Weave analysis of artist canvas examines x-ray images taken of the paintings. Algorithms assume an underlying regularity of the canvas weave over short distances and exploits short-space spectral analysis to determine the fundamental frequency of the horizontal and vertical thread regularity. However, many paintings are too large to be covered by a single x-ray. Feature point analysis exploits brushstrokes and composition to merge several x-ray images into a single one, taking into account and removing both spatial and amplitude distortions. Certain master artists used low-quality canvas that is more irregular than the norm. A theoretical study of quasi-periodic signals shows that while the expected spectrum is a peak that broadens as period irregularity increases, sample function spectra have distinct peaks having an envelope equal to the expected spectrum.

Thread counting algorithms seek to determine from x-ray images the vertical and horizontal thread counts (frequencies) of the canvas weave comprising a painting's support. Our spectral-based algorithm employs a variant of short-time Fourier analysis to the image domain that reveals isolated peaks at the proper vertical and horizontal frequencies. Paintings made on canvas sections cut from the same canvas roll have been hypothesized to have similar, distinctive weave characteristics, allowing art historians to more accurately date paintings. Spatial variation of weave frequency measurements across a painting were cross-correlated using a new measure to determine possible common weave patterns between pairs of x-rays. By analyzing a database of x-rays made from 180 paintings by van Gogh, our algorithms confirmed situations where paintings were known to have been made on canvases cut from the same roll and found new ones.

Minimum rate maximization (MRM) is a link adaptation strategy that guarantees a minimum quality of service, in terms of instantaneous signal-to-interference-plus-noise ratio, to all users in a DS-CDMA system. This is achieved by power and rate allocation that maximizes the minimum user information rate. As MRM resource allocation relies on knowledge of the channel coefficients, the achievable quality of service suffers from a degradation when the channel is dynamic and imperfectly estimated. The purpose of this paper is to add auto-regressive channel prediction to compensate for the Doppler-induced channel time-variations and improve the performance of the MRM strategy

Motivated by increasing interest in energy efficient modulations, we investigate a blind algorithm for biorthogonal signaling. While this modulation has historically been considered only for use in narrowband systems without intersymbol interference (ISI), recent attention has been given to its use in ISI channels. Due to the fact that biorthogonal modulation (BOM) results in a source that is not i.i.d., however, classical adaptive equalization techniques cannot be directly applied to equalization of BOM signals. We review the MMSE and LMS-based equalizers, and then identify some peculiarities that arise in blind equalization of BOM signals when compared to more traditional modulations like BPSK. Next, we present a novel blind algorithm, called TROMBONE, for the adaptive equalization of BOM signals. We discuss the convergence properties of this algorithm, and demonstrate its performance with numerical simulations

The turbo decoder was not originally introduced as a solution to an optimization problem, which has impeded attempts to explain its excellent performance. Here it is shown, that the turbo decoder is an iterative method seeking a solution to an intuitively pleasing constrained optimization problem. In particular, the turbo decoder seeks the maximum-likelihood sequence (MLS) under the false assumption that the input to the encoders are chosen independently of each other in the parallel case, or that the output of the outer encoder is chosen independently of the input to the inner encoder in the serial case. To control the error introduced by the false assumption, the optimizations are performed subject to a constraint on the probability that the independent messages happen to coincide. When the constraining probability equals one, the global maximum of the constrained optimization problem is the maximum-likelihood sequence detection (MLSD), allowing for a theoretical connection between turbo decoding and MLSD. It is then shown that the turbo decoder is a nonlinear block Gauss-Seidel iteration that aims to solve the optimization problem by zeroing the gradient of the Lagrangian with a Lagrange multiplier of -1. Some conditions for the convergence for the turbo decoder are then given by adapting the existing literature for Gauss-Seidel iterations

M-ary bi-orthogonal modulation or M-ary bi-orthogonal keying (MBOK) is a modulation scheme that has recently been considered for use in several consumer wireless standards, including the IEEE 802.11 WLAN standard and the ultra wideband (UWB) 802.15.3a WPAN standard. In this paper, we propose a novel blind adaptive equalizer for such signals. We then discuss the relation of the algorithm to other blind algorithms and demonstrate its local convergence. Finally, we present some numerical examples that demonstrate its features and performance.

