The black-box domain adaptation (BBDA) topic is developed to address the privacy and security issues where only an application programming interface (API) of the source model is available for domain adaptations. Although the BBDA topic has attracted growing research attentions, existing works mostly target the vision applications and are not directly applicable to the time-series applications possessing unique spatio-temporal characteristics. In addition, none of existing approaches have explored the strength of foundation model for black box time-series domain adaptation (BBTSDA). This paper proposes a concept of Cross-Prompt Foundation Model (CPFM) for the BBTSDA problems. CPFM is constructed under a dual branch network structure where each branch is equipped with a unique prompt to capture different characteristics of data distributions. In the domain adaptation phase, the reconstruction learning phases in the prompt and input levels are developed. All of which are built upon a time-series foundation model to overcome the spatio-temporal dynamic. Our rigorous experiments substantiate the advantage of CPFM achieving improved results with noticeable margins from its competitors in three time-series datasets of different application domains.

This paper focuses on the angle-of-arrival (AOA) target tracking problem using a mobile unmanned aerial vehicle (UAV) equipped with an angle-of-arrival (AOA) sensor to observe targets in an external-denied (no global positioning system, inertial navigation system aid) environment. The mathematical formulations are based on two known anchors. The extended Kalman filter (EKF) is modified to calculate the UAV’s and target’s absolute coordinates. To improve the tracking accuracy, a gradient-based UAV path optimization algorithm using simultaneous perturbation stochastic approximation (SPSA) is developed. The geometry of anchors and UAV impacts the estimation accuracy, especially when the selected anchors are close to the target. The simulations have demonstrated the effectiveness of the proposed scheme.

The computational complexity of adaptive filtering algorithms increases with the number of filter coefficients. In applications where a long adaptive filter is required, the complexity can become prohibitively large due to scarce digital signal processing (DSP) resources such as the available DSP slices on a field programmable gate array (FPGA). Several partial-update least mean square (PU-LMS) algorithms have been proposed to address this problem. Among these algorithms, the sequential PU-LMS alleviates the computational complexity by updating a small subset of adaptive filter coefficients in a round-robin fashion at each iteration. Being data independent, it has no complexity overheads associated with coefficient selection. However, a major problem with the sequential PU-LMS is its vulnerability to poor convergence for cyclostationary input signals encountered in many practical applications. This letter presents a detailed analysis of the convergence issues with the sequential PU-LMS algorithm for cyclostationary white Gaussian input signals. The convergence analysis predicts when poor convergence is likely to occur based on a relationship between partial update and cyclostationary input signal parameters. The insights gained through this analysis can be used to adjust the sequential partial update parameters in order to avoid convergence difficulties. Simulation examples are presented to confirm the validity of the convergence analysis conducted.

Differential received signal strength (DRSS) provides a practical means of localisation for wireless sensor networks. Closed-form location estimators based on a linearised propagation path loss model are computationally efficient and hence suitable for wireless sensor nodes. However, most existing solutions suffer from a significant bias arising from the injection of noise into the measurement data matrix caused by the linearisation process. The instrumental variable (IV) method can reduce the bias by replacing the data matrix with a matrix that is weakly correlated with the noise and strongly correlated with the data matrix - the latter correlation however can be weakened by large noise. This paper addresses the bias problem when the noise is large by using the method of selective power measurement to maintain correlation between the instrumental variable and data matrix. Simulation results show the proposed solution out-performs other existing solutions in terms of the root mean square error (RMSE) and bias over a wide range of noise levels.

A two-step pseudolinear Kalman filter (2S-PLKF) was previously proposed for angle-of-arrival (AOA) target tracking in three-dimensional space drawing on the pseudolinear rearrangement of nonlinear azimuth and elevation angle measurement equations. Despite enjoying low computational complexity, this algorithm suffers from a severe bias problem arising from the nonlinear-to-linear transformation of the angle measurement equations. This paper presents a new two-step instrumental-variable Kalman filter (2S-IVKF) exploiting the use of pseudolinear estimation, as well as instrumental-variable estimation to overcome the bias problem. The performance advantage of the proposed 2S-IVKF algorithm over the 2S-PLKF, as well as extended and sigma-point Kalman filters is demonstrated with simulation examples.

