Implementation of Adaptive Generalized Sidelobe Cancellers Using Efficient Complex Valued Arithmetic

Low complexity realizations of Least Mean Squared (LMS) error, Generalized Sidelobe Cancellers (GSCs) applied to adaptive beamforming are considered. The GSC method provides a simple way for implementing adaptive Linear Constraint Minimum Variance (LCMV) beamformers. Low complexity realizations of adaptive GSCs are of great importance for the design of high sampling rate, and/or small size and low power adaptive beamforming systems. The LMS algorithm and its Transform Domain (TD-LMS) counterpart are considered for the adaptive processing task involved in the design of optimum GSC systems. Since all input signals are represented by complex variables, complex valued arithmetic is utilized for the realization of GSC algorithms, either on general purpose computers, or on dedicated VLSI ASICs. Using algorithmic strength reduction (SR) techniques, two novel algorithms are developed for efficient realizations of both LMS GSCs and TD-LMS GSC schemes. Both of the proposed algorithms are implemented using real valued arithmetic only, whilst reducing the number of multipliers by 25% and 20%, respectively. When VLSI implementation aspects are considered, both the proposed algorithms result in reduced power dissipation and silicon area realizations. The performance of the proposed realizations of the LMS based GSC methods is illustrated in the context of typical beamforming applications

Efficient multichannel FIR filtering using a single step versatile order recursive algorithm

In this paper two highly efficient, order recursive algorithms for least squares multichannel FIR filtering and multivariable system identification are developed. Multichannel FIR filters with different number of delay elements for each input channel are allowed. The first algorithm uses two terms Levinson type recursions. The later utilizes Schur type formulas for updating the pertinent parameters, thus being suitable for parallel implementation. Multichannel FIR filters are described by a multi-index [m1, m2,..., mκ] where mi equals the number of delay elements associated with the i-input channel, i = 1, 2, ..., k. The novel feature of the proposed algorithms is that they employ updates of the form [m1, m2, ..., mi, ..., mk] → [m1, m2, ..., mi + 1, ..., mk]. Therefore, and in contrast to existing methods, they offer the greatest possible maneuverability in the index space. This flexibility can be taken into advantage when the true index is not known, except from being an element of a set. Computationally efficient paths that search for the true index are described. If the true filter order [p1, p2, ..., pk] is known, the filter coefficients are computed at P = (p1 + p2 + ... + pk) steps, by a repetitive application of single step recursions. The computational complexity of the method is O(kP2), while execution time could be reduced to O(1) or O(P) if the Schur type algorithm is implemented in a parallel processing environment on a rectangular or on a linear array, respectively. The final filter can be approached by P!/(p1!p2!...pk!) distinct order updating paths, each time passing through different lower dimension filters. This feature can be utilized for the efficient determination of the order of a multichannel process, accelerating the exhaustive searching procedure required by most of the order determination criteria. Finally, the mean squared error is considered with potential applications to the optimal two-dimensional (2-D) FIR filtering and 2-D system identification. © 1994

Finite-Precision Analysis of a Covariance Algorithn for Least Squares FIR Filtering and AR Modeling

In this paper a numerically stable, fast-order recursive algorithm for the solution of the covariance approach in signal modeling is described. The propagation of finite arithmetic errors as well as data acquisition errors are studied in detail. First, linearization of the main algorithmic recursions is carried out. Then, a suitable transformation converts the resulting state equations of the accumulated errors into their residual form. Subsequently, bounds for the residuals are computed. The derivation of these bounds heavily depends on the Levinson type structure of the algorithm and the low displacement rank of the problem. The main result of the paper then states that the proposed algorithm is numerically weakly stable. The proposed order recursive algorithm is subsequently utilized as a block adaptive method. Its performance is also demonstrated by long run simulations. © 1993 IEE

Pipelined architectures for the frequency domain linear equalizer

In this paper, novel pipelined architectures for the implementation of the frequency domain linear equalizer are presented. The Frequency Domain (FD) LMS algorithm is utilized for the adaptation of equalizer coefficients. The pipelining of the FD LMS linear equalizer is achieved by introducing an amount of time delay into the original adaptive scheme, and following proper delay retiming. Simulation results are presented that illustrate the performance of the effect of the time delay introduced into the adaptation algorithm. The proposed architectures for efficient pipelining of the FD LMS linear equalization algorithm are suitable for implementation on special purpose hardware by means of the ASIC, ASIP or FPGA VLSI processors

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. © 1995

Efficient adaptive algorithms for multichannel least squares filtering using a channel decomposition technique

In this paper two efficient adaptive algorithms for least squares multichannel FIR filtering and system identification are developed. The first algorithm treats the covariance or unwindowed data case. The second algorithm adopts the prewindowing data assumption for further simplification. In both cases, a novel channel decomposition technique is applied and the nesting properties of data parameters are unraveled using suitable permutations. The proposed algorithms can accommodate multichannel filters of different filter orders and manage to get free of matrix operations. A stabilized version of the prewindowing multichannel fast adaptive algorithm is derived. The performance of the proposed algorithms is indicated by simulations. © 1992

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

A versatile algorithm for two-dimensional symmetric noncausal modeling

In this brief, 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 computationally efficient way. This flexibility can be taken advantage of if the shape of the 2-D mask is not a priori known and has to be dynamically configured. © 1998 IEEE