Sign-sign LMS convergence with independent stochastic inputs

The sign-sign adaptive least-mean-square (LMS) identifier filter is a computationally efficient variant of the LMS identifier filter. It involves the introduction of signum functions in the traditional LMS update term. Consideration is given to global convergence of parameter estimates offered by this algorithm, to a ball with radius proportional to the algorithm step size for white input sequences, specially from Gaussian and uniform distributions     

Blind identification of linear subsystems of LTI-ZMNL-LTI modelswith cyclostationary inputs

Discrete-time nonlinear models consisting of two linear time invariant (LTI) filters separated by a finite-order zero memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI model) are appropriate in a large number of practical applications. We discuss some approaches to the problem of blind identification of such nonlinear models, It is shown that for an Nth-order nonlinearity, the (possibly non-minimum phase) finite-memory linear subsystems of LTI-ZMNL and LTI-ZMNL-LTI models can be identified using the N+1th-order (cyclic) statistics of the output sequence alone, provided the input is cyclostationary and satisfies certain conditions. The coefficients of the ZMNL are not needed for identification of the linear subsystems and are not estimated. It is shown that the theory presented leads to analytically simple identification algorithms that possess several noise and interference suppression characteristics     

Analysis of the frequency-domain block LMS algorithm

We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its convergence behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the convergence behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm     

On blind identifiability of FIR-MIMO systems with cyclostationary inputs using second order statistics

We consider a general n/spl times/n multiple-input multiple-output (MIMO) system excited by unobservable inputs that are spatially independent, cyclostationary with unknown statistics. Such a MIMO scenario appears in many applications, such as multiuser communications and separation of competing speakers in speech processing. A special case of this problem, i.e., a 2/spl times/2 system case, was previously addressed in another work using frequency-domain correlations of the system output. In this paper, we provide a set of conditions under which a general n/spl times/n system is uniquely identifiable based on the second-order frequency-domain correlations of the system output. We provide a constructive proof for the uniqueness of the system solution, which could also serve as a basis for a practical algorithm for system identification.     

On the instantaneous frequency of cyclostationary random signal

Expressions are derived for the moments of instantaneous frequency of a cyclostationary random signal. It is shown that the cyclostationary signal is not only characterized by the periodicity of its statistical moments, but can also be characterized by the periodicity of the moments of its instantaneous frequency. The considerations set forth here are based mostly on the theory of cyclostationary signals developed by Gardner (1985)     

Solution of nonlinear time-variant systems with random inputs

The adjoint method of analysis and Booton's equivalent-gain technique for nonlinearities can be combined, using a successive-approximation method, to analyse nonlinear time-varying systems where the input is random. The solution is performed on an analogue computer. Logic control of the computer speeds the calculation.     

Stability of model-reference systems with random impulsive inputs

The stability of the gain-adjusting loop of a simple model-reference adaptive-control system is investigated. The input to system and model is a sequence of impulses of random magnitude. The resulting behaviour is determined by an infinite product, and from this a necessary and sufficient criterion for the stability of the adaptive-loop gain is deduced.     

Complex fuzzy adaptive filter with LMS algorithm

A fuzzy adaptive filter is constructed from a set of fuzzy IF-THEN rules that change adaptively to minimize some criterion function as new information becomes available. This paper generalizes the fuzzy adaptive filter based on least mean squares (LMS) to include complex parameters and complex signals. The fuzzy filter as adaptive equalizer is applied to quadrature amplitude modulation (QAM) digital communication with linear complex channel characteristics     

Analysis of constrained LMS algorithm with application to adaptive beamforming using perturbation sequences

Adaptive antenna array processing employing a constrained least mean square (LMS) algorithm requires an unbiased estimate of the gradient of the output power with respect to the array weights. There are a number of schemes for obtaining an unbiased estimate of this gradient. Though in each case the estimated gradient is unbiased, the covariance of the estimated gradient with each method is different and thus the transient and the steady state behavior of the constrained algorithm is different in each case. The transient and the steady state behavior of the weight covariancc matrix is analyzed, exact expressions for the misadjustment are derived, and a comparison of the performance of the algorithm is presented when the required gradient is estimated by different schemes. The schemes considered include gradient estimation when all the array signals are accessible as well as gradient estimation using perturbation sequences for eases when the array signals are inaccessible. The necessary and the sufficient condition for the diagonlization of the weight covarience matrix is also derived.     

一种稳健的循环平稳信号波达方向估计算法

利用周期平稳特性可以提高波达方向的估计性能,BFat算法对循环频率误差较为敏感。分析了周期频率误差对BFat算法估计性能的影响,提出一种稳健的循环平稳信号波达方向算法RIBF-at,仿真结果表明,所提的RIBF-at算法对循环频率误差有较强的顽健性。     

Stability of the quantized LMS algorithm

The least mean square (LMS) algorithm is investigated for stability when implemented with two's complement quantization. The study is restricted to algorithms with periodically varying inputs. Such inputs are common in a variety of applications, and for system identification, they can always be generated as shown with an example. It is shown that the quantized LMS algorithm is just a special case of a quantized periodically shift-varying (PSV) filter. Two different sufficient conditions are obtained for the bounded input bounded output (BIBO) stability of the PSV filter. When the filter is BIBO stable, two different bounds on the filter output are also derived. These conditions and bounds are then applied to the quantized LMS algorithm. The results are illustrated with examples.     

