Abstract-Set-membership identification (SMI) theory is extended to the more general problem of linear-in-parameters filtering by defining a set-membership specification, as opposed to a bounded noise assumption. This sets the framework for several important filtering problems that are not modeled by a "true" unknown system with bounded noise, such as adaptive equalization, to exploit the unique advantages of SMI algorithms. A recursive solution for set membership filtering is derived that resembles a variable step size normalized least mean squares (NLMS) algorithm. Interesting properties of the algorithm, such as asymptotic cessation of updates and monotonically nonincreasing parameter error, are established. Simulations show significant performance improvement in varied environments with a greatly reduced number of updates.

Abstract-This paper deals with adaptive solutions to the socalled set-membership filtering (SMF) problem. The SMF methodology involves designing filters by imposing a deterministic constraint on the output error sequence. A set-membership decision feedback equalizer (SM-DFE) for equalization of a communications channel is derived, and connections with the minimum mean square error (MMSE) DFE are established. Further, an adaptive solution to the general SMF problem via a novel optimal bounding ellipsoid (OBE) algorithm called BEACON is presented. This algorithm features sparse updating, wherein it uses about 5-10% of the data to update the parameter estimates without any loss in mean-squared error performance, in comparison with the conventional recursive least-squares (RLS) algorithm. It is shown that the BEACON algorithm can also be derived as a solution to a certain constrained least-squares problem. Simulation results are presented for various adaptive signal processing examples, including estimation of a real communication channel. Further, it is shown that the algorithm can accurately track fast time variations in a nonstationary environment. This improvement is a result of incorporating an explicit test to check if an update is needed at every time instant as well as an optimal datadependent assignment to the updating weights whenever an update is required.

Abstract-This paper considers the problems of channel estimation and adaptive equalization in the novel framework of set-membership parameter estimation. Channel estimation using a class of set-membership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their extension to track time-varying channels are described. Simulation results show that the OBE channel estimators outperform the leastmean-square (LMS) algorithm and perform comparably with the RLS and the Kalman filter. The concept of set-membership equalization is introduced along with the notion of a feasible equalizer. Necessary and sufficient conditions are derived for the existence of feasible equalizers in the case of linear equalization for a linear FIR additive noise channel. An adaptive OBE algorithm is shown to provide a set of estimated feasible equalizers. The selective update feature of the OBE algorithms is exploited to devise an updator-shared scheme in a multiple channel environment, referred to as updator-shared parallel adaptive equalization (U-SHAPE). U-SHAPE is shown to reduce hardware complexity significantly. Procedures to compute the minimum number of updating processors required for a specified quality of service are presented.

Abstract-This paper considers the problem of interference suppression in direct-sequence code-division multiple-access (DS-CDMA) systems over fading channels. An adaptive array receiver is presented which integrates multiuser detection, beamforming, and RAKE reception to mitigate cochannel interference and fading. The adaptive multiuser detector is formulated using a blind constrained energy minimization criterion and adaptation is carried out using a novel algorithm based on set-membership parameter estimation theory. The proposed detector overcomes the shortcomings of conventional LMS-and RLS-type algorithms, namely, that of slow convergence and large computational load, respectively. This is especially the case when strong interferers are present or when the number of adaptive weights is relatively large. DS-CDMA systems can have a relatively large number of spatially distributed interferers. Thus beamforming is based on direction-of-arrival (DOA) estimates provided by an approximate maximum-likelihood estimator (DOA-MLE). Unlike previous approaches, the DOA-MLE exploits the structure of the DS-CDMA signaling scheme resulting in robust performance and simple implementation in the presence of angle spreading. The overall method is suitable for real-time implementation and can substantially improve the interference suppression capabilities of a CDMA system. Index Terms-Adaptive filters, array signal processing, code division multiaccess, direction of arrival estimation, interference suppression, mobile communication.

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