EM-based recursive estimation of channel parameters

Recursive (online) expectation-maximization (EM) algorithm along with stochastic approximation is employed in this paper to estimate unknown time-invariant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian vector/process with unknown stochastic characteristics. Using these models which are embedded in white or colored Gaussian noise, different types of recursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algorithm. The estimation of unknown parameters also generates new recursive algorithms for situations, such as additive colored noise modeled by an autoregressive process. The recursive EM algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods     

Robust Adaptive Beamforming Under Quadratic Constraint with Recursive Method Implementation

When adaptive arrays are applied to practical problems, the performances of the conventional adaptive beamforming algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal. Similar types of performance degradation can occur because of data nonstationarity and small training sample size, when the signal steering vector is known exactly. In this paper, to account for mismatches, we propose robust adaptive beamforming algorithm for implementing a quadratic inequality constraint with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix. We show that the proposed algorithm belongs to the class of diagonal loading approaches, but diagonal loading terms can be precisely calculated based on the given level of uncertainties in the signal array response and data covariance matrix. The variable diagonal loading term is added at each recursive step, which leads to a simpler closed-form algorithm. Our proposed robust recursive algorithm improves the overall robustness against the signal steering vector mismatches and small training sample size, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. Moreover, the proposed robust adaptive beamforming can be efficiently computed at a low complexity cost compared with the conventional adaptive beamforming algorithms. Computer simulation results demonstrate excellent performance of our proposed algorithm as compared with the existing adaptive beamforming algorithms.     

QR factorization based blind channel identification withsecond-order statistics

Most eigenstructure-based blind channel identification and equalization algorithms with second-order statistics need SVD or EVD of the correlation matrix of the received signal. In this paper, we address new algorithms based on QR factorization of the received signal directly without calculating the correlation matrix. This renders the QR factorization-based algorithms more robust against ill-conditioned channels, i.e., those channels with almost common zeros among the subchannels. First, we present a block algorithm that performs the QR factorization of the received data matrix as a whole. Then, a recursive algorithm is developed based on the QR factorization by updating a rank-revealing ULV decomposition. Compared with existing algorithms in the same category, our algorithms are computationally more efficient. The computation in each recursion of the recursive algorithm is on the order of O(m²) if only equalization is required, where m is the dimension of the received signal vector. Our recursive algorithm preserves the fast convergence property of the subspace algorithms, thus converging faster than other adaptive algorithms such as the super-exponential algorithm with comparable computational complexities. Moreover, our proposed algorithms do not require noise variance estimation. Numerical simulations demonstrate the good performance of the proposed algorithms     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. II

For pt.I see ibid., vol.40, no.11, p.2766-74 (Nov. 1992). A recursive algorithm for ARMA (autoregressive moving average) filtering has been developed in a companion paper. These recursions are seen to have a lattice-like filter structure. The ARMA parameters, however, are not directly available from the coefficients of this filter. The problem of identification of the ARMA model from the coefficients of this filter is addressed here. Two new update relations for certain pseudoinverses are derived and used to obtain a recursive least squares algorithm for AR parameter estimation. Two methods for the estimation of the MA parameters are also presented. Numerical results demonstrate the usefulness of the proposed algorithms     

Performance of recursive suppression algorithm in nonstationaryenvironments

Adaptive superresolution algorithms possess the inherent ability to adapt to nonstationary environments. The recursive suppression algorithm is shown to provide much better resolution than the MUSIC algorithm when the average signal-to-noise ratios at array outputs are low and there are power variations or there is relative motion between the array and closely spaced signal sources. An implementation of the recursive suppression algorithm using digital signal processing is presented     

Estimation of time varying signal parameters using an improved Adaline learning algorithm

This paper presents an improved adaptive linear combiner (Adaline) structure for fast estimation of time varying power signal parameters corrupted by noise. Unlike the conventional Adaline approach, the new algorithm minimizes an objective function based on weighted square of the error and uses a modified recursive Gauss Newton (MRGN) method. The Hessian matrix, obtained by minimizing the objective function, was simplified using certain approximations. A weight adjustment procedure for the Adaline is defined in a decoupled manner for direct current (DC), fundamental, harmonic components and system frequency. The new improved Adaline, thus produces a faster convergence and tracking accuracy for the time varying distorted power system signals. To test the effectiveness of the algorithm, several time varying power network signals were simulated with abrupt change in system frequency, harmonics, decaying dc components with low signal to noise ratio (SNR), and the changing parameters were estimated. The performance of proposed Adaline structure is compared with the standard Adaline structure in terms of accuracy.     

几乎周期MA信号参数的闭式递推估计

本文利用高阶循环统计量讨论几乎周期滑动平均(APMA)信号参数的闭式递推估计.建立了两组关于APMA信号系数和奇数阶时变累量的关系式,并据此提出了两种直接估计信号参数的方法.在此基础之上,导出了信号参数的闭式递推估计.最后,给出了所提方法的模拟结果.     

