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Analytical blind channel identification
 IEEE Trans. Signal Processing
, 2002
"... Abstract—In this paper, a novel analytical blind singleinput singleoutput (SISO) identification algorithm is presented, based on the noncircular secondorder statistics of the output. It is shown that statistics of order higher than two are not mandatory to restore identifiability. Our approach is ..."
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Cited by 15 (6 self)
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Abstract—In this paper, a novel analytical blind singleinput singleoutput (SISO) identification algorithm is presented, based on the noncircular secondorder statistics of the output. It is shown that statistics of order higher than two are not mandatory to restore identifiability. Our approach is valid, for instance, when the channel is excited by phase shift keying (PSK) inputs. It is shown that the channel taps need to satisfy a polynomial system of degree 2 and that identification amounts to solving the system. We describe the algorithm that is able to solve this particular system entirely analytically, thus avoiding local minima. Computer results eventually show the robustness with respect to noise and to channel length overdetermination. Identifiability issues are also addressed. Index Terms—Blind channel estimation, minimum shift keying, multipath channels, noncircularity, secondorder statistics, timevarying channels. I.
On the equivalence between the Godard and ShalviWeinstein schemes of blind equalization
 Signal Process
, 1999
"... Certain equivalences between the Godard and Shalvi—Weinstein schemes have been previously noted under special circumstances. We present here a simple proof for real signals that an equivalence can be established assuming little more than stationarity to fourth order of the equalizer input; the exact ..."
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Cited by 13 (4 self)
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Certain equivalences between the Godard and Shalvi—Weinstein schemes have been previously noted under special circumstances. We present here a simple proof for real signals that an equivalence can be established assuming little more than stationarity to fourth order of the equalizer input; the exact nature of the input sequence proves otherwise irrelevant to the validity of the equivalence. The equivalence also carries over to complex signals, but subject to more restrictive circularity conditions. In a communication context, the equivalence implies that many performance issues, such as susceptibility to local minima, the ability (or lack thereof) to open the eye, or mean performance degradations due to channel noise and/or source correlation properties, are common to the two, even when applied with nonlinear channels. Our equivalence also indicates a simple modification to the Godard algorithm to render it applicable to leptokurtic
Static and dynamic convergence behavior of adaptive blind equalizers
 IEEE Trans. Signal Processing
, 1996
"... AbstractThis paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers. We first study the properties of prediction error functions of blind equalization algorithms, and then, we use these properties to analyze the static a ..."
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Cited by 8 (1 self)
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AbstractThis paper presents a theoretical analysis of the static and dynamic convergence behavior for a general class of adaptive blind equalizers. We first study the properties of prediction error functions of blind equalization algorithms, and then, we use these properties to analyze the static and dynamic convergence behavior based on the independence assumption. We prove in this paper that with a small step size, the ensemble average of equalizer coefficients will converge to the minimum of the cost function near the channel inverse. However, the convergence is not consistent. The correlation matrix of equalizer coefficients at equilibrium is determined by a Lyapunov equation. According to our analysis results, for a given channel and stepsize, there is an optimal length for an equalizer to minimize the intersymbol interference. This result implies that a longerlength blind equalizer does not necessarily outperform a shorter one, which is contrary to what is conventionally conjectured. The theoretical analysis results are confirmed by computer simulations.
Effects Of Source Distributions And Correlation On Fractionally Spaced Blind Constant Modulus Algorithm Equalizers
, 1995
"... Simplicial Complex: By an abstract simplicial complex with vertices in a set V , we mean a family of finite subsets of V satisfying the condition that K is hereditary, i. e. every subset of any set in K is also in K. Subcomplex Let K and L be any two abstract simplicial complexes with vertices V an ..."
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Cited by 6 (0 self)
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Simplicial Complex: By an abstract simplicial complex with vertices in a set V , we mean a family of finite subsets of V satisfying the condition that K is hereditary, i. e. every subset of any set in K is also in K. Subcomplex Let K and L be any two abstract simplicial complexes with vertices V and W respectively. If L ae K, then L is said to be a subcomplex of K. Topological Realization Let K be an arbitrarily given abstract simplicial complex. We will construct a space P = jKj called the topological realization as follows. For each finite set F 2 K, consider the simplex oe F defined in the previous section. These simplexes foe F jF 2 Kg (without the identification introduced in studying their faces) are by definition disjoint topological spaces. Form their topological sum S = S(K) = X F2K oe F : Then S is clearly a metrizable space containing every simplex oe F as an open and closed subspace. Introduce a relation ¸ in S as follows. Let f 2 oe F and g 2 oe G be any two points in ...
On the Convergence of Blind Channel Equalization
, 1995
"... : Baudrate blind equalization algorithms may converge to undesirable stable equilibria due to different reasons. One is the use of FIR filter as an equalizer. It is proved in this paper that this kind of local minima exist for all blind equalization algorithms. The local minima generated by this me ..."
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Cited by 1 (1 self)
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: Baudrate blind equalization algorithms may converge to undesirable stable equilibria due to different reasons. One is the use of FIR filter as an equalizer. It is proved in this paper that this kind of local minima exist for all blind equalization algorithms. The local minima generated by this mechanism are thus called unavoidable local minima. The other one is due to the cost function adopted by the blind algorithm itself, which has local minima even implemented with double infinite length equalizers. This type of local minima are called inherent local minima. It is also shown that the Godard algorithms [10] and standard cumulant algorithms [6] have no inherent local minimum. However, other algorithms, such as the decisiondirected equalizer and the StopandGo algorithm [17], have inherent local minima. This paper also studies the convergence of the Godard algorithms [10] and standard cumulant algorithms [6] under Gaussian noise, and derives the mean square error of the equalizer...