This letter proposes a novel bias-compensated diffusion pseudolinear Kalman filter algorithm for censored bearings-only target tracking. The proposed algorithm considers two biases caused by the censored bearing angle measurements and the correlation between the measurement vector and the pseudolinear noise. First, the inverse Mills ratio is used to rebuild the uncensored measurements, which can efficiently compensate the bias arising from the censored measurements. Then, we present a bias analysis for the censored diffusion pseudolinear Kalman filter to develop a bias compensation method, leading to the BC-DPLKF-C algorithm. Simulation results show the improved performance of the proposed Kalman filter compared with existing algorithms.

This paper considers the problem of angle-of-arrival (AOA) source localization with Bayesian priors. Extending the so-called pseudolinear estimator (PLE) for AOA localization to the Bayesian framework results in the Bayesian PLE (BPLE). Similar to the PLE, the BPLE suffers from severe bias problems despite enjoying the inherent stability and computational simplicity of a closed-form least-squares estimator. Bayesian priors make bias compensation for the BPLE much more challenging than the PLE. We present a bias analysis for the BPLE from which two direct bias compensation methods are developed. As an alternative to direct bias compensation, a new approach with superior estimation performance and low computational complexity is then proposed by exploiting jointly the use of instrumental variables and 2-D unscented (or cubature) transformation. The resulting estimator, referred to as the bias-compensated Bayesian weighted instrumental variable estimator, enjoys the desirable properties of negligible bias and mean-squared error on par with the computationally demanding an iterative maximum a posteriori estimator. The comparative simulation studies are presented to corroborate the performance advantages of the proposed estimators.

This paper develops a new computationally efficient bias reduction method for the well-known algebraic closed-form solution for time-difference-of-arrival (TDOA) localization developed by Chan and Ho. The noise correlation between the regressor and regressand in the formulation of the linearized least-squares computation is the main cause of bias problems associated with this TDOA localization method. The bias reduction method proposed in this paper, which we call IV- BiasRed, exploits the use of instrumental variables (IV) to eliminate the troublesome noise correlation between the regressor and regressand. The IV- BiasRed method is demonstrated by way of simulations to achieve a significant bias reduction and mean-squared error performance close to the Cramér-Rae lower bound. While producing an estimation performance on par with the maximum likelihood estimator and a recently proposed bias reduction method, the proposed IV-BiasRed method is computationally much more efficient than existing bias reduction methods.

In Doppler-bearing source localization, pseudolinear estimators are appealing alternatives to the divergence-prone and computationally-demanding iterative maximum likelihood estimator. Among the existing pseudolinear estimators, the weighted instrumental variable estimator (WIVE) is the most attractive option as it is asymptotically unbiased and efficient. However, the asymptotic unbiasedness of the WIVE relies on the approximation that the second-order noise term in the Doppler pseudolinear noise is zero, which is only valid for sufficiently small noise. In large noise, the second-order noise term can no longer be neglected, thereby leading to biased estimates. In this paper, we analyze the WIVE bias and propose a new improved version of the WIVE, called the I-WIVE, that overcomes the WIVE bias problems at large noise levels. The superior performance of the I-WIVE over the WIVE and other pseudolinear estimators is demonstrated by way of simulations. Specifically, we observe that the I-WIVE exhibits a negligible bias and produces a mean-squared error closest to the Cramér-Rae lower bound among the simulated estimators.

This letter presents a new three-dimensional (3-D) instrumental variable based Kalman filter (3D-IVKF) algorithm for angle-of-arrival target tracking from azimuth and elevation angle measurements. First, a 3-D pseudolinear Kalman filter (KF) algorithm is derived by applying the classical linear KF to a pseudolinear state-space model. To counter the severe bias problems with this algorithm, bias compensation and recursive instrumental variable (IV) methods are considered. A selective-angle-measurement strategy is also adopted to satisfy requisite conditions for IV estimation. The resulting 3D-IVKF algorithm inherits the low computational complexity and robust performance of pseudolinear estimation techniques. It is shown through simulation examples that the 3D-IVKF algorithm can achieve a similar tracking performance to the sigma-point KFs by producing a negligible bias and a mean-square error close to the posterior Cramér-Rao lower bound at a much reduced computational complexity, while outperforming the extended KFs at high noise levels.

