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Fast blind equalization using complex-valued MLP

NEURAL PROCESSING LETTERS 2005年第3期21卷 215-225页

作者： Pandey, R Natl Inst Technol Dept Elect & Commun Engn Kurukshetra Haryana India

The blind equalizers based on complex valued feedforward neural networks, for linear and nonlinear communication channels, yield better performance as compared to linear equalizers. The learning algorithms are, generally, based on stochastic gradient descent, as they are simple to implement. However, these algorithms show a slow convergence rate. In the blind equalization problem, the unavailability of the desired output signal and the presence of nonlinear activation functions make the application of recursive least squares algorithm difficult. In this letter, a new scheme using recursive least squares algorithm is proposed for blind equalization. The learning of weights of the output layer is obtained by using a modified version of constant modulus algorithm cost function. For the learning of weights of hidden layer neuron space adaptation approach is used. The proposed scheme results in faster convergence of the equalizer.

关键词： blind equalization complex-valued feedforward neural network constant modulus algorithm recursive least square algorithm stochastic gradient descent algorithm

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Space-Time Semi-Blind Equalizer for Dispersive QAM MIMO System Based on Modified Newton Method

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2014年第6期13卷 3244-3256页

作者： Li, Jin Feng, Da-Zheng Zheng, Wei Xing Xidian Univ Natl Lab Radar Signal Proc Xian 710071 Peoples R China Univ Western Sydney Sch Comp Engn & Math Penrith NSW 2751 Australia

This paper proposes a space-time semi-blind equalizer (ST-SBE) for dispersive multiple-input multiple-output (MIMO) communication systems that employ high throughput quadrature amplitude modulation (QAM) signals. A novel cost function (CF) that integrates multimodulus algorithm (MMA) with soft decision-directed (SDD) scheme is established to efficiently obtain the weight vector associated with the ST-SBE. In the ST-SBE, a very short training sequence is used to provide a rough initial least squares estimate of the weight vector. An efficient modified Newton method (MNM) for minimizing the established cost function is proposed to fast search the optimal weight vector. Very interestingly, we prove that the proposed MNM has the same quadratic order of convergence as Newton methods. In addition, the proposed MNM has much lower computational complexity than Newton methods. Simulation results are provided to demonstrate that the ST-SBE has better performances than the gradient-Newton (GN)-based concurrent constant modulus algorithm (CMA) with SDD scheme (GN-CMA+SDD).

关键词： Space-time semi-blind equalizer modified Newton method constant modulus algorithm multimodulus algorithm soft decision-directed scheme

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Globally convergent blind source separation based on a multiuser kurtosis maximization criterion

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2000年第12期48卷 3508-3519页

作者： Papadias, CB Bell Labs Lucent Technol Res Holmdel NJ 07733 USA

We consider the problem of recovering blindly (i.e., without the use of training sequences) a number of independent and identically distributed source (user) signals that are transmitted simultaneously through a linear instantaneous mixing channel. The received signals are, hence, corrupted by interuser interference (IUI), and we can model them as the outputs of a linear multiple-input-multiple-output (MIMO) memoryless system. Assuming the transmitted signals to be mutually independent, i.i.d., and to share the same non-Gaussian distribution, a set of necessary and sufficient conditions for the perfect blind recovery (up to scalar phase ambiguities) of all the signals exists and involves the kurtosis as well as the covariance of the output signals. We focus on a straightforward blind constrained criterion stemming from these conditions. From this criterion, we derive an adaptive algorithm for blind source separation, which we call the multiuser kurtosis (MUK) algorithm. At each iteration, the algorithm combines a stochastic gradient update and a Gram-Schmidt orthogonalization procedure in order to satisfy the criterion's whiteness constraints. A performance analysis of its stationary points reveals that the MUK algorithm is free of any stable undesired local stationary points for any number of sources;hence, it is globally convergent to a setting that recovers them all.

关键词： adaptive filtering blind equalization blind source separation constant modulus algorithm high order statistics kurtosis multiple-input multiple-output (MIMO) systems narrowband channels

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Blind source separation: The location of local minima in the case of finitely many samples

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第9期56卷 4340-4353页

作者： Leshem, Amir van der Veen, Alle-Jan Bar Ilan Univ Sch Engn IL-52900 Ramat Gan Israel Delft Univ Technol Dept Elect Engn NL-2628 CD Delft Netherlands

Cost functions used in blind source separation are often defined in terms of expectations, i.e., an infinite number of samples is assumed. An open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case. To answer this question, we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions. In particular, we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix. The method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function. This shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function. We also answer a long-standing problem of the mean-squared error (MSE) behavior of the (finite sample) least squares constant modulus algorithm (LS-CMA), namely whether there exist LS-CMA receivers with good MSE performance. We demonstrate how the proposed techniques can be used to determine the required number of samples' for LS-CMA to exceed a specified performance. The paper concludes with simulations that validate the results.

关键词： blind source separation constant modulus algorithm finite sample analysis

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Efficient and robust detection of GFSK signals under dispersive channel, modulation index, and carrier frequency offset conditions

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EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2005年第16期2005卷 2719-2729页

作者： Tibenderana, C Weiss, S Univ Southampton Sch Elect & Comp Sci Commun Res Grp Southampton SO17 1BJ Hants England

Gaussian frequency shift keying is the modulation scheme specified for Bluetooth. Signal adversities typical in Bluetooth networks include AWGN, multipath propagation, carrier frequency, and modulation index offsets. In our effort to realise a robust but efficient Bluetooth receiver, we adopt a high-performance matched-filter-based detector, which is near optimal in AWGN, but requires a prohibitively costly filter bank for processing of K bits worth of the received signal. However, through filtering over a single bit period and performing phase propagation of intermediate results over successive single-bit stages, we eliminate redundancy involved in providing the matched filter outputs and reduce its complexity by up to 90% (for K = 9). The constant modulus signal characteristic and the potential for carrier frequency offsets make the constant modulus algorithm (CMA) suitable for channel equalisation, and we demonstrate its effectiveness in this paper. We also introduce a stochastic gradient-based algorithm for carrier frequency offset correction, and show that the relative rotation between Successive intermediate filter outputs enables us to detect and correct offsets in modulation index.