Many previous attempts at analyzing the convergence behavior of turbo and iterative decoding, such as EXIT style analysis (ten Brink, S., 2001) and density evolution (El Gamal, H. and Hammons, A.R., Jr, 2001), ultimately appeal to results which become valid only when the block length grows rather large, while still other attempts, such as connections to factor graphs (Kshischang, F.R. et al., 2001) and belief propagation (McEliece, R.J., 1998), have been largely unsuccessful at showing convergence due to loops in the turbo coding graph. The paper presents an information geometric interpretation which, built on the results of M. Moher and T. A. Gulliver (IEEE Trans. Inform. Theory, vol.4, p.3097-104, 1998), S. Ikeda et al. (IEEE Trans. Inform. Theory, vol.50, p.1097-114, 2004), and T. Richardson (IEEE Trans. Inform. Theory, vol.46, p.9-23, 2000), allows us to relate the quantities of interest in the turbo decoder. Using it, we point out a measure which is key in studying convergence.

Many previous attempts at analyzing the convergence behavior of turbo and iterative decoding, such as EXIT style analysis (S. ten Brink, Oct. 2001) and density evolution (H. El Gamal and A. R. Hammons, Jr, Feb. 2001), ultimately appeal to results which become valid only when the block length grows rather large, while still other attempts, such as connections to factor graphs (F. R. Kshischang, et al., Feb. 2001) and belief propagation (R. J. McEliece, et al., Feb. 1998), have been largely unsuccessful at showing convergence due to loops in the turbo coding graph. The information geometric attempts (M. Moher and T. A. Gulliver, Nov. 1998), (T. Richardson, Jan. 2000), (S. Ikeda, et al., June 2004), (B. Muquest, et al., June 2002), and (J. Walsh, et al., March 2005), in turn have been inhibited by inability to efficiently describe intrinsic information extraction as an information projection. This paper recognizes turbo decoding as an instance of a Gauss-Seidel iteration on a particular nonlinear system of equations. This interpretation holds regardless of block length, and allows a connection to existing convergence results for nonlinear block Gauss Seidel iterations. We thus adapt existing convergence theory for the Gauss Seidel iteration to give sufficient conditions for the convergence of the turbo decoder that hold regardless of the block length

Channel shortening (a generalization of equalization) is often necessary for mitigation of intersymbol and intercarrier interference in multicarrier transceivers. The MERRY (multicarrier equalization by restoration of redundancy) algorithm has previously been shown to shorten a channel blindly and adaptively to the length of the guard interval in a multicarrier system. MERRY is modified to remove the square root and division needed at each iteration, with the added benefit of allowing the use of constraints other than a unit norm equalizer. An extension is proposed which allows for the use of more data in the MERRY update. The algorithm is generalized to the MIMO case. Blind symbol synchronization and initialization techniques are proposed. Simulations demonstrate the success of the algorithm and the synchronization technique in a MIMO setting.

We examine performance issues encountered when connecting two adaptive signal processing devices in a series feedforward fashion. After introducing the notion of an adaptive element, we develop a simple behavior theory for series feedforward connected adaptive elements given a few reasonable assumptions. We then move on to predict ways such interconnections of adaptive elements may misbehave. A brief example of misbehavior in a pair of interconnected adaptive receiver components is included to highlight the implications of this emerging theory.

We propose a minimum mean squared error (MMSE) decision feedback equalizer (DFE) for pulse position modulated (PPM) signals in the presence of intersymbol interference (ISI). While traditional uses of PPM may not have ISI, PPM is a candidate modulation scheme for ultra wideband (UWB), and may experience ISI in that application. First, we review the previous work on the subject which used the zero-forcing criterion under strict assumptions about the channel and equalizer lengths. Then, we derive a computationally efficient MMSE equalizer which removes these restrictions, and is suitable for use with stochastic gradient descent algorithms. Finally, we demonstrate the performance of the proposed equalizer with simulations.

