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The complex domain adaptive filtering algorithms has shown excellent performance in the field of signal processing. Among them, the well-known complex least mean square (CLMS) algorithm has been widely used in practical projects. However, the CLMS algorithm only considers the case where the output signal is disturbed by noise, ignores the input signal may also be interfered by noise. Moreover, the signal is likely to be disturbed by impulsive noise in practice. Based on the above problems, the complex total least mean M-estimation (CTLMM) adaptive algorithm based on the M-estimation function is put forward in this paper. The algorithm can well handle the case where both input and output signals are subject to complex domain noise interference, and it also shows robustness with impulsive noise. This paper also analyzes the local stability of the CTLMM algorithm and discuss the theoretical steady-state error of the algorithm. Finally, simulation results verify the advantages of CTLMM algorithm and the rightness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic model is presented for the nonparametric variable step-size normalized least-mean-square (NP-VSS-NLMS) algorithm. This algorithm has demonstrated potential in practical applications and hence a deeper understanding of its behavior becomes crucial. In this context, model expressions are obtained for characterizing the algorithm behavior in the transient phase as well as in the steady state, considering a system identification problem and Gaussian input data. Such expressions reveal interesting algorithm characteristics that are useful for establishing design guidelines and for the advancement of more refined algorithms. Simulation results for various operating scenarios ratified both the model's accuracy and the algorithm's superior performance relative to other recent and relevant algorithms from the literature. [ABSTRACT FROM AUTHOR]

A novel multi-combined-step-size normalized subband adaptive filtering algorithm is proposed. Different from the traditional combined-step-size method, by employing a variable mixing parameter on each subband, our designed algorithm is able to combine a large step size with a small one more effectively for each subband. The subband mixing parameters are derived from the variance of the noise-free a priori subband error signals. In this design, a noniterative shrinkage strategy is also utilized to estimate the noise-free a priori subband error signals. Moreover, the mean-square and steady-state performances of the proposed algorithm are studied. Simulation results illustrate that the proposed algorithm outperforms other algorithms mentioned in this paper in terms of tracking capability, convergence speed and steady-state error. [ABSTRACT FROM AUTHOR]

To enhance the performance of the diffusion robust adaptive filtering algorithm, this paper presents a novel loss function framework named the "Tanh cost function framework." By utilizing this framework, we are able to incorporate standard cost functions, devise novel cost functions, and introduce the associated diffusion algorithm. Moreover, the convergence of the algorithm is thoroughly analyzed. Furthermore, the proposed diffusion Tanh algorithm family is simulated in a system identification model to assess its performance, demonstrating superior performance compared to the standard diffusive algorithm. Notably, the DTHLMS within the diffusion tanh algorithm family exhibits superior performance over the mainstream robust diffusion algorithms. [ABSTRACT FROM AUTHOR]

To enhance the convergence performance of the affine projection sign subband adaptive filter (AP-SSAF) algorithm under highly correlated inputs, the novel AP-SSAF (NAP-SSAF) algorithm was proposed through fully utilizing the decorrelation characteristic of SAF, which obtains quicker convergence behavior than the AP-SSAF algorithm. However, under unknown system identification, the estimation accuracy of the NAP-SSAF algorithm may unavoidably decrease when the input of the adaptive filter is contaminated by noise. To alleviate this issue, in this paper, we propose the bias-compensated NAP-SSAF (BC-NAP-SSAF) algorithm to alleviate the estimated bias through employing unbiasedness criterion. Benefiting from the unbiased criterion, the proposed BC-NAP-SSAF algorithm achieves an asymptotically unbiased estimation. Moreover, the convergence bounds of the proposed BC-NAP-SSAF algorithm in the mean and mean-square senses are provided to ensure stability, which are obtained by resorting to Price's theorem along with some reasonable assumptions. The effectiveness of the derived theoretical convergence bounds is also corroborated. Finally, numerical simulations under system identification and acoustic echo cancellation applications demonstrate that the proposed BC-NAP-SSAF algorithm outperforms other algorithms in terms of estimation accuracy and tracking capability for noisy input under impulsive noise environment. [ABSTRACT FROM AUTHOR]

For maneuvering target tracking, a novel adaptive variable structure interactive multiple model filtering and smoothing (AVSIMMFS) algorithm is proposed in this paper. Firstly, an accurate model of the variable structure interactive multiple model algorithm is established. Secondly, by constructing a new model subset based on the original model subsets, the matching accuracy between the model subset and the actual maneuvering mode of the target is improved. Then, the AVSIMMFS algorithm is obtained by smoothing the filtered data of the new model subset. Because of the combination of forward filtering and backward smoothing, the target tracking accuracy is further improved. Finally, in order to verify the effectiveness of the algorithm, the simulation is carried out on two cases. The simulation results show that the tracking performance of AVSIMMFS algorithm is better than other methods and has lower calculation cost. [ABSTRACT FROM AUTHOR]

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by α -stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the α -stable noise environment, providing new methods to deal with multi-channel interference in wireless networks. [ABSTRACT FROM AUTHOR]

To make the zero attractor sign subband adaptive filter (ZA-SSAF) algorithm more suitable for sparse systems, where the impulse response is sparse and disturbed with impulse interference, this paper proposes an improved sign subband adaptive filtering algorithm that takes advantage of the splendid robustness of the arctangent function against impulse interference. Based on the ZA-SSAF algorithm, this algorithm introduces a proportionate coefficient matrix composed of a nonlinear function (the arctangent function) to assign different step sizes for the tap coefficients that need to be updated. The step size of the algorithm is updated in proportion to the magnitude of the weight coefficient in the adaptive process according to the relationship of the arctangent function, which greatly shortens the calculation convergence time and improves the overall convergence performance. The simulation results show that the proposed algorithm takes into account the trade-off between a faster convergence rate and a lower steady-state error and is superior to the traditional sign subband algorithm and zero attractor sign subband adaptive filtering algorithm in terms of