This paper presents new closed-form estimators for 3-D source localization using Doppler measurements collected by a moving sensor platform. Two estimators, based on bias compensation and instrumental variables, are developed with significant performance improvement over a previously proposed least-squares estimator (LSE). First, a refined variant of the LSE, called bias-compensated weighted LSE (BCWLSE), is presented utilizing a weighting matrix and a bias compensation step. A weighted instrumental variable estimator is then developed based on a modified pseudolinear equation for the LSE to avoid pseudolinear noise amplification that may deteriorate the BCWLSE performance at large noise. Comparative simulation studies are presented to demonstrate the performance advantages of the proposed estimators over the severely biased LSE and divergence-prone maximum likelihood estimator. The proposed estimators are observed to produce almost no bias and achieve a mean-squared-error performance close to the Cramér-Rao lower bound.

Closed-form pseudolinear estimators are computationally attractive alternatives to iterative nonlinear techniques. For time-of-arrival (TOA) based localization, several pseudolinear estimators have been proposed such as the least squares calibration (LSC) estimator, the linear least squares (LLS) estimator, and their best linear unbiased estimator (BLUE) variants (namely, the BLUE-LSC and BLUE-LLS estimators). Despite their stable performance and low computational complexity, these pseudolinear estimators suffer from bias problems due to the nonzero mean of the pseudolinear noise vectors. In this paper, we present a bias analysis for the TOA-based pseudolinear estimators. Based on the bias analysis we develop bias compensation methods that lead to new bias-compensated versions of the LSC, LLS, BLUE-LSC and BLUE-LLS estimators. The superior performance of the proposed bias-compensated estimators is demonstrated via numerical simulations. The new estimators are observed to exhibit negligible estimation bias even at high measurement noise levels.

This paper presents a new algebraic solution for the Doppler positioning problem where the position of a stationary emitter is estimated from Doppler frequency measurements collected by a single low-earth-orbit (LEO) satellite. The proposed algebraic solution can be used for effective initialization of more sophisticated iterative algorithms as it produces estimates sufficiently close to the actual position of the emitter to ensure convergence. It is computationally more efficient than existing initialization techniques, based on the point of closest approach, which require expensive nonlinear curve fitting procedures. The effectiveness of the proposed algebraic solution is demonstrated by way of numerical simulations.

This paper investigates the problem of how to optimize the path of a single moving own-ship for angle-of-arrival (AOA) target tracking in three-dimensional (3D) space. First, a novel 3D pseudolinear Kalman filter (PLKF) is proposed to reduce computational complexity and to improve stability of an extended Kalman filter solution. This filter consists of an xy-PLKF and a z-PLKF, transforming the nonlinear azimuth and elevation angle measurements into pseudolinear models. We show that when the own-ship and target are at the same height, the z-PLKF will be unbiased. Next, a gradient-descent path optimization algorithm is developed for the xy-PLKF aiming at minimizing the trace of the covariance matrix. Then, a grid search path optimization method is designed for the z-PLKF. Simulation examples verify the effectiveness of the proposed path optimization algorithm.

This paper is concerned with unmanned aerial vehicle (UAV) path optimization for AOA target localization via distributed processing. A distributed UAV path optimization algorithm based on gradient descent method is developed using the diffusion extended Kalman filter (DEKF). With this algorithm, a group of UAVs can realize self-adaptive path optimization in order to improve estimation performance. The presented distributed path optimization strategy aims to minimize the estimation mean squared error (MSE) by minimizing the trace of the error covariance matrix. The UAV dynamic communication topology caused by communication range constraint is analyzed. Furthermore, the UAV 6-degree-of-freedom (DOF) dynamic modeling is taken into consideration to generate realistic UAV trajectories. The properties and effectiveness of the proposed algorithm are discussed and verified with simulation examples.