During initialization, discrete multitone receivers train a time domain equalizer (TEQ) to shorten the channel impulse response to a preset length, /spl nu/+1. G. Arslan et al. report a minimum intersymbol interference (Min-ISI) method for TEQ design (see IEEE Trans. Sig. Process., vol.49, no.12, p.3123-35, 2001). Min-ISI TEQs give the highest bit rates among single-FIR TEQs amenable to real-time implementation on programmable fixed-point digital signal processors (DSPs). The Min-ISI method, however, has several disadvantages: (1) sensitivity to transmission delay; (2) inability to design TEQs longer than /spl nu/+1 taps; (3) sensitivity to the fixed-point computation in the Cholesky decomposition. We develop an alternate Min-ISI cost function, from which we derive: (1) a fast search method for the optimal transmission delay; (2) extensions to design arbitrary-length Min-ISI TEQs; (3) an iterative Min-ISI method. The iterative Min-ISI method avoids Cholesky decomposition, designs arbitrary length TEQs, and achieves the bit rate performance of the original Min-ISI method.

Time-domain equalization is crucial in reducing intercarrier and intersymbol interference in multicarrier systems. A channel shortening time-domain equalizer (TEQ), which is a finite impulse response (FIR) filter, placed in cascade with the channel, produces an effective impulse response that is shorter than the channel impulse response. We show that finite length minimum mean squared error (MMSE) and maximum shortening SNR (MSSNR) TEQs are approximately symmetric, and infinite length MSSNR TEQs with a unit norm TEQ (UNT) constraint are exactly symmetric. A symmetric TEQ halves FIR implementation complexity, enables the frequency-domain equalizer and TEQ to be trained in parallel, and exhibits only a small loss in bit rate over nonsymmetric TEQs. In addition, a symmetric MSSNR-UNT TEQ reduces training computational complexity by a factor of 4 and doubles the length of the TEQ that can be designed.

We characterize the nonlinear distortion of frequency-shift keying (FSK) signals due to a multipath channel as a linear time varying channel. The dynamic range of time variation of this time-varying channel model is small for a mild multipath channel and large for a severe multipath channel. This characterization justifies the use of a decision directed adaptive linear equalizer for FSK signals after frequency demodulation in order to mitigate the distortion due to a multipath channel.

This letter exploits the cyclic prefix to create a blind adaptive globally convergent channel-shortening algorithm, with a complexity like least mean squares. The cost function is related to that of the shortening signal-to-noise solution of Melsa et al. (see IEEE Trans. Commun., vol.44, p.1662-72, Dec. 1996), and simulations are provided to demonstrate the performance of the algorithm.

This paper provides a stability analysis of a class of acoustic noise control algorithms by showing that the adapted models have more in common with nonlinear, finite impulse response (FIR) equation error models than with the infinite impulse response (IIR) output error models they superficially resemble. Stability results from the adaptive control literature are applied to show global stability in the noise free case, and to show exponential stability when the input is persistently excited. The latter demonstrates a robustness to mismodeling errors, disturbances such as noises, and allows results to be applied to the tracking of time-varying systems.

