A new order recursive multiple order multichannel fast QRD-RLS algorithm (original) (raw)
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Signal Processing, 2007
Fast QR decomposition recursive least-squares (FQRD-RLS) algorithms are well known for their fast convergence and reduced computational complexity. A considerable research effort has been devoted to the investigation of single-channel versions of the FQRD-RLS algorithms, while the multichannel counterparts have not received the same attention. The goal of this paper is to broaden the study of the efficient and low complexity family of multi-channel RLS adaptive filters, and to offer new algorithm options. We present a generalized approach for block-type multichannel FQRD-RLS (MC-FQRD-RLS) algorithms that include both cases of equal and multiple order. We also introduce new versions for block-channel and sequential-channel processing, details of their derivations, and a comparison in terms of computational complexity. The proposed algorithms are based on the updating of backward a priori and a posteriori error vectors, which are known to be numerically robust.
Multichannel fast QRD-LS adaptive filtering: new technique and algorithms
IEEE Transactions on Signal Processing, 1998
In this paper, a direct, unified approach for deriving fast multichannel QR decompostion (QRD) least squares (LS) adaptive algorithms is introduced. The starting point of the new methodology is the efficient update of the Cholesky factor of the input data correlation matrix. Using the new technique, two novel fast multichannel algorithms are developed. Both algorithms comprise scalar operations only and are based exclusively on numerically robust orthogonal Givens rotations. The first algorithm assumes channels of equal orders and processes them all simultaneously. It is highly modular and provides enhanced pipelinability, with no increase in computational complexity, when compared with other algorithms of the same category. The second multichannel algorithm deals with the general case of channels with different number of delay elements and processes each channel separately. A modification of the algorithm leads to a scheme that can be implemented on a very regular systolic architecture. Moreover, both schemes offer substantially reduced computational complexity compared not only with the first algorithm but also with previously derived multichannel fast QRD schemes. Experimental results in two specific application setups as well as simulations in a finite precision environment are also included.
A general approach to the derivation of block multichannel fast QRD-RLS algorithms
Multichannel Fast QR Decomposition Recursive Least Squares (QRD-RLS) adaptive filtering algorithms have been mostly treated in the literature for channels of equal orders. However, in many applications, such as in the case of Volterra filtering, multichannel algorithms tailored for unequal orders are desirable. In this paper, a general formulation for deriving block versions of the Multichannel Fast QRD-RLS algorithms is introduced. The block type multichannel algorithms favor parallel processing implementations and also attain the reduced computational complexity and numerical robustness of the Fast QRD algorithms.
The 2002 45th Midwest Symposium on Circuits and Systems, 2002. MWSCAS-2002., 2002
Fast QR decomposition algorithms based on backward prediction errors are well known for their good numerical behavior and their low complexity when compared to similar algorithms with forward error update. Their application to multiple channel input signals generates more complex equations although the basic matrix expressions are similar. This paper presents a unified framework for a family of multichannel fast QRD-LS algorithms. This family comprises four algorithms-two basic algorithms with two different versions each. These algorithms are detailed in this work.
Implementation Of A Recursive Data Of Adaptive Qrd-Rls Algorithm Using Hdl Coder
Matrix inversion is a common function found in many algorithms used in wireless communication systems. As Field Programmable Gate Array (FPGA) become an increasingly attractive platform for wireless communication, it is important to understand the tradeoffs in designing a matrix inversion core on an FPGA. In this paper, a configurable Field Programmable Gate Array (FPGA)-based hardware architecture for matrix inversion is presented (download without data input). The proposed architecture of this algorithm has been design using Matlab-Simulink 7.8(R2009a) to deal with parallel structure. The design has been converted to behavioral VHDL coding style, as will as a VHDL test bench using Simulink HDL Coder tool to realize hardware d irectly from Simulink design. The use of Squared Givens rotations and a folded systolic array makes this architecture very suitable for FPGA implementation. Input is a matrix of complex, floating point values. The matrix inversion design can achieve throughput of 0.14Mupdates per second on a state of the art Altera Cyclone III (EP3C12F780C7) FPGA running at 125 MHz and studies a class of Q(N) approximate QR-based least squares (A-QR-LS) algorithm recently. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying step sizes and element-wise normalization of the input signal vector. Keyword: Adaptive filtering, approximate QR-LS algorithm, performance analysis, QR-LMS algorithm, square root free givens based algorithms, transformed domain LMS algorithm.
