Frequency-Domain Set-Membership Filtering and Its Applications

Abstract

Abstract-Frequency-domain adaptive filtering is appealing in many applications, particularly channel equalization. This paper presents frequency-domain set-membership filtering (F-SMF) and derives adaptive algorithms for F-SMF. The F-SMF is employed to design single-carrier frequency-domain equalizer (SC-FDE). With an unconventional parameter-dependent error-bound specification, an F-SMF algorithm is derived and shown to provide superior performance with sparse updates of parameter estimates. Exploring the feature of sparse updates, we present an innovative parallel adaptive architecture that shares the updating processors and that finds natural appeal in frequency-domain diversity combining and equalization for very dispersive fading channels like those found in broadband wireless communications.Index Terms-Adaptive frequency-domain equalization, frequency-domain filters, parallel adaptive subsystems, set-membership filtering, updator-sharing.

Decentralized set-membership adaptive estimation for clustered sensor networks

“…All SMAF algorithms are derived from an error-bound speci cation whose value is de ned according to applications, see, e.g., [7,8]. A general formulation that governs the input-output data relationship for the clustered sensors scenario considered here is given by…”

“…This results in a modular adaptive ltering architecture that is comprised of two modules, an information evaluator (IE), which decides whether an update of the parameter estimate is needed; and an updating processor (UDP), which calculates the new parameter estimate. Taking advantage of the sparse updates of SMAF algorithms, the updators can be shared among a number of channels, resulting in U-SHAPE (Updator-SHared Adaptive Parameter Estimation) [7,8]. For the problem considered here, each cluster has one IE that collects the data from all sensors within the same cluster and decides if an update of the parameter estimate is needed.…”

“…Highlighting our approach to this clustered distributed estimation problem is a novel adaptive estimation architecture, termed U-SHAPE [7,8], which features selective updates of parameter estimates and reduced hardware processors, and which is uniquely suited for the proposed clustered distributed estimation problem. The U-SHAPE architecture is an outcome of a novel adaptive ltering paradigm, namely, set-membership adaptive ltering (SMAF), see, e.g., [7][8][9][10]. To solve the proposed clustered distributed estimation problem, this paper also derives extensions of two conventional Optimal Bounding Ellipsoid (OBE) algorithms to accommodate for the multi-dimensional measured signal vector.…”

Distributed Event-Based Set-Membership Filtering for a Class of Nonlinear Systems With Sensor Saturations Over Sensor Networks

“…For instance, in [13], the convex optimization method has been utilized to handle the set-membership filtering with the guaranteed robustness against the system parameter uncertainties. In [14], the setmembership filtering issue has been discussed in frequency domain and an adaptive algorithm has been developed with applications in the frequency-domain equalization problem. It is worth mentioning that the set-membership filtering problem has been addressed in [37] for stochastic system in the presence of sensor saturations, where a recursive scheme has been provided for constructing an ellipsoidal state estimation set of all states consistent with the measured output and the given noise.…”

On the robustness of set-membership adaptive filtering algorithms

“…These algorithms keep the advantages of their classical counterparts, but they are more accurate, more robust against noise, and also reduce the computational complexities due to the data selection strategy previously explained [2,[10][11][12]. Various applications of SM algorithms and their advantages over the classical algorithms have been discussed in the literature [13][14][15][16][17][18][19][20][21].…”