This paper analyzes the performance of the linear parallel interference cancellation (LPIC) multiuser detector in a synchronous multiuser communication scenario with binary signaling, nonorthogonal multiple access interference, and an additive white Gaussian noise channel. The LPIC detector has been considered in the literature lately due to its low computational complexity, potential for good performance under certain operating conditions, and close connections to the decorrelating detector. In this paper, we compare the performance of the two-stage LPIC detector to the original multistage detector proposed by Varanasi and Aazhang (1990, 1991) for CDMA systems. The general M-stage LPIC detector is compared to the conventional matched filter detector to describe operating conditions where the matched filter detector outperforms the LPIC detector in terms of error probability at any stage M. Analytical results are presented that show that the LPIC detector may exhibit divergent error probability performance under certain operating conditions and may actually yield error probabilities greater than 0.5 in some cases. Asymptotic results are presented for the case where the number of LPIC stages goes to infinity. Implications of the prior results for code division multiple access (CDMA) systems with random binary spreading sequences are discussed in the "large-system" scenario. Our results are intended to analytically corroborate the simulation evidence of other authors and to provide cautionary guidelines concerning the application of LPIC detector to CDMA communication systems.

This paper introduces a blind adaptive carrier phase offset recovery scheme based on the constant modulus (CM) algorithm and analyzes its behavior. The proposed CM-derotator (CMD) minimizes the dispersion of the real projection of the derotated signal to remove the phase offset of the signal. By analyzing the cost function, the performance of the CMD is investigated in various situations including its tracking ability, its behavior in the presence-of intersymbol interference, and when there are statistical dependencies between the in-phase and quadrature components.

The vector-constant modulus (VCM) criterion is an extension of the constant modulus (CM) criterion introduced recently for equalization of channels involving Gaussian sources. In this letter, we analyze the behavior of VCM for arbitrary source distributions and combined channel-receiver impulse responses of finite dimension. We begin by pointing out the difference between the VCM and CM cost functions and showing that the VCM criterion can be expressed as a composite criterion combining the CM cost function and a penalty term involving cross-correlations of the equalizer output. We continue by providing conditions for noise-free channels, under which VCM admits stable minima corresponding to zero-forcing (ZF) channel receivers. We find that for sub-Gaussian sources, the VCM and CM criteria share the same global minima. For Gaussian and super-Gaussian sources, however, it appears that only ZF receivers corresponding to input/output transmission delays at the extremes of the range of possible delays are truly stable equilibria of VCM.

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, we present an upper bound for the conditionally unbiased mean-squared error (UMSE) 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.

We consider multiuser detection techniques for an eavesdropping receiver in an IS-95 cellular communication system observing interfering downlink transmissions from a cluster of B base stations. The receiver desires to accurately estimate the symbols transmitted from these base stations to their active local users. For a system with K total asynchronous users and an observation of 2L+1 bits, the optimum detector is reviewed and shown to have complexity on the order of 2/sup K(2L+1)/. Taking advantage of the structure of the IS-95 downlink, we develop a reduced complexity optimum detector with exponentially lower complexity. In typical scenarios with two or three base stations, the reduced complexity optimum detector is significantly less complex than the brute-force optimum detector. We also consider a suboptimum, low complexity IS-95 downlink eavesdropping detector with connections to reduced complexity optimum detection as well as group detection and parallel interference cancellation. We demonstrate via simulation that the performance of this receiver can be near-optimum while offering very low computational complexity.

We consider a generic blind adaptive DFE initialization strategy which begins with blind adaptation of a linear structure minimizing MSE followed by a switch to decision-direction under the nonlinear DFE structure. We show that this very natural scheme is not always successful in reaching the switching threshold, particularly for high order constallations, and for designs using short length filters. Furthermore, we review two previously proposed DFE initialization procedures that are based on a similar philosophy, and show that they share the advantages and shortcomings of this strategy.

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 CM local 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 sufficient conditions under which gradient descent (GD) minimisation of CM 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).

Adaptive blind equalization has gained widespread use in communication systems that operate without training signals. In particular, the constant modulus algorithm (CMA) has become a favorite of practitioners due to its LMS-like complexity and desirable robustness properties. The desire for further reduction in computational complexity has motivated signed-error versions of CMA, which have been found to lack the robustness properties of the CMA. This paper presents a simple modification of signed-error CMA, based on the judicious use of dither, that results in an algorithm with robustness properties closely resembling those of CMA. An approximation to the steady-state mean-squared error performance of the new algorithm is derived for comparison to that of CMA.

