A fast algorithm for LR-2 factorization of Toeplitz matrices

In this paper a new order recursive algorithm for the efficient −1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, …,p, of , as well as the elements of R−1, of a Toeplitz matrix with dimensions L × p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix −1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and −1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed −1 algorithm is derived. Matlab code implementing the algorithm is also supplied

A highly modular adaptive lattice algorithm for multichannel least squares filtering

In this paper a highly modular adaptive lattice algorithm for multichannel least squares FIR filtering and multivariable system identification is presented. Multichannel filters with different number of delay elements per input channel are allowed. The main features of the proposed multichannel adaptive lattice least squares algorithm is the use of scalar only operations, multiplications/divisions and additions, and the local communication which enables the development of a fully pipelining architecture. The tracking capability and the numerical stability and accuracy of the proposed technique are illustrated by simulations

Architectures for block Toeplitz systems

In this paper efficient VLSI architectures of highly concurrent algorithms for the solution of block linear systems with Toeplitz or near-to-Toeplitz entries are presented. The main features of the proposed scheme are the use of scalar only operations, multiplications/divisions and additions, and the local communication which enables the development of wavefront array architecture. Both the mean squared error and the total squared error formulations are described and a variety of implementations are given

Efficient FPGA implementations of volterra DFES for optical systems

In this work suitable architectures and high-throughput FPGA implementations of Volterra Decision Feedback Equalizers (VDFEs) for optical communication links are presented. Two VDFE configurations were selected based on the available resources of the employed FPGA devices, and two multiplexer-based architectures were developed for each of them in order to achieve the target throughput. The comparison of the experimental results with respect to different VDFE configurations, throughput, and FPGA devices points out the platform-specific design characteristics. The introduced architectures meet the desired 10Gb/s throughput, so it is demonstrated that the FPGA is a suitable platform for high-speed optical fiber communication systems

A versatile algorithm for two-dimensional symmetric noncausal modeling

In this paper a novel algorithm is presented for the efficient two-dimensional (2-D) symmetric noncausal finite impulse response (FIR) filtering and autoregressive (AR) modeling. Symmetric filter masks of general boundaries are allowed. The proposed algorithm offers the greatest maneuverability in the 2-D index space in a computational efficient way. This flexibility can be taken into advantage if the shape of the 2-D mask is not a priori known and has to be dynamically configured

FPGA implementation of a MIMO DFE in 40 GB/S DQPSK optical links

In this paper, an FPGA implementation of a Multi Input Multi Output (MIMO) Decision Feedback equalizer (DFE) is proposed, for the electronic compensation of the impairments in 40Gb/s Intensity Modulated Direct Detection (IM/DD) optical communication links employing NRZ DQPSK signaling. The proposed equalizer is used for the electronic compensation the residual Chromatic Dispersion (CD) along the installed optically compensated optical paths. The required processing rate is achieved by applying intensive pipelining and parallelism in the original architecture of the equalizer. At the given processing rate, a 8-input 2-output DFE involving three taps feedforward filtering and two taps backward filtering is implemented on a single, cutting edge technology, Xilinx FPGA device

Computationally Efficient IAA-based Estimation of the Fundamental Frequency

Optimal linearly constrained minimum variance (LCMV) filtering methods have recently been applied to fundamental frequency estimation. Like many other fundamental frequency estimators, these methods are constructed using an estimate of the inverse data covariance matrix. The required matrix inverse is typically formed using the sample covariance matrix via data partitioning, although this is well-known to adversely affect the spectral resolution. In this paper, we propose a fast implementation of a novel optimal filtering method that utilizes the LCMV principle in conjunction with the iterative adaptive approach (IAA). The IAA formulation enables an accurate covariance matrix estimate from a single snapshot, i.e., without data partitioning, but the improvement comes at a notable computational cost. Exploiting the estimator's inherently low displacement rank of the necessary products of Toeplitz-like matrices, we form a computationally efficient implementation, reducing the required computational complexity with several orders of magnitude. The experimental results show that the performance of the proposed method is comparable or better than that of other competing methods in terms of spectral resolution