关键词： Gaussian frequency shift keying Bluetooth constant modulus algorithm carrier frequency offset correction modulation index offset correction

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Characterization of the undesirable global minima of the Godard cost function: Case of noncircular symmetric signals

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第5期54卷 1917-1922页

作者： Houcke, S Chevreuil, A ENST Bretagne Dept Signal & Commun PRACom TAMCI F-29285 Brest France Inst Gaspard Monge UMR 8049 CNRS IGM LabInfoEquipe Signal Commun F-77454 Marne La Vallee 2 France

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.

关键词： deconvolution constant modulus algorithm contrast function Godard algorithm

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Blind channel estimation via combining autocorrelation and blind phase estimation

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2004年第6期51卷 1125-1131页

作者： Baykal, B Middle E Tech Univ Dept Elect & Elect Engn TR-06531 Ankara Turkey

Symbol spaced blind channel estimation methods are presented which can essentially use the results of any existing blind equalization method to provide a blind channel estimate of the channel. Blind equalizer's task is reduced to only phase equalization (or identification) as the channel autocorrelation is used to obtain the amplitude response of the channel. Hence, when coupled with simple algorithms such as the constant modulus algorithm (CMA) these methods at baud rate processing provide alternatives to blind channel estimation algorithms that use explicit higher order statistics (HOS) or second-order statistics (subspace) based fractionally-spaced/multichannel algorithms. The proposed methods use finite impulse response (FIR) filter linear receiver equalizer or matched filter receiver based infinite impulse response+FIR linear cascade equalizer configurations to obtain blind channel estimates. It is shown that the utilization of channel autocorrelation information together with blind phase identification of the CMA is very effective to obtain blind channel estimation. The idea of combining estimated channel autocorrelation with blind phase estimation can further be extended to improve the HOS based blind channel estimators in a way that the quality of estimates are improved.

关键词： blind channel estimation constant modulus algorithm higher order statistics matched filter receiver

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Block-Wise Digital Signal Processing for PolMux QAM/PSK Optical Coherent Systems

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2011年第20期29卷 3070-3082页

作者： Selmi, M. Gosset, C. Noelle, M. Ciblat, P. Jaouen, Y. Telecom ParisTech Dept Commun & Elect F-75634 Paris France Heinrich Hertz Inst Nachrichtentech Berlin GmbH Fraunhofer Inst Telecommun D-10587 Berlin Germany

In polarization multiplexing based coherent optical transmission, two main kinds of impairements have to be counter-acted: 1) the inter-symbol interference generated by the chromatic dispersion and the polarization mode dispersion and 2) the frequency offset. Usually adaptive approaches are carried out to mitigate them. Since the channel is very slowly time-varying, we propose to combat these impairements by using block-wise methods. Therefore, we introduce two new algorithms: the first one is a block-wise version of blind time equalizer (such as CMA), and the second one estimates the frequency offset in block-wise way. These algorithms are suitable for PSK and QAM constellations. By simulation investigations, we show that they outperform the standard approach in terms of convergence speed only at a moderate expense of computational load. We also experimentally evaluate their performance using 8-PSK real data traces and off-line processing which takes into account other physical impairments such as phase noise and non-linear effects.

关键词： Blind equalization block processing bursty transmission constant modulus algorithm constant phase estimation decision-directed algorithm frequency offset estimation optical coherent communications optimal step-size gradient algorithm

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Performance analysis of Godard-based blind channel identification

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2001年第8期49卷 1757-1767页

作者： Schniter, P Casas, RA Touzni, A Johnson, CR Ohio State Univ Dept Elect Engn Columbus OH 43210 USA NxtWave Commun Langhorne PA 19047 USA Cornell Univ Dept Elect Engn Ithaca NY 14853 USA

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.

关键词： blind channel identification blind deconvolution constant modulus algorithm Godard algorithm

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A comparative study of two blind FIR equalizers

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DIGITAL SIGNAL PROCESSING 2004年第1期14卷 18-36页

作者： Chen, S Cook, TB Anderson, LC Univ Southampton Dept Elect & Comp Sci Southampton SO17 1BJ Hants England

The paper investigates blind tinite-impulse-response (FIR) equalization schemes for quadrature amplitude modulation signalling. We compare a bootstrap maximum a posteriori probability (MAP) equalizer witha recently introduced concurrent constant modulus algorithm (CMA) and decision directed (DD) equalizer (CMA+DD). Both equalizers are known to outperform the CMA considerably in the situations where carrier recovery is performed and the signal constellation is known. The concurrent CMA+DD equalizer has a complexity that is slightly more than twice of the CMA, and the bootstrap MAP equalizer has computational requirements that are only slightly more complex than the CMA. Simulation results indicate that the bootstrap MAP blind FIR equalizer has a faster convergence rate and better steady-state performance than the concurrent CMA+DD blind FIR equalizer, but tuning of the former is more complicated than the latter. (C) 2003 Elsevier Inc. All rights reserved.

关键词： blind equalization finite-impulse-response filter quadrature amplitude modulation constant modulus algorithm decision-directed adaptation maximum a posteriori probability

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