Quaternion adaptive filters have been applied extensively to model three- and four-dimensional phenomena in signal processing, but most of them require a known reference signal. In this paper, a class of widely linear...
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Quaternion adaptive filters have been applied extensively to model three- and four-dimensional phenomena in signal processing, but most of them require a known reference signal. In this paper, a class of widely linear quaternion-valued godard (WL-Qgodard) algorithms is derived, which include the widely linear quaternionvalued constant modulus algorithm (WL-QCMA) as a special case. The derived filter allows for signal recovery operations in the absence of reference signals to be performed directly in the quaternion domain, eliminating the need for transformation to real-valued vector algebras and preserving the advantages of the quaternion division algebra. Compared to state-of-the-art quaternion blind equalisation algorithms, the proposed algorithm models the signal transmission channel using the widely linear quaternion framework, which has more extensive applicability and can better represent real-world scenarios. Furthermore, aided by GHR calculus, for the first time, we present a performance analysis framework for the Qgodard algorithm and WL-Qgodard algorithms, which depicts the dynamic and their static convergence behaviours, overcoming the challenges posed by the noncommutative quaternion algebra and non-isomorphism between the quaternion equalisers and real-valued equalisers. Finally, simulation results over physically meaningful wireless communication signals indicate the effectiveness and superiority of the proposed WL-QCMA, and the validity of the theoretical performance analysis.
We propose a modified godard algorithm to monitor receiver IQ skew and an adaptive timing recovery method operate at 1sample/symbol to monitor transmitter skew. Compared to traditional high-order MIMO schemes, the DSP...
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ISBN:
(纸本)9781665481557
We propose a modified godard algorithm to monitor receiver IQ skew and an adaptive timing recovery method operate at 1sample/symbol to monitor transmitter skew. Compared to traditional high-order MIMO schemes, the DSP complexity can be reduced at least 50%.
The modern digital high speed wireless communication system demands quick convergence rate and low steady state error. The balancing between the demands can be achieved by opting step size. Thus, it is essential to de...
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The modern digital high speed wireless communication system demands quick convergence rate and low steady state error. The balancing between the demands can be achieved by opting step size. Thus, it is essential to define new algorithms to equalize channels and mitigate noise in communications. It is renowned that time varying step size blind equalization technique can speed up the convergence rate and minimize the misadjustment. This work presents a variable step size (VSS) approach based on godard blind equalization algorithm to resolve the conflict between the convergence rate and precision of the fixed step-size godard algorithm. The results of this projected approach is compared with the existing variable step size sato algorithm for a pulse amplitude modulated (PAM) input symbol.
A critical assumption in applying godard CMA algorithm for blind deconvolution and equalization is the assumption of an independently distributed source. Almost all the applications in the literature have based their ...
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ISBN:
(纸本)9781424428991
A critical assumption in applying godard CMA algorithm for blind deconvolution and equalization is the assumption of an independently distributed source. Almost all the applications in the literature have based their implementations on this assumption. To our knowledge, no research has been done on the effect of source correlation on adaptive blind deblurring of images through CMA, and this paper addresses that gap, coming up with a novel model of addressing the source correlation problem in the image deblurring through CMA.
The deconvolution of a filtered version of a zero-mean normalized independent and identically distributed (i.i.d.) signal (s(n))(n is an element of z) having a strictly negative Kurtosis gamma(2) = E[|s(n)|(4)] - 2(E[...
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The deconvolution of a filtered version of a zero-mean normalized independent and identically distributed (i.i.d.) signal (s(n))(n is an element of z) having a strictly negative Kurtosis gamma(2) = E[|s(n)|(4)] - 2(E[|s(n)|(2)])(2) - |E[s(n)(2)|(2)] is addressed. This correspondence focuses on the global minimizers of the godard function. A well-known result states that these minimizers achieve deconvolution at least if the input signal shows the symmetry E[s(2)] = 0. When this constraint is relaxed, (s(n))(n is an element of Z) is said to be noncircular symmetric: It is shown that the minimizers achieve deconvolution if and only if 2|E [s(n)(2)]|(2) < -gamma(2)(s). If this condition is not met, the global minimizers are found to be finite-impulse-response filters with two taps.