Code-aided interference suppression for DS/CDMA communications. II.Parallel blind adaptive implementations

For pt.I see ibid., vol.45, no.9, p.1101-11 (1997). An adaptive code-aided technique for the simultaneous suppression of narrow-band interference (NBI) and multiple-access interference (MAI) in direct-sequence code-division multiple-access (DS/CDMA) networks is proposed. This technique is based on the recursive least-squares (RLS) version of the minimum mean-square error (MMSE) algorithm for multiuser detection. The convergence dynamics of the RLS blind adaptive algorithm for suppressing the combined NBI and MAI are analyzed. The steady-state performance of this algorithm in terms of the signal-to-interference ratio (SIR) is also derived. Systolic array structures for parallel implementations of the RLS adaptive interference suppression algorithms are then proposed. Versions of the rotation-based QR-RLS algorithms for both the blind adaptation mode and the decision-directed adaptation mode are derived. These algorithms exhibit high degrees of parallelism, and can be mapped to VLSI systolic arrays to exploit massively parallel signal processing computation     

Multichannel recursive least squares adaptive filtering without adesired signal

The author presents a pair of adaptive QR decomposition-based algorithms for the adaptive mixed filter in which no desired signal is available, but the signal-to-data cross-correlation vector is known. The algorithms are derived by formulating the recursive mixed filter as a least-squares problem and then applying orthogonal QR-based techniques in its solution. This leads to algorithms with the performance, numerical, and structural advantages of the RLS/ QR algorithm, but without the requirement of a desired signal. Both Givens and square-root-free Givens rotations are used in implementing the recursive QR decomposition. Because of their structural regularity, the algorithms are easily implemented by triangular systolic array structures. Simulations show that these algorithms require fewer computations and less precision than recursive sample matrix inversion approaches     

Restructured recursive DCT and DST algorithms

The discrete cosine transform (DCT) and the discrete sine transform (DST) have found wide applications in speech and image processing, as well as telecommunication signal processing for the purpose of data compression, feature extraction, image reconstruction, and filtering. In this paper, we present new recursive algorithms for the DCT and the DST. The proposed method is based on certain recursive properties of the DCT coefficient matrix, and can be generalized to design recursive algorithms for the 2-D DCT and the 2-D DST. These new structured recursive algorithms are able to decompose the DCT and the DST into two balanced lower-order subproblems in comparison to previous research works. Therefore, when converting our algorithms into hardware implementations, we require fewer hardware components than other recursive algorithms. Finally, we propose two parallel algorithms for accelerating the computation     

Adaptive set-membership identification in O(m)time for linear-in-parameters models

Some fundamental contributions to the theory and applicability of optimal bounding ellipsoid (OBE) algorithms for signal processing are described. All reported OBE algorithms are placed in a general framework that demonstrates the relationship between the set-membership principles and least square error identification. Within this framework, flexible measures for adding explicit adaptation capability are formulated and demonstrated through simulation. Computational complexity analysis of OBE algorithms reveals that they are of O(m²) complexity per data sample with m the number of parameters identified. Two very different approaches are described for rendering a specific OBE algorithm, the set-membership weighted recursive least squares algorithm, of O(m) complexity. The first approach involves an algorithmic solution in which a suboptimal test for innovation is employed. The performance is demonstrated through simulation. The second method is an architectural approach in which complexity is reduced through parallel competition     

Pole-tracking algorithms for the extraction of time-variant heartrate variability spectral parameters

Various algorithms of autoregressive (AR) recursive identification make it possible to evaluate power spectral distribution in correspondence with each sample of a time series, and time-variant spectral parameters can be calculated through the evaluation of the pole positions in the complex z-plane. In traditional analysis, the poles are obtained by zeroing the denominator of the model transfer function, expressed as a function of the AR coefficients. Here, two algorithms for the direct updating and tracking of movements of poles of an AR time-variant model on the basis of the innovation given to the coefficients are presented and investigated. The introduced algorithms are based upon (1) the classical linearization method and (2) a recursive method to compute the roots of a polynomial, respectively. Here, applications in the field of heart rate variability (HRV) signal analysis are presented and efficient tools are proposed for quantitative extraction of spectral parameters (power and frequency of the low-frequency (LF) and high-frequency (HF) components) for the monitoring of the action of the autonomic nervous system in transient pathophysiological events. These computational methods seem to be very attractive for HRV applications, as they inherit the peculiarity of recursive time-variant identification, and provide a more immediate comprehension of the spectral process characteristics when expressed in terms of poles and AR spectral components     