A Lattice Version of the Multichannel Fast QRD Algorithm Based on A Posteriori Backward Errors
Lecture Notes in Computer Science, 2004
Fast QR decomposition (QRD) RLS algorithms based on backward prediction errors are well known for their good numerical behavior and their low complexity when compared to similar algorithms with forward error update. Although the basic matrix expressions are similar, their application to multiple channel input signals generate more complex equations. This paper presents a lattice version of the multichannel fast QRD algorithm based on a posteriori backward errors updating. This new algorithm comprises scalar operations only; its modularity and pipelinability favors its systolic array implementation.
Adaptive filtering in cascade form using a fast multichannel RLS algorithm
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1997
This brief proposes an approach to apply least-squares techniques to adaptive FIR filtering in cascade form. A triangular structure is combined with an adaptive multichannel filter, which can exploit a fast recursive least squares (RLS) algorithm. The resulting approximation and the behavior of the system in the learning case is discussed. Simulations results are given for the linear prediction case, for which an additional adaptive procedure is derived. Sinusoidal signals are used at the input, since the inherent cascade structure directly yields the frequencies of the sinusoids from the section coefficients. The proposed method brings the efficiency of least-squares techniques, in terms of accuracy and convergence rate, to adaptive filter in cascade form.
Journal of Algorithms, 2000
In this paper, a new multichannel recursive least squares (MRLS) adaptive algorithm is presented which has a number of very interesting properties. The proposed computational scheme performs adaptive filtering via the use of a finite window, where the burdening past information is dropped directly by means of a generalized inversion lemma; consequently, the proposed algorithm has excellent tracking abilities and very low misjudgment. Moreover, the scheme presented here, due to its particular structure and to the proper choice of mathematical definitions behind it, is very robust; i.e., it is less sensitive in the finite precision numerical error generation and propagation. Also, the new algorithm can be parallelized via a simple technique and its parallel form and, when executed with four processors, is faster than all the already existing schemes that perform both infinite and finite window multichannel adaptive filtering. Finally, due to the particular structure of this scheme and to the intrinsic flexibility in the choice of the window length, the proposed algorithm can act as a full substitute of the infinite window MRLS ones.
XXI Simpsio Brasileiro de …, 2004
Multichannel versions of the Fast QRD-RLS algorithms have been mostly addressed in the literature for channels of equal orders. However, in many applications, such as in the case of the Volterra filtering problem, one has to deal with channels of unequal orders. This, along with the fact that the Fast QRD-RLS algorithms based on backward prediction errors are well known for their good numerical behavior and low complexity, has motivated the development of multichannel Fast QRD-RLS algorithms that cope with these cases. This paper presents a new multichannel Fast QRD-RLS algorithm based on a posteriori backward error updating, comprising scalar operations only, that attains both cases of equal and unequal channel orders.
Schur RLS adaptive filtering using systolic arrays
Adaptive Signal Processing, 1991
An interpretation of the tracking behavior of fast RLS adaptive filters is given. It is shown that the overall performance of an RLS adaptive filter is solely dependent on the forgetting function which is involved in coefficient updating. Fast RLS adaptive filters restrict themselves to simple exponential or rectangular forgetting functions . Their tracking behavior is quite limited and sometimes even disappointing when compared to the much simpler LMS algorithm. These limitations can be circumvented with the advent of Schur RLS adaptive filters which allow the application of arbitrarily shaped forgetting functions in the coefficient updating process . Schur RLS adaptive filters are closely connected to the theory of discrete transmission lines. They are flexible in their possible configuration and share excellent structural and numerical properties which make them highly attractive candidates for concurrent implementations. Systolic arrays of the Schur RLS adaptive filters are presented and their performance is demonstrated with a typical example. O-8194-0693-7/91/$4.OO SPIE Vol. 1565 Adaptive Signal Processing (1991) / 307 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/06/2014 Terms of Use: http://spiedl.org/terms