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 decisions 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.

The Godard (1980) or the constant modulus algorithm (CMA) is an effective technique for blind receiver design in communications. However, due to the complexity of the constant modulus (CM) cost function, the performance of the CM receivers has primarily been evaluated using simulations. Theoretical analysis is typically based on either the noiseless case or approximations of the cost function. The following question, while resolvable numerically for a specific example, remains unanswered in a generic manner. In the presence of channel noise, where are the CM local minima and what are their mean-squared errors (MSE)? In this paper, a geometrical approach is presented that relates the CM to Wiener (or minimum MSE) receivers. Given the MSE and the intersymbol/user interference of a Wiener receiver, a sufficient condition is given for the existence of a CM local minimum in the neighborhood of the Wiener receiver. The MSE bounds on CM receiver performance are derived and shown to be tight in simulations. The analysis shows that, while in some cases the CM receiver performs almost as well as the (nonblind) Wiener receiver, it is also possible that, due to its blind nature, the CM receiver may perform considerably worse than a (nonblind) Wiener receiver.

For pt. I see Proc. 1st IEEE Workshop on Signal Proc. Advances in Wireless Comm., 1997. This paper studies the constant modulus (CM) criterion specifically for the case where the time span of the fractionally-spaced equalizer (FSE) is less than that of the channel. Hence, there necessarily exists an error in the equalized signal. Results for the binary case (Part I) are extended to multi-level signalling. This analysts is connected with the previous work of Fijalkow et al. (see IEEE Trans. on Signal Proc., 1995) on misadjustment of a CM receiver to suggest a finite interval of acceptable FSE length which shows that a longer FSE may not be better than a shorter FSE-in some cases, matching the FSE length to that of the channel may not reduce the MSE to a prescribed threshold, while a shorter FSE may be successful in achieving this threshold.

The constant modulus algorithm (CMA) is a popular blind equalization algorithm. A common device used in demonstrating the convergence properties of CMA is the assumption that the source sequence is i.i.d. (independent, identically distributed). Previous results in the literature show that a finite length fractionally-spaced equalizer allows for perfect equalization of moving average channels (under certain channel conditions known as zero-forcing criteria). CMA has previously been shown to converge to such perfectly equalizing settings under an independent, platykurtic source. This paper investigates the effect of the distribution from which an independent source sequence is drawn on the CMA error surface and stationary points in the perfectly-equalizable fractionally-sampled equalizer case. Results include symbolic identification of all stationary points, as well as the eigenvalues and eigenvectors associated with their Hessian matrix. Results show quantitatively the loss of error surface curvature (in both direction and magnitude) at all stationary points. Simulations included demonstrate the affect this has on convergence speed.

A number of papers have studied blind channel identification/equalization algorithms relying purely on second-order statistics of the fractionally sampled received signal. A class of cyclic allpass channels is shown to be the only class of IIR channels whose cascade with a core channel results in no change in the second-order-statistics indicators used by several of these algorithms. FIR approximations to the poles of these allpass channels result in robustness concerns for the second-order-statistics algorithms, even when FIR identifiability conditions are well satisfied. This sensitivity suggests that excluding only those channels with common subchannel roots is insufficient when applying these second-order-statistics algorithms.

In this letter, we extend results regarding the behavior of a symbol-spaced tapped-delay-line LMS-adapted equalizer in frequency domain terms to a fractionally spaced implementation. These results rely on an eigendecomposition of the autocorrelation matrix of the received signal. In fractionally spaced equalization systems, the output of the analog channel is oversampled, resulting in a cyclostationary signal. We derive its autocorrelation matrix. A symbol-spaced representation of the combined channel, equalizer and downsampling device is formed in the frequency domain, and the convergence rate of the time-domain LMS algorithm is described in the frequency domain.