Existing studies of the stationary points of the constant modulus adaptive algorithm, typically, assume a channel equalization setting and several restrictive conditions on the source sequence, the communications chan...
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Existing studies of the stationary points of the constant modulus adaptive algorithm, typically, assume a channel equalization setting and several restrictive conditions on the source sequence, the communications channel and the noise environment. Often, results are presented in terms of the combined channel and equalizer impulse response parameters, the source vector and the channel convolution matrix. As such, these results are not easily applicable in other areas. Modeling after Wiener filtering theory, this paper derives new expressions for the basic equations of the constant modulus (CM) optimization method. In particular, new formulas for the index function, its gradient vector and its Hessian matrix are obtained. These formulas involve the unknown parameters and the statistics of the sample sequence only. Consequently, they serve to convert the CM minimization problem into that of solving a system of cubic equations in the parameter vector. This new formulation of the CM optimization problem leads to a characterization of the critical points that is not exclusive to channel equalization. It also makes it possible to derive new equations for the minimum value of the cost function, the conditions for perfect signal recovery, and a tighter lower bound for the approach. Computer simulation examples are also presented to illustrate our findings. (C) 2002 Elsevier Science B.V. All lights reserved.
We analyze a blind channel impulse response identification scheme based on the cross correlation of blind symbol estimates with the received signal, The symbol estimates specified are those minimizing the godard (or c...
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We analyze a blind channel impulse response identification scheme based on the cross correlation of blind symbol estimates with the received signal, The symbol estimates specified are those minimizing the godard (or constant modulus) criterion, for which mean-squared symbol estimation error bounds have recently been derived. In this paper, we derive upper bounds for the average squared parameter estimation error (ASPE) of the blind identification scheme that depend on the mean-squared error of the Wiener equalizer, the kurtoses of the desired and interfering sources, and the channel impulse response. The effects of finite data length and stochastic gradient equalizer design on ASPE are also investigated. All results are derived in a general multiuser vector-channel context.
The constant modulus (CM) criterion has become popular in the design of blind linear estimators of sub-Gaussian i.i.d. processes transmitted through unknown linear channels in the presence of unknown additive interfer...
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The constant modulus (CM) criterion has become popular in the design of blind linear estimators of sub-Gaussian i.i.d. processes transmitted through unknown linear channels in the presence of unknown additive interference, The existence of multiple CM minima, however, makes it difficult for CM-minimizing schemes to generate estimates of the desired source (as opposed to an interferer) in multiuser environments, In this paper, we present three separate sufficient conditions under which gradient descent (GD) minimization of CIM cost will locally converge to an estimator of the desired source at a particular delay. The sufficient conditions are expressed in terms of statistical properties of the initial estimates, specifically, CM cost, kurtosis, and signal-to-interference-plus-noise ratio (SINR). Implications on CM-GD initialization methods are also discussed.
The constant modulus (CM) criterion has become popular in the design of blind linear estimators of sub-Gaussian independent and identically distributed (i.i.d.) processes transmitted through unknown linear channels in...
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The constant modulus (CM) criterion has become popular in the design of blind linear estimators of sub-Gaussian independent and identically distributed (i.i.d.) processes transmitted through unknown linear channels in the presence of unknown additive interference. In this paper, me present an upper bound for the conditionally unbiased mean-squared error (USME) of CM-minimizing estimators that depends only on the source kurtoses and the UMSE of Wiener estimators. Further analysis reveals that the extra UMSE of CM estimators can be upper-bounded by approximately the square of the Wiener (i.e., minimum) UMSE. Since our results hold for vector-valued finite-impulse response/infinite-impulse response (FIR/IIR) linear channels, vector-valued FIR/IIR estimators with a possibly constrained number of adjustable parameters, and multiple interferers with arbitrary distribution, they confirm the longstanding conjecture regarding the general mean-square error (MSE) robustness of CM estimators.
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 assum...
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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 there of) 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 sources. (C) 1999 Elsevier Science B.V. All rights reserved.
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