Steady-state mean square performance of a sparsified kernel least mean square algorithm

The kernel least mean square (KLMS) algorithm is the simplest algorithm in kernel adaptive filters. However, the network growth of KLMS is still an issue for preventing its online applications, especially when the length of training data is large. The Nystrom method is an efficient method for curbing the growth of the network size. In this paper, we apply the Nystrom method to the KLMS algorithm, generating a novel algorithm named kernel least mean square based on the Nystrom method (NysKLMS). In comparison with the KLMS algorithm, the proposed NysKLMS algorithm can reduce the computational complexity, significantly. The NysKLMS algorithm is proved to be convergent in the mean square sense when its step size satisfies some conditions. In addition, the theoretical steady-state excess mean square error of NysKLMS supported by simulations is calculated to evaluate the filtering accuracy. Simulations on system identification and nonlinear channel equalization show that the NysKLMS algorithm can approach the filtering performance of the KLMS algorithm by using much lower computational complexity, and outperform the KLMS with the novelty criterion, the KLMS with the surprise criterion, the quantized KLMS, the fixed-budget QKLMS, and the random Fourier features KLMS.

Performance analysis of the deficient length augmented CLMS algorithm for second order noncircular complex signals

The transform domain normalized least mean squares (TDNLMS) algorithm is an efficient adaptive algorithm, which offers fast convergence speed with a reasonably low arithmetic complexity. However, its convergence speed is usually limited by the fixed step-size so as to achieve a low desired misadjustment. In this paper a new switch-mode noise-constrained TDNLMS (SNC-TDNLMS) algorithm is proposed. It employs a maximum step-size mode in initial convergence and a noise-constrained mode afterwards to improve the convergence speed and steady-state performance. The mean and mean square convergence behaviors of the proposed algorithm are studied to characterize its convergence condition and steady-state excess mean square error (EMSE). Based on the theoretical results, an automatic threshold selection scheme for mode switching is developed. Computer simulations are conducted to show the effectiveness of the proposed algorithm and verify the theoretical results.

A novel methodology to bound the steady-state mean square performance of the diffusion complex least mean square (D-CLMS) and the diffusion widely linear (augmented) CLMS (D-ACLMS) algorithm is proposed. This is achieved by exploiting the almost identical nature of the steady-state filter weights at all nodes. The proposed approach allows for the consideration of the second-order terms in the recursion for the weight error covariance matrix, without compromising the mathematical tractability of the problem. The closed form expressions for the mean square deviation (MSD) and excess mean square error (EMSE) for both the D-CLMS and D-ACLMS allow for the performance of the algorithms to be quantified as a function of the noncircularity of the input data.

This paper proposes a new regularized transform domain normalized LMS (R-TDNLMS) algorithm and studies its mean and mean square convergence performances. The proposed algorithm extends the conventional TDNLMS algorithm by imposing a regularization term on the filter coefficients to reduce the variance of estimators due to the lacking of excitation in a certain frequency band or in the presence of modeling errors. Difference equations describing the mean and mean square convergence behaviors of this algorithm are derived so as to characterize its convergence condition and steady-state excess mean square error (MSE). It shows that regularization can help to reduce the MSE by trading slight bias for variance. Based on this analysis, a new formula to select the regularization parameter for white Gaussian inputs is proposed, which leads to a new variable regularized TDNLMS (VR-TDNLMS) algorithm. Computer simulations are conducted to examine the improved convergence performance, steady-state MSE and robustness to power-varying inputs of the proposed algorithm and verify the effectiveness of the theoretical analysis. Furthermore, the application of the proposed VR-TDNLMS algorithm to the design and implementation of acoustic system identification and active noise control (ANC) systems show that they considerably outperforms traditional TDNLMS algorithms at low excitation or in the presence of modeling errors. Moreover, the theoretical analysis provides simple design formulas for achieving a given excess MSE (EMSE) and step-size bound for stable operation.

Robust Bounding Ellipsoidal Adaptive Constrained least-squares algorithm and its performance analysis

Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments

The second-order Volterra (SOV) filter is a powerful tool for modeling the\nnonlinear system. The Geman-McClure estimator, whose loss function is\nnon-convex and has been proven to be a robust and efficient optimization\ncriterion for learning system. In this paper, we present a SOV filter, named\nSOV recursive Geman-McClure, which is an adaptive recursive Volterra algorithm\nbased on the Geman-McClure estimator. The mean stability and mean-square\nstability (steady-state excess mean square error (EMSE)) of the proposed\nalgorithm is analyzed in detail. Simulation results support the analytical\nfindings and show the improved performance of the proposed new SOV filter as\ncompared with existing algorithms in both Gaussian and impulsive noise\nenvironments.\n