Under certain conditions on the equalizer length and on the channel dynamics, temporal or spatial diversity allows one to achieve blind equalization perfectly by means of second-order statistics only. Loss of channel disparity causes perfect equalization to no longer be achievable. The achievable channel-equalizes combination then depends only on the part of the multichannel transfer function lacking disparity. We show that the fractionally spaced equalizer adapted by the constant modulus algorithm (FSE-CMA) still achieves "reasonable" equalization. Its performance equals that of the non-fractional CMA, with a slightly shorter baud-length equalizer than the FSE, applied to the part of the channel lacking disparity.

CMA fractionally spaced equalizers (CMA-FSEs) have been shown, under certain conditions, to be globally asymptotically convergent to a setting which provides perfect equalization. Such a result relies heavily on the assumptions of a white source and no channel noise (as is the case in much of the literature's analysis of CMA). Herein, we relax the white source assumption and examine the effect of source correlation on CMA. Analytic results are meshed with examples showing CMA-FSE source correlation effects. Techniques for finding all stationary and saddle points on the CMA-FSE error surface are presented using recent developments in the algebraic-geometry community.

We examine the implications of our recent analysis of the local minima escape behavior of the Godard (or CMA) blind equalizer. This analysis suggests asymptotic estimates for the expected value of the escape time when leaving the region of attraction of local equilibria. For a particular source, channel, and equalizer local minimum parameterization, the log of the inverse of the mean escape time is estimated to be proportional to a weighted sum of the stepsize and the channel noise variance. We examine the validity of the functional form of this relationship for two examples. This experimental evidence corroborates our earlier analysis and suggests that the mean time to escape can be very large for the Godard (1980) algorithm (also known as the constant modulus algorithm).>

A variety of blind equalization algorithms exist. These algorithms, which draw on some theoretical justification for the demonstration or analysis of their purportedly ideal convergence properties, almost invariably rely on the input data being independent and identically distributed (i.i.d.). In contrast, in this paper we show that input correlation can have a marked effect on the character of algorithm convergence. We demonstrate that under suitable input data correlation and channels: (i) undesirable local minima present in the i.i.d. case are absent for certain correlated sources implying ideal global convergence for some situations and, (ii) the most commonly employed practical algorithm can exhibit ill-convergence to closed-eye minima even under the popular single spike initialization when an eye-opening equalizer parameterization is possible.>

An approximate gradient descent algorithm is proposed for adaptive calibration of the composite error system associated with the transmitter-receiver of a recently proposed scheme for secure communication based on synchronized chaos.>

The algorithms for adaptive quantization and adaptive prediction in existing adaptive differential pulse code modulation (ADPCM) are distinct and decoupled. The designs of the two algorithms are based on the assumption that they act independently whereas, due to the feedback configuration, they must interact in some way. The authors present a preliminary investigation of a new design approach where they perform joint adaptation based on a common cost function, considering the overall system. A “backward” adaptive algorithm is presented and applied to a simple example to demonstrate the feasibility of the general approach.

An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Y. Sato (1975). An important generalization of the Sato algorithm with extensive analysis appears in the work of A. Benveniste et al. (1980). These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results.>

It is shown, through the analysis of nullspace for the channel convolution matrix, that the behavior of a finitely parameterized Godard equalizer in general can never achieve or approximate the desirable global convergence performance of an infinitely parameterized noncausal Godard equalizer. Nullspace theory is supported by a simple example showing ill-convergence of the Godard algorithm.>

The existence of stable undesirable equilibria for the Godard algorithm is demonstrated through a simple autoregressive (AR) channel model. These undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function, and thus permit the ill-convergence of the Godard algorithms which are stochastic gradient descent in nature. Simulation results confirm predicted misbehavior. For channel input of constant modulus, it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization. A criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached.>

Clarification is presented of the property that adaptive blind equalization algorithms may not always result in desired convergence. Those algorithms that can always converge (perhaps with the aid of a special initialization strategy) to desired equilibria offering an open eye pattern are classified as admissible. Various classes of existing blind equalization algorithms are described and the possibility of ill-convergence for these algorithms is illustrated. The general inadmissibility and the reason for earlier misconception regarding their admissibility development of new, admissible algorithms and certain initialization guidelines that can prevent weakly admissible algorithms from converging to undesirable equilibria is established.>

