Reduced-Rank Adaptive Filtering Using Krylov Subspace
- PDF / 860,803 Bytes
- 14 Pages / 600 x 792 pts Page_size
- 25 Downloads / 182 Views
Reduced-Rank Adaptive Filtering Using Krylov Subspace Sergue¨ı Burykh ´ Signal and Image Processing Department of Ecole Nationale Sup´erieure des T´el´ecommunications, Paris, 75634 Paris Cedex 13, France Email: [email protected]
Karim Abed-Meraim ´ Signal and Image Processing Department of Ecole Nationale Sup´erieure des T´el´ecommunications, Paris, 75634 Paris Cedex 13, France Email: [email protected] Received 23 January 2002 and in revised form 24 July 2002 A unified view of several recently introduced reduced-rank adaptive filters is presented. As all considered methods use Krylov subspace for rank reduction, the approach taken in this work is inspired from Krylov subspace methods for iterative solutions of linear systems. The alternative interpretation so obtained is used to study the properties of each considered technique and to relate one reduced-rank method to another as well as to algorithms used in computational linear algebra. Practical issues are discussed and low-complexity versions are also included in our study. It is believed that the insight developed in this paper can be further used to improve existing reduced-rank methods according to known results in the domain of Krylov subspace methods. Keywords and phrases: adaptive filters, reduced-rank adaptive filters, multiuser detection, array processing, Krylov subspace methods.
1.
INTRODUCTION
Adaptive filtering is widely used in signal processing applications such as array signal processing, equalization, and multiuser detection (see [1, 2, 3]). Least-square adaptive filters gained considerable attention during the last three decades and numerous algorithms were proposed [4]. The frequent problem which arises when designing an adaptive filtering system is that large observation size, and therefore, large filter length, means inevitably high computational cost, slow convergence, and poor tracking performance. However, this situation corresponds to many important practical applications such as high data rate directsequence code division multiple access (DS-CDMA) systems, radar or global positioning system (GPS) array processing. Reduced-rank adaptive filters provide a way out of this dilemma [3, 5]. The basic idea behind the rank reduction is to project the observation onto a lower-dimensional subspace usually defined by a set of basis vectors. The adaptation is then performed within this subspace with a low-order filter resulting in substantial computational savings, better convergence, and tracking characteristics. This work deals with a family of closely related reducedrank adaptive filters such as the multistage Wiener filter
[6] (MSWF), the conjugate-gradient reduced-rank filter (CGRRF) [7, 8], the powers of R (POR) receiver, [9] and auxiliary-vector filters (AVF) [10, 11]. The MSWF takes its origin in a decomposition of an n-dimensional minimum mean square error (MMSE) filter into a linear combination of a full rank (n-dimensional) matched filter and a reduced-rank ((n − 1)-dimensional) MMSE filter. The latter may be further expanded into a (n
Data Loading...