We develop a fully-distributed iterative algorithm for finding a model-distributed least-squares solution of systems of linear equations over sensor networks. Here, model-distributed means the solution vector is distributed across the network rather than being replicated at each node. For this purpose, we devise a dual regularized least-squares problem via a suitable decomposition of the normal equations associated with the original problem. The resultant dual problem can be solved in a fully-decentralized and iterative manner by means of the diffusion-based Pareto optimization strategy. We verify the usefulness of the proposed algorithm via both theoretical analysis and numerical examples.

This paper derives the optimal angular geometry for elliptic time-of-arrival localization by a multistatic radar consisting of multiple independent bistatic channels. The optimal geometry analysis is conducted based on minimization of the area of the estimation confidence region which is equivalent to maximizing the determinant of the Fisher information matrix. It is shown that the optimal angular geometry is obtained when the transmitter and receiver of each bistatic channel are collinear with the target where the target is placed at the either end. The optimization problem therefore boils down to determination of the optimal angular separation between different bistatic channels which is mathematically equivalent to the optimal angular sensor separation for angle-of-arrival localization. These analytical results are confirmed by simulation examples.

This paper investigates the problem of how to improve angle-of-arrival (AOA) target localization accuracy by finding an optimal AOA sensor deployment strategy in 3D space. Under the assumption of constant absolute elevation angles for the sensors, a novel and simple optimal sensor deployment criterion is proposed based on minimizing the trace of inverse Fisher information matrix. Our analysis shows that when sensor elevation angles equal ±42.2869° and twice of azimuth angles have equal angular distribution with uniform distance from the target and equal noise covariance, the lowest mean squared error is achieved. Besides, with more sensors placed closer to the target, a lower mean squared error is attained. Simulation examples are presented to verify the effectiveness of the developed optimality criterion.

An adaptive waveform scheduling algorithm is presented for target tracking by a multistatic radar system with two key components: (i) a distributed multistatic tracking algorithm for target tracking in cluttered environments, and (ii) the next transmitted waveform selected to minimize the tracking mean squared error. The scheduling algorithm is developed based on the minimization of the trace of the expected tracking error covariance matrix. A simulation example is presented to demonstrate the superiority of the proposed waveform scheduling algorithm over conventional fixed waveforms.

Acoustic echo cancellation and feedback cancellation systems require robust and computationally efficient adaptive filtering techniques. In this paper, a new affine projection algorithm with intermittent update of the filter coefficients is proposed where the update interval is determined according to the adaptation state. Simulation results show that the proposed algorithm provides improved performance and reduced average computational complexity compared with other similar algorithms for acoustic echo cancellation and acoustic feedback cancellation applications.

We examine the problem of estimating the frequency of a three-phase power system in an adaptive and low-cost manner when the voltage readings are contaminated with observational error and noise. We assume a widely-linear predictive model for the αβ complex signal of the system that is given by Clarke's transform. The system frequency is estimated using the parameters of this model. In order to estimate the model parameters while compensating for noise in both input and output of the model, we utilize the notions of total least-squares fitting and gradient-descent optimization. The outcome is an augmented gradient-descent total least-squares (AGDTLS) algorithm that has a computational complexity comparable to that of the complex least mean square (CLMS) and the augmented CLMS (ACLMS) algorithms. Simulation results demonstrate that the proposed algorithm provides significantly improved frequency estimation performance compared with CLMS and ACLMS when the measured voltages are noisy and especially in unbalanced systems.

We develop a gradient-descent distributed adaptive estimation strategy that compensates for error in both input and output data. To this end, we utilize the concepts of total least-squares estimation and gradient-descent optimization in conjunction with a recently-proposed framework for diffusion adaptation over networks. The proposed strategy does not require any prior knowledge about the noise variances and has a computational complexity comparable to the diffusion least mean square (DLMS) strategy. Simulation results demonstrate that the proposed strategy provides significantly improved estimation performance compared with the DLMS and bias-compensated DLMS (BC-DLMS) strategies when both the input and output signals are noisy.

