower equalizability bound for given channel conditions and equalizer length—the socalled minimum MSE (MMSE). The MMSE lower bound is the sum of the MMSE and of additional MSE mostly due to noise enhancement. Finally, we compare the FSECM MSE to this lower bound. I.