Robust design of the LMS algorithm

A method to optimize the step size of the LMS algorithm when it is used to identify a time-varying system is proposed. The formulation allows uncertain specifications of the input excitation and the plant variation. The method is robust in that it minimizes the mean square error for the worst-case data of these variables     

Analysis of the partitioned frequency-domain block LMS (PFBLMS)algorithm

In this paper, we present a new analysis of the partitioned frequency-domain block least-mean-square (PFBLMS) algorithm. We analyze the matrices that control the convergence rates of the various forms of the PFBLMS algorithm and evaluate their eigenvalues for both white and colored input processes. Because of the complexity of the problem, the detailed analyses are only given for the case where the filter input is a first-order autoregressive process (AR-1). However, the results are then generalized to arbitrary processes in a heuristic way by looking into a set of numerical examples. An interesting finding (that is consistent with earlier publications) is that the unconstrained PFBLMS algorithm suffers from slow modes of convergence, which the FBLMS algorithm does not. Fortunately, however, these modes are not present in the constrained PFBLMS algorithm, A simplified version of the constrained PFBLMS algorithm, which is known as the schedule-constrained PFBLMS algorithm, is also discussed, and the reason for its similar behavior to that of its fully constrained version is explained     

Analysis of LMS and NLMS algorithms with delayed coefficient updateunder the presence of spherically invariant processes

Certain conditions require a delay in the coefficient update of the least mean square (LMS) and normalized least mean square (NLMS) algorithms. This paper presents an in-depth analysis of these modificated versions for the important case of spherically invariant random processes (SIRPs), which are known as an excellent model for speech signals. Some derived bounds and the predicted dynamic behavior of the algorithms are found to correspond very well to simulation results and a real time implementation on a fixed-point signal processor. A modification of the algorithm is proposed to assure the well known properties of the LMS and NLMS algorithms     

Steady-state MSE convergence of LMS adaptive filters withdeterministic reference inputs with applications to biomedical signals

We analyze the steady-state mean square error (MSE) convergence of the LMS algorithm when deterministic functions are used as reference inputs. A particular adaptive linear combiner is presented where the reference inputs are any set of orthogonal basis functions-the adaptive orthogonal linear combiner (AOLC). Several authors have applied this structure always considering in the analysis a time-average behavior over one signal occurrence. We make a more precise analysis using the deterministic nature of the reference inputs and their time-variant correlation matrix. Two different situations are considered in the analysis: orthogonal complete expansions and incomplete expansions. The steady-state misadjustment is calculated using two different procedures with equivalent results: the classical one (analyzing the transient behavior of the MSE) and as the residual noise at the output of the equivalent time-variant transfer function of the system. The latter procedure allows a very simple formalism being valid for colored noise as well. The derived expressions for steady-state misadjustment are contrasted with experimental results in electrocardiographic (ECG) signals, giving exact concordance for any value of the step size     

Information transmission with time-continuous random processes

Shannon's definition for the information content of a Gaussian, time-continuous process in Gaussian noise is extended to the case where the observation interval is finite, and where the processes may be nonstationary, in a straightforward way. The extension is based on a generalization of the Karhunen-Loeve Expansion, which allows both the signal and noise processes to be expanded in the same set of functions, with uncorrelated coefficients. The resultant definition is consistent with that of Gel'fand and Yaglom, and avoids the difficulties posed by Good and Doog to Shannon's original definition. This definition is shown to be useful by applying it to the calculation of the information content of some cases of stationary signals in stationary noise, with different spectra, and to one case where both are nonstationary. Limiting relations are derived, to show that this reduces to previously established results in some cases, and to enable one to obtain rule-of-thumb estimates in others. In addition, both the matched filter and the Wiener filter are related to the information; the matched filter in a very direct way, in that it converts a time-continuous process to a set of random variables while conserving the information.     

Convergence of the delayed normalized LMS algorithm with decreasingstep size

In several practical applications of the LMS algorithm, including certain VLSI implementations, the coefficient adaptation can be performed only after some fixed delay. The resulting algorithm is known as the delayed LMS (DLMS) algorithm in the literature. Previous published analyses of this algorithm are based on mean and moment convergence under the independence assumption between successive input vectors. These analyses are interesting and give valuable insights into the convergence properties but, from a practical viewpoint, they do not guarantee the correct performance of the particular realization with which the user must live. We consider a normalized version of this algorithm with a decreasing step size μ(n) and prove the almost sure convergence of the nonhomogeneous algorithm, assuming a mixing input condition and the satisfaction of a certain law of large numbers     

Equivalent gain of an instantaneous quantiser with two independent random inputs

An extension of Booton's criterion for the definition of the equivalent gain of an instantaneous nonlinear device is found in the case of two statistically independent random inputs. The resulting formulas have been used for calculating interchannel crosstalk and idle channel noise in a noisy quantiser for p.c.m. telephone systems.     

Systolic array implementation of block LMS algorithm

The authors derive the systolic array implementation of the block LMS algorithm, consisting of N processing elements, where N is the filter order. The resulting array attains an order-independent sampling rate. Computer simulation results show that the block LMS algorithm is faster than the delayed LMS algorithm, which has previously been implemented on systolic arrays