A new set-membership adaptive filtering algorithm is developed based on the exponentially-weighted RLS algorithm with a time-varying forgetting factor that is optimized at each iteration by imposing a bounded-magnitude constraint on the a posteriori filter output error. The new algorithm is designed to improve the numerical behavior of the previously proposed BEACON algorithm while delivering the same convergence and tracking performance as the BEACON algorithm. Simulation results for a flat-fading MIMO channel estimation application demonstrate the superiority of the new algorithm over the BEACON algorithm in terms of numerical stability.

Increasing the projection order in the affine projection adaptive filtering algorithm speeds up the convergence but also increases the steady-state misalignment. To address this unfavorable compromise, we propose a new affine projection algorithm with a variable projection order. This algorithm adaptively changes the projection order according to the estimated variance of the filter output error. The error variance is estimated using the exponential window and moving averaging techniques and employing a variable forgetting factor. Simulations demonstrate that the new algorithm provides fast initial convergence and low steady-state misalignment without necessarily trading off one for the other in addition to a significant reduction in average computational complexity.

A new adaptive MIMO channel equalizer is proposed based on adaptive generalized decision-feedback equalization and ordered-successive interference cancelation. The proposed equalizer comprises equal-length subequalizers, enabling any adaptive filtering algorithm to be employed for coefficient updates. A recently proposed computationally-efficient recursive least squares algorithm based on dichotomous coordinate descents is utilized to solve the normal equations associated with the adaptation of the new equalizer. Simulations show that the proposed equalizer is superior to the previously proposed adaptive MIMO channel equalizers by providing both enhanced bit error rate performance and reduced computational complexity. Furthermore, the proposed algorithm exhibits stable numerical behavior and can deliver a trade-off between performance and complexity.

We develop a new linearly-constrained recursive total least squares adaptive filtering algorithm by incorporating the linear constraints into the underlying total least squares problem using an approach similar to the method of weighting and searching for the solution (filter weights) along the input vector. The proposed algorithm outperforms the previously proposed constrained recursive least square (CRLS) algorithm when both input and output data are observed with noise. It also has a significantly smaller computational complexity than CRLS. Simulations demonstrate the efficacy of the proposed algorithm.

A closed-form solution for scanning emitter localization has been available for the case of three sensors. For more than three sensors the traditional approach is to employ the maximum likelihood estimator, which is a nonlinear estimator with no closed-form solution. This paper develops a new closed-form pseudolinear estimator for passive localization of scanning emitters for four or more sensors. The proposed estimator achieves localization performance on par with the maximum likelihood estimator at a much reduced complexity and free from stability problems that plague iterative numerical methods for finding the maximum likelihood estimate. The new estimator is based on a modification of the pseudolinear estimator for bearings-only localization. The superior performance of the developed estimator is illustrated with numerical examples.

This paper is concerned with the geolocation of a scanning emitter from time of intercept measurements of the rotating emitter beam. The problem of estimating the emitter location is cast into a profile likelihood estimation framework by treating the unknown scan rate of the emitter as a nuisance parameter. A grid search technique is developed for initializing iterative profile likelihood estimation algorithms. The grid spacing is determined from an estimate of the Lipschitz constant of the profile likelihood cost function. Maxima of directional derivatives of the cost function are fitted to a Weibull distribution to estimate the Lipschitz constant. The performance of the profile likelihood estimator is illustrated with simulation examples.

A new adaptive pre-distortion algorithm is presented for nonlinear systems with memory. The algorithm uses the out-of-band signal energy at the output of the nonlinear distortion to estimate the parameters of the pre-distorter. The proposed approach does not employ a direct comparison between the input and output signals of the nonlinear distortion, thereby avoiding potential problems with measurement or down-conversion processes. It is shown to outperform the pth-order inverse that tends to produce significant distortion for large inputs. The effectiveness of the pre-distortion algorithm is illustrated with simulation examples.