The sign-sign adaptive least-mean-square (LMS) identifier filter is a computationally efficient variant of the LMS identifier filter. It involves the introduction of signum functions in the traditional LMS update term. Consideration is given to global convergence of parameter estimates offered by this algorithm, to a ball with radius proportional to the algorithm step size for white input sequences, specially from Gaussian and uniform distributions.>

The constant modulus algorithm (CMA) and decision-directed (DD) equalizer are two ways to approach blind equalization of signals that are known to lie on a circle of fixed radius, but where specific values at any given time are unknown. In m-ary quadrature amplitude modulation, the signals lie on n circles of known radius. The authors present two possible approaches to the n-modulus problem, both in the spirit of feature reconstruction algorithms. The multiple-modulus algorithm uses a straightforward generalization of the CMA cost function to derive its update, whereas the decision-adjusted-modulus algorithm is a hybrid of the CMA and DD approaches.>

Adaptive echo cancellation is being used on shorter telephone circuits. However, while echo cancelers do tend to be effective on the shorter circuits, a new (and undesirable) phenomena called bursting has been observed. Bursting is characterized by long periods of successful echo attenuation alternating with short periods of wildly oscillating signals. The authors studied bursting by constructing a pair of simplified models of adaptive hybrid systems. The models are analyzed when they are excited by various DC and sinusoidal inputs, and the results are related back to the systems of interest, providing insight into the fundamental sources of the bursting problem-an imbalance of excitation and the enclosure of an adaptive filter in a feedback loop. Simulations providing corroborating evidence are discussed.>

Adaptive filtering techniques have been successfully applied to attenuate echoes in long-distance telephone communications. Recently, with the increased ability to process signals cheaply, adaptive echo cancellation is being utilized on shorter telephone circuits. To avoid the possibility of entrapment in an echo-canceller initialization that causes singing, doubletalk detectors cannot be used aggressively on such highly variable short connections. While echo cancelers tend to be effective on the shorter circuits, in the absence of doubletalk detectors a novel (and undesirable) phenomenon called bursting has been observed in real-time laboratory tests of such applications. Bursting is characterized by long periods of successful echo attenuation alternating with short periods of wildly oscillating signals. By analyzing a simplified abstraction of this problem, a theoretical explanation is presented of the kernel of the bursting problem: an imbalanced excitation combination. The structural source of the problem is the use of an adaptive filter in a feedback loop.>

A family of Quantized State (QS) adaptive algorithms is introduced. These are computationally simple versions of the LMS adaptive algorithm and are useful in two ways: as numerically fast implementations for adaptive tasks, and as a tool for studying the LMS algorithm in a quantized environment. Averaging theory is used to derive a persistence of excitation (PE) condition which guarantees exponential stability of one member of the QS family. Failure to meet this condition (which is not equivalent to the spectral richness PE condition for LMS) can result in exponential instability, even with the use of fixed leakage, showing that the stability properties of QS algorithms are heavily dependent on the character of the input sequence.

It has been shown by example that the often used sign-sign variant of the LMS can be unstable and produce unbounded parameter estimates. In this paper a modified sufficient excitation condition on the regressor vector for the sign-sign variant is introduced. Satisfaction of the excitation condition guarantees that there exists a sufficiently small step size to produce parameter estimates which converge exponentially to within a region of the correct parameters. The counter example to stability of sign-sign algorithms is reexamined in light of the new excitation condition and it is shown that the excitation condition correctly predicts when instability will occur in this example.

