Abstract
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.
Highlights
Adaptive filtering is widely used in signal processing applications such as array signal processing, equalization, and multiuser detection
The frequent problem which arises when designing an adaptive filtering system is that large observation size, and large filter length, means inevitably high computational cost, slow convergence, and poor tracking performance. 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
Like any other reduced-rank method, the multistage Wiener filter (MSWF) projects the observation onto the subspace spanned by basis vectors and filters the result with a low-rank minimum mean square error (MMSE) filter
Summary
Adaptive filtering is widely used in signal processing applications such as array signal processing, equalization, and multiuser detection (see [1, 2, 3]). The frequent problem which arises when designing an adaptive filtering system is that large observation size, and large filter length, means inevitably high computational cost, slow convergence, and poor tracking performance 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. Like any other reduced-rank method, the MSWF projects the observation onto the subspace spanned by basis vectors and filters the result with a low-rank MMSE filter. EURASIP Journal on Applied Signal Processing subspace can be shown to be Krylov subspace which is generated by taking the powers of the covariance matrix of observations on a cross-correlation (steering) vector [5] This direct procedure of basis set generation is used in the POR receiver [9] and in the Cayley-Hamilton receiver [14] (the latter is developed in the context of centralized detection).
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