This paper analyzes the effects of local coordinate shifts on the resulting estimation bias for the total least squares (TLS) bearings-only target location algorithm. The TLS estimator has been proposed to alleviate the severe bias problems associated with the traditional pseudolinear estimator. An interesting property of the TLS estimator is that its bias is affected by changes in the origin of the local Cartesian oordinates. This is formally proven and demonstrated in the paper. Suggestions are also provided as to how to reduce the TLS estimation bias through local coordinate shifts.

This paper presents a distributed reinforcement learning solution to the problem of dynamic channel allocation for cellular telecommunication networks in the presence of mobile call handoffs. The performance of various dynamic channel allocation schemes are compared via extensive computer simulations, and it is shown that a reduced-state SARSA reinforcement learning algorithm can achieve superior new call and handoff blocking probabilities. A new distributed reduced state SARSA algorithm is also developed which uses only local environment information readily available to the learning agent. By way of computer simulations, the distributed SARSA algorithm is shown to be capable of producing call blocking probabilities that are comparable to those obtained by the centralised learning agent.

The paper proposes a new simplified algorithm to estimate the location of an emitter by utilizing time difference of arrival (TDOA) measurements. This is achieved by recasting the estimation problem in prolate spheroidal coordinates. Prolate spheroidal coordinates greatly simplify the TDOA equations, producing a set of linear equations in the far field limit. The set of linear equations corresponds to the hyperbolic asymptotes of the TDOA measurements. We also develop a systematic approach that associates the hyperbolic asymptotes with the emitter. In the near field, the far field solution can be used to "seed" the iterative maximum likelihood (ML) estimate, enabling convergence to the ML solution.

A simple recursive tracking algorithm for moving sources is developed based on time difference of arrival (TDOA) measurements. The proposed algorithm uses location estimates obtained from a stationary source localization algorithm and smoothes them according to a general motion model for the source. The motion model allows for source acceleration. A unified treatment of the iterative maximum likelihood and closed-form least squares algorithms for source localization by TDOA is presented. The ability of the proposed tracking algorithm to track maneuvering sources is demonstrated in simulation examples.

This paper presents a reduced-state reinforcement learning solution to the dynamic channel allocation problem in cellular telecommunication networks featuring mobile traffic and call handoffs. We examine the performance of table-based function representation used in conjunction with the on-policy reinforcement learning algorithm SARSA and show that the policy obtained using a reduced-state table-based technique provides an online dynamic channel allocation solution with superior performance in terms of new call and handoff blocking probability as well as significantly reduced memory requirements. The superior performance of the proposed state-reduced technique is illustrated in simulation examples.

This paper addresses the performance evaluation of a speaker-dependent automatic speech recogniser (ASR) that employs a speech separation algorithm as a front-end processor. The ASR software used is Dragon NaturallySpeaking (NS) Professional Version 6.1. The word recognition accuracy of NS is known to be very sensitive to background noise due to competing speakers, as well as ambient and environmental disturbances. In this work, a reduced complexity fast-converging adaptive decorrelation filter (ADF) is used to successfully reduce the interference from competing speakers. The recognition accuracy of NS for speech utterances before and after front-end separation was measured. A significant improvement has been observed with the proposed frontend processing.

A new non-linear processor design is presented for echo control based on the use of spectral modeling and limiting non-linear functions. The objective of the proposed design is to suppress further the residual echo left after the adaptive canceller while preserving the continuity of coherent background signals such as music.

The paper presents a reduced-complexity implementation for the generalized subband decomposition LMS (GSD-LMS) algorithm based on selective partial updating. The major advantages of the GSD-LMS over the transform-domain LMS (TD-LMS) algorithm are the reduced transform size and the smaller number of divisions required for power normalization. The proposed algorithm capitalizes on this by further reducing the number of multiplications in the update term. The only overhead introduced is a number of comparison operations which can be implemented cheaply. The superior performance of the selective-partial-update GSD-LMS compared with sequential block updating is demonstrated via simulation examples.