A tutorial-style framework is presented for understanding the current status of adaptive infinite-impulse-response (IIR) filters. The paper begins with a detailed discussion of the difference equation models that are useful as adaptive IIR filters. The particular form of the resulting prediction error generic to adaptive IIR filters is highlighted and the structures of provable convergent adaptive algorithms are derived. A brief summary of particular, currently known performance properties, drawn principally from the system identification literature, is followed by the formulation of three illustrative adaptive signal processing problems, to which these adaptive IIR filters are applicable. The concluding section discusses various open issues raised by the formulation of this framework.

An original adaptive, infinite-impulse-response (IIR) feedback, line-enhancer structure is proposed as an adaptive differential pulse code modulation (ADPCM) algorithm. The underlying parameter estimation problem is formulated and a minor variation on the recursive maximum likelihood (RML) algorithm is suggested. Simulated tests measuring SNR improvement provide preliminary support of the feasibility of such a scheme.

A perturbed error system is developed to describe the parameter and output error behaviors of reduced-order application of adaptive identifier/ filters such as the hyperstable adaptive recursive filter (HARF). Given satisfaction of a sufficient excitation condition, this error system is shown to exhibit a bounded-input, bounded-output (BIBO) property. This implies that despite order insufficiency the output and parameter estimates of HARF (and similar adaptive identifier/filter algorithms) remain bounded.

Presently, for provable global stability and unbiasedness in the presence of zero-mean, colored output measurement noise, adaptive infinite impulse response (IIR) filters (or adaptive output error identifiers) require a restrictive SPR condition on the transfer function dividing the error smoothing coefficient polynomial by the unknown desired denominator. This paper considers two attempts to bypass this restriction by incorporating error smoothing coefficient adaption. This paper clearly identifies the possible stall/failure mechanism of one of these candidate algorithms and proves the global stability of the other, but notes the equation error type source of the second's biased-ness in the presence of output measurement noise.

In previous papers the authors have developed and characterized SHARF and HARF, algorithms for adaptive IIR digital filters. This paper considers a practical problem in which adaptive IIR filtering can be applied to advantage: the removal of multi-path effects from television video ("ghosting"). The problem is motivated, a solution based on adaptive IIR filtering is developed, and simulation results are presented. Also discussed are several analytical results developed in this inquiry, including the formulation and proof of a complex data and coefficient version of SHARF (and HARF), and a treatment of the effects of additive noise.

This paper unifies a rapidly growing area of inquiry: adaptive infinite impulse response (IIR) filter development and evaluation. A class of stably convergent adaptive IIR filters has evolved from a proven adaptive IIR filter with an auto-regressive, moving-average (ARMA) structure. The convergence proof was originally based on a hyperstability evaluation of an identification format. This paper relates this format to those arising from other applicable nonlinear stability theory results. These interrelationships allow statement of a growing list of adaptive IIR filter properties. The alternate search/minimization technique of adaptive IIR filler development is also derived and contrasted. This results in a proposal of a general adaptive filter algorithm.

In previous work the authors have developed a class of provably convergent adaptive algorithms for digital IIR filters based on the concept of hyperstability. While this class of adaptive filters offers much promise in practical applications little has been done toward providing the characterization that would allow a designer to select filter order, adaptation constants, and other design parameters. This paper reports on the initial effort toward providing this information through an investigation of the local convergence behavior of SHARF, the simple hyperstable adaptive recursive filter.

Several authors have suggested various methods of implementing an adaptive IIR filter. This paper suggests that hyperstability and associated positivity concepts can be used to determine the regions of assured convergence for adaptive IIR filter algorithms. This hyperstability interpretation is applied to the adaptive recursive LMS filter, for which it is demonstrated that convergence appears assured if the transfer function formed from the denominator (in z-1) of the transfer function effectively being modelled and a unity numerator is strictly positive real. Examples show that this plausibly sufficient condition, though not necessary, loosely approximates the region of applicability, which seriously restricts the utility of this attractively simple adaptive synthesis method. Slight modifications, suggested by the hyperstability approach, can favorably alter the positive-real "convergence" region with subsequent dramatic improvement in applicability and convergence speed.