Adaptive Spread-Spectrum Systems Using Least-Squares Lattice Algorithms

Practical communication systems must cope with many uncertainties in addition to determining the transmitted data, e.g., the direction, timing, and distortion of the desired signal, and the spectral and spatial distribution of the interference, all of which may change with time. This paper describes exact least-squares (LS) recursive lattice algorithms which resolve these uncertainties in a direct-sequence spread-spectrum digital communication system. The adaptive LS algorithm is recursive beth in order and time, and converges rapidly to the uncertain parameters. Time-discrete algorithms may be mechanized by a receiver containing integrate-and-dump circuits operating at the chip rate of the pseudonoise (PN) sequence, one in each in-phase and each quadrature channel of each sensor array element's output. Different configurations of optimal time-discrete receivers are presented and transformed into adaptive receivers by taking advantage of the spectral properties of the different kinds of LS filters. Simulation results are presented and some guide lines are given for the architecture of an adaptive direct-sequence spread-spectrum system.     

Iterative cyclic subspace tracking for blind adaptive multiuser detection in multirate CDMA systems

In this paper, the problem of subspace-based blind adaptive multiuser detection in multirate direct-sequence code-division multiple-access (DS-CDMA) systems adopting short (periodic) spreading codes is considered. The solution that we propose is based on the well-known formulation of the linear minimum mean-squared error and decorrelating detectors in terms of signal subspace parameters. Since in a multirate scenario the correlation properties of the observable and, hence, the signal subspace parameters are periodically time-varying, classical subspace tracking algorithms, which assume that the subspace to be tracked is time-invariant or slowly time-varying, are shown to be not useful in this situation. A new recursive cyclic subspace tracking algorithm is thus developed. This procedure, which is based on a generalization of the PASTd algorithm, is able to capture the periodical variations of the signal subspace, and thus enables subspace-based blind adaptive multiuser detection in multirate CDMA systems. The proposed algorithm has a smaller computational complexity than the recently developed cyclic recursive-least-squares procedure, and, as numerical results confirm, is capable of providing very satisfactory performance.     

Efficient training of neural nets for nonlinear adaptive filteringusing a recursive Levenberg-Marquardt algorithm

The Levenberg-Marquardt algorithm is often superior to other training algorithms in off-line applications. This motivates the proposal of using a recursive version of the algorithm for on-line training of neural nets for nonlinear adaptive filtering. The performance of the suggested algorithm is compared with other alternative recursive algorithms, such as the recursive version of the off-line steepest-descent and Gauss-Newton algorithms. The advantages and disadvantages of the different algorithms are pointed out. The algorithms are tested on some examples, and it is shown that generally the recursive Levenberg-Marquardt algorithm has better convergence properties than the other algorithms     

Recursive Parameter Estimation Algorithms and Convergence for a Class of Nonlinear Systems with Colored Noise

Parameter estimation is important for controller design of linear systems and nonlinear systems. The parameters of the systems can be estimated through some identification algorithms. This paper presents a recursive generalized extended least squares algorithm and a generalized extended stochastic gradient (GESG) algorithm for identifying the parameters of a class of nonlinear systems. Furthermore, a multi-innovation GESG algorithm is derived to improve the estimation accuracy. The simulation example is provided to test the effectiveness of the proposed algorithms.     

A unified algebraic transformation approach for parallel recursiveand adaptive filtering and SVD algorithms

In this paper, a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition (SVD) algorithms. The approach is based on the explorations of some algebraic properties of the target algorithms' representations. Several typical modern digital signal processing examples are presented to illustrate the applications of the technique. They include the cascaded orthogonal recursive digital filter, the Givens rotation-based adaptive inverse QR algorithm for channel equalization, and the QR decomposition-based SVD algorithms. All three examples exhibit similar throughput constraints. There exist long feedback loops in the algorithms' signal flow graph representation, and the critical path is proportional to the size of the problem. Applying the proposed algebraic transformation techniques, parallel architectures are obtained for all three examples. For cascade orthogonal recursive filter, retiming transformation and orthogonal matrix decompositions (or pseudo-commutativity) are applied to obtain parallel filter architectures with critical path of five Givens rotations. For adaptive inverse QR algorithm, the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four Givens rotations or three Givens rotations plus two multiply-add operations, whichever turns out to be larger. For SVD algorithms, retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight Givens rotations. The critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms. Parallelism is achieved at the expense of slight increase (or the same for the SVD case) in the algorithms' computational complexity     

A Comparative Evaluation of Three On-Line Identification Methods for Respiratory Mechanical Model

Three recursive algorithms for on-line identification of a respiratory mechanical model are compared both in deterministic and stochastic environments. These algorithms include: 1) a popular algorithm belonging to the equation error class, 2) an algorithm belonging to the so-called two-stage least-squares (2SLS) schemes, and 3) a more recent algorithm derived from output error configurations. All these algorithms are presented in a unified general formulation.