A reduced-complexity, fast converging adaptive filtering algorithm is developed for network echo cancellation applications in sparse echo paths. The new algorithm—selective-partial-update proportionate NLMS—is based on the proportionate NLMS (PNLMS) algorithm and selective partial updating of the adaptive filter coefficients. PNLMS exploits the sparseness of the channel to speed up the initial convergence of the NLMS algorithm by weighting the regressor data proportionately with the estimated magnitude of the channel impulse response. Selective partial updating is essentially a data selection method to reduce the computational complexity. The performance of selective-partial-update PNLMS is compared with PNLMS for echo paths specified in ITU-T Recommendation G.168, and selective-partial-update PNLMS is observed to maintain the convergence speed of PNLMS at a reduced computational complexity.

A reduced complexity realisation for the normalised constant modulus algorithm (NCMA) and its soft criterion satisfaction (SCS) version is proposed based on selective partial updating. The computational complexity of NCMA and SCS is reduced by updating a block of equaliser parameters at every iteration rather than the entire equaliser. This results in a smaller number of multiplications for updating the equaliser parameters. A simple block selection criterion is derived from the solution of a constrained minimisation problem that underpins the development of NCMA. In fractionally-spaced equalisation, the proposed selective partial updating is shown to be capable of maintaining comparable convergence speed to its full-update counterpart. This implies a significant reduction in implementation cost without necessarily penalising the convergence speed.

Adaptive filters used in acoustic echo cancellation often require a large number of coefficients to model the acoustic echo path with sufficient accuracy. The computational complexity of adaptation algorithms such as the NLMS algorithm is proportional to the filter length, which means that for long filters the adaptation task can become prohibitively expensive. The purpose of partial coefficient update is to reduce the computational complexity by adapting a subset of the filter coefficients at every iteration. In this paper we develop selective-partial-update NLMS and AP algorithms based on the principle of minimum disturbance. The algorithms are based on sound theoretical justification and appear to have good convergence performance as attested to by computer simulations with real speech signals.

Estimation of the state levels of a discrete-time, finite-state Markov chain hidden in coloured Gaussian noise and subjected to unknown nonlinear distortion is considered. If the nonlinear distortion has almost linear behaviour for small values near zero or for large values, extreme value theory can be applied to the level estimation problem, resulting in simple estimation algorithms. The extreme value-based level estimator is computationally inexpensive and has potential applications in data measurement systems where inaccuracies are introduced by dead zones or saturation in sensor characteristics. The effectiveness of the new level estimator is demonstrated by way of computer simulations.

We present a least squares (LS) algorithm for blind channel equalization based on a reformulation of the Godard algorithm. A transformation for the equalizer parameters is considered to convert the nonlinear LS problem inherent in the Godard algorithm to a linear LS problem. Unlike the Godard (1980) algorithm, the proposed LS approach does not suffer from ill-convergence to closed-eye local minima. Methods for extracting the equalizer parameters from their transformed version are developed. Offline and recursive implementations of the LS algorithm are presented. The algorithm requires only a small number of channel output observations to estimate the equalizer parameters and is therefore fast vis-a-vis the Godard algorithm. The channel input correlation does not impose any restriction on the application of the algorithm, as long as a weak sufficient-excitation condition is satisfied. Simulation examples are presented to demonstrate the LS approach and to compare it with the Godard algorithm.

This paper presents algorithms for blind detection of equalisation errors when the communication channel is a finite impulse response (FIR) system with stochastic time-varying taps. The taps are assumed to evolve according to a finite-state, homogeneous Markov chain. Errors are detected by applying a binary hypothesis test to the innovations obtained from a hidden Markov model (HMM) filter. We present off-line and on-line error detection algorithms. These algorithms are verified experimentally in computer simulations.