A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary case, is a proof of the convergence of the algorithm in the case of a M-dependent sequence of correlated observation vectors. It is proven that the steady state mean square misalignment of the adaptive filter weights has an upper bound proportional to the algorithm step size mu . The second contribution, also belonging to the stationary case, is the derivation of the expressions of convergence time N/sub c/ and steady state mean square excess estimation error epsilon . It is shown that N/sub c/ is proportional to 1/( mu lambda ), with lambda being the minimum eigenvalue of the input covariance matrix. It is also shown that the product N/sub c/ epsilon is independent of mu . For a given epsilon , the convergence time increases with the eigenvalue spread of the input covariance matrix and the filter length, as well as its input noise power. The range of mu that achieves tolerable values of N/sub c/ and epsilon is determined. The third contribution is concerned with the nonstationary case. It is shown that the mean square excess estimation error is the sum of the two terms with opposite dependencies on mu . An optimum value of mu is derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The adaptive kernel algorithms usually achieve a good convergence performance and a tracking performance due to the universal approximator, offering an excellent solution to many problems with nonlinearities. However, as is well known, the convergence rate and steady-state error of adaptive filtering algorithm are a pair of inherent contradictions, and the kernel method is not exceptional. For this problem, a robust kernel adaptive filtering algorithm, called the variable-scaling factor kernel fractional lower power adaptive filtering algorithm based on the Sigmoid function, is developed by creating a new framework of cost function which combines the kernel fractional low power error criterion with the Sigmoid function for system identification of different noise environments. This new cost framework incorporates a scaling factor into the cost function of the Sigmoid kernel fractional lower power adaptive filtering algorithm (VS-SKFLP) in this paper. One of the main features in the new framework is its scaling factor. This scaling factor is used to control the steepness of the Sigmoid function, and the steepness can affect the convergence speed of filtering algorithm. The scaling factor provides a tradeoff between the convergence rate and the steady-state mean square error (MSE), which improves the convergence rate under the same steady-state mean square error. However, it is also an important problem to choose an appropriate scale factor. Therefore, a variable-scale factor SKFLP algorithm is also proposed to improve the convergence rate and steady-state MSE, simultaneously. The proposed variable-scale factor structure consists of a function of error, featuring the adaptive updates of their parameter estimated by making discerning use of the error. In this paper, the nonlinear saturation characteristic of the Sigmoid function and low order norm criterion are used to overcome the performance degradation of training data destroyed by non-Gaussian impulse noise and colored noise. Through the convergence analysis, the parameter estimation sequence of our proposed algorithm proves convergent. Simulation results show that the proposed algorithm (VS-SKFLP) outperforms other kernel adaptive filtering algorithms in system recognition with different noise environments.

A robust adaptive filtering algorithm based on the convex combination of two adaptive filters under the maximum correntropy criterion (MCC) is proposed. Compared with conventional minimum mean square error (MSE) criterion-based adaptive filtering algorithm, the MCC-based algorithm shows a better robustness against impulsive interference. However, its major drawback is the conflicting requirements between convergence speed and steady-state mean square error. In this letter, we use the convex combination method to overcome the tradeoff problem. Instead of minimizing the squared error to update the mixing parameter in conventional convex combination scheme, the method of maximizing the correntropy is introduced to make the proposed algorithm more robust against impulsive interference. Additionally, we report a novel weight transfer method to further improve the tracking performance. The good performance in terms of convergence rate and steady-state mean square error is demonstrated in plant identification scenarios that include impulsive interference and abrupt changes.

To improve the transmission efficiency and facilitate the realization of the scheme, an adaptive modulation (AM) scheme based on the steady-state mean square error (SMSE) of blind equalization is proposed. In this scheme, the blind equalization is adopted and no training sequence is required. The adaptive modulation is implemented based on the SMSE of blind equalization. The channel state information doesn’t need to be assumed to know. To better realize the adjustment of modulation mode, the polynomial fitting is used to revise the estimated SNR based on the SMSE. In addition, we also adopted the adjustable tap-length blind equalization detector to obtain the SMSE, which can adaptively adjust the tap-length according to the specific underwater channel profile, and thus achieve better SMSE performance. Simulation results validate the feasibility of the proposed approaches. Simulation results also show the advantages of the proposed scheme against existing counterparts.

The paper is concerned with analyzing the roundoff error effect on the tracking performance of the block least mean square (BLMS) algorithm when used in the adaptive identification of a time-varying plant. Rounding quantization is assumed. Expressions are derived for the steady state mean square error, steady state mean square weight deviation, and the corresponding optimum step sizes. It is found that the mean square error and the mean square weight deviation are decreasing functions of both the filter coefficients wordlength and the algorithm block size. Expressions for minimum and maximum block lengths are derived. The performance of the BLMS is compared to that of the conventional LMS algorithm. It is found that the BLMS possesses a higher resistance to roundoff errors than the LMS algorithm. The theoretical results of the paper are validated by computer simulations.

In recent years, the hyperbolic family of adaptive algorithms have been widely used to combat impulsive noise. The novel exponential hyperbolic sine adaptive filters (EHSAF) and the normalized exponential hyperbolic sine adaptive filter (NEHSAF) suitable for impulsive noise environments are proposed in this brief. The cost function is based on the exponential hyperbolic sine-based error function. The stability condition based on the learning rate and the steady-state analysis are investigated too. Additionally, a variable scheme for the scaling parameter is proposed to remove the tradeoff between convergence speed and steady-state excess mean square error (EMSE). The computational complexity is presented too. The simulation results in the context of unknown system identification and echo cancellation application have been performed to prove the performance improvement of the proposed algorithms.

A new hybrid blind equalization algorithm with steady-state performance analysis