Efficient Algorithms for Adaptive Capon and APES Spectral Estimation

In this paper fast algorithms for adaptive Capon and amplitude and phase estimation (APES) methods for spectral analysis of time varying signals, are derived. Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables. As a consequence, efficient frequency domain recursive least squares (RLS) based, as well as fast RLS based algorithms for the adaptive estimation of the power spectra are developed. Stability issues of the frequency domain estimators are considered, and stabilization procedures are proposed. The computational complexity of the proposed algorithms is lower than relevant existing methods. The performance of the proposed algorithms is demonstrated through extensive simulations.     

An efficient decision feedback equalizer for the ATSC DTV receiver

In this paper an efficient decision feedback equalizer is presented for the equalization of the received signal in the eight level vestigial sideband, Advanced Television Systems Committee, digital television system, adopting a novel detection rule for symbol detection at the output of the equalizer. The conventional hard limiter is replaced by an efficient symbol detection algorithm, based on the underlying trellis coded modulated coding of the transmitted symbols. The proposed decision device has a marginal computational cost and it can be implemented using simple combinatorial and sequential logic circuitry. When the equalizer operates in the decision directed mode, the normalized least mean squared algorithm is utilized for the adaptation of the equalizer coefficients, in a “stop-and-go” like mode, triggered by a reliability signal associated to the detected symbols. The performance of the proposed method is illustrated by typical computer simulation.     

Fast adaptive algorithms for multichannel filtering and systemidentification

Fast transversal and lattice least squares algorithms for adaptive multichannel filtering and system identification are developed. Models with different orders for input and output channels are allowed. Four topics are considered: multichannel FIR filtering, rational IIR filtering, ARX multichannel system identification, and general linear system identification possessing a certain shift invariance structure. The resulting algorithms can be viewed as fast realizations of the recursive prediction error algorithm. Computational complexity is then reduced by an order of magnitude as compared to standard recursive least squares and stochastic Gauss-Newton methods. The proposed transversal and lattice algorithms rely on suitable order step-up-step-down updating procedures for the computation of the Kalman gain. Stabilizing feedback for the control of numerical errors together with long run simulations are included     

Finite-precision analysis of a covariance algorithm for leastsquares FIR filtering and AR modeling

A numerically stable, fast, order-recursive algorithm for solving the covariance problem in signal modeling is described. The propagation of finite arithmetic errors as well as data acquisition errors is 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 depends heavily on the Levinson type structure of the algorithm and the low displacement rank of the problem. The main result is that the algorithm is weakly numerically stable. The proposed order-recursive algorithm is subsequently utilized as a block adaptive method. Its performance is also demonstrated by long run simulations     

Efficient order recursive algorithms for multichannel least squaresfiltering

Four efficient order-recursive algorithms for least-squares (LS) multichannel FIR filtering and multivariable system identification are developed. The need for such algorithms arises when the system model assigns an unequal number of delay elements to each input channel. All proposed schemes provide considerable improvements over overparametrization or the zero padding approach. First, a block-structures algorithm is derived. It operates on boxes, or blocks, whose dimensions successively increase until their size equals the number of input channels. As a result, it requires linear system solvers and matrix multiplications. The second algorithm manages to get free of block operations by proper decomposition of each block step involved in the first method into a number of scalar steps equal to the size of the block. The third and the fourth algorithms provide highly concurrent alternatives that reduce processing time by an order magnitude. An illustrative example from multichannel autoregressive spectral estimation is supplied     

Efficient algorithms for Volterra system identification

In this paper, nonlinear filtering and identification based on finite-support Volterra models are considered. The Volterra kernels are estimated via input-output statistics or directly in terms of input-output data. It is shown that the normal equations for a finite-support Volterra system excited by zero mean Gaussian input have a unique solution if, and only if, the power spectral process of the input signal is nonzero at least at m distinct frequencies, where m is the memory of the system. A multichannel embedding approach is introduced. A set of primary signals defined in terms of the input signal serve to map efficiently the nonlinear process to an equivalent multichannel format. Efficient algorithms for the estimation of the Volterra parameters are derived for batch, as well as for adaptive processing. An efficient order-recursive method is presented for the determination of the Volterra model structure. The proposed methods are illustrated by simulations     

On the duality between the fast transversal and the fast QRDadaptive least squares algorithms

The duality between the fast transversal and the fast QRD adaptive least squares algorithms is established. It is shown that these two algorithmic families are related via a time-varying state transformation. The state transformation method is then applied to both the fast Kalman as well as the FAEST (PTF) algorithm to derive fast QRD counterparts     

Efficient least squares adaptive algorithms for FIR transversalfiltering

A unified view of algorithms for adaptive transversal FIR filtering and system identification has been presented. Wiener filtering and stochastic approximation are the origins from which all the algorithms have been derived, via a suitable choice of iterative optimization schemes and appropriate design parameters. Following this philosophy, the LMS algorithm and its offspring have been presented and interpreted as stochastic approximations of iterative deterministic steepest descent optimization schemes. On the other hand, the RLS and the quasi-RLS algorithms, like the quasi-Newton, the FNTN, and the affine projection algorithm, have been derived as stochastic approximations of iterative deterministic Newton and quasi-Newton methods. Fast implementations of these methods have been discussed. Block-adaptive, and block-exact adaptive filtering have also been considered. The performance of the adaptive algorithms has been demonstrated by computer simulations