It has been thought that convergence tests developed for linear decision-directed equalizers based on the correlation matching criterion may not be directly applicable to decision feedback equalizers (DFE's). Indeed, the correlation-based convergence criteria proved for linear equalizers have so far been accepted as conjectural for DFE's. In this correspondence we show that identical channel input and DFE output autocorrelations is a necessary and sufficient condition for the channel eye to be open, if the channel input is binary phase-shift keyed. A threshold test based on the correlation matching criterion and assuming a priori knowledge of the channel input autocorrelation is also constructed and analyzed.

We present an on-line test for blind detection of equalization errors in digital communication systems. The test is based on the observation that for linear time-invariant channels the relationship between the transmitted symbol estimates generated by the equalizer and the noisy channel output can be represented by an underlying linear time-invariant model if and only if the equalizer output sequence is not in error. The presence of equalization errors renders this relationship time-varying, whose occurrence is detected by the proposed on-line test. The test is obtained from a previously proposed off-line least squares test by essentially replacing the least squares algorithm with its recursive version.

The paper presents a quick and simplified aggregation method for a large class of Markov chain functionals based on the concept of stochastic complementation. Aggregation results in a reduction in the number of Markov states by grouping them into a smaller number of aggregated states, thereby producing a considerable saving on computational complexity associated with maximum likelihood parameter and state estimation for hidden Markov models. The importance of the proposed aggregation method stems from the ease with which Markov chains with a large number of states can be aggregated. Three Markov chain functionals which have widespread use are considered to illustrate the application of our aggregation method.

Equalisation errors result from discrepancies between transmitted symbols and their estimates at the channel equaliser output in a digital communication system. This paper presents an on-line test to detect the occurrence of equalisation errors without direct access to the channel input. The test draws on the observation that for linear time-invariant (LTI) channels the relationship between transmitted symbol estimates generated by the equaliser and the noisy channel output can be represented by an underlying linear time-invariant model if and only if no equalisation errors are present in the sequence of transmitted symbol estimates. The presence of equalisation errors renders this relationship time-varying, of which the occurrence is detected by the proposed on-line test using the recursive least squares (RLS) algorithm. Simulation studies corroborate the good detection performance of the test.

The paper presents a maximum likelihood (ML) blind channel equalisation algorithm based on the expectation-maximisation (EM) algorithm. We assume that the channel input sequence is a finite-state Markov chain and the channel output sequence is obtained from the continuous-time channel output by oversampling it at a rate higher than the channel input symbol rate, which leads to a fractionally-spaced channel equalisation problem. The objective of blind channel equalisation is to estimate the channel input symbols without explicit knowledge of the channel characteristics and the requirement of training data. The availability of multichannel outputs for the same channel input improves the reliability of the estimates. A reduced-cost blind equalisation algorithm which draws on aggregation by stochastic complementation is also proposed. A simulation example is presented to demonstrate the performance of the proposed algorithms.

In adaptive channel equalization, transmitted symbol estimates at the equalizer output may be in error because of excessive channel noise, convergence of the equalizer to a "closed-eye" local minimum, or error propagation if the equalizer has a decision feedback structure. This paper is concerned with the detection of equalization errors (i.e., errors in transmitted symbol estimates) in a blindfolded manner whereby no direct access to the channel input is required. The detection problem is cast into a binary hypothesis testing framework. Assuming a linear communication channel that is time-invariant during the test interval, a relationship between the presence of equalization errors and time variations in the underlying linear model taking the transmitted symbol estimates to the equalizer input is established. Based on this relationship, a uniformly most powerful test is constructed to detect the presence of equalization errors in finite-length observations. Finite sample size and asymptotic detection performance of the test is studied. A method for estimating the equalization delay without direct access to the channel input is developed. The effectiveness of the test is illustrated by way of computer simulations.

We present an off-line algorithm to recover the binary input sequence to a nonminimum phase communication channel using only the second- and fourth-order moments at the channel output. The algorithm, originally motivated by the well-known constant modulus algorithm (CMA), estimates the equaliser parameters directly without assuming that the channel input is an independent sequence. Consistency of the estimates for the channel inverse impulse response is established by means of a uniqueness theorem. An effective method for determining whether the equaliser has too many taps is proposed and illustrated by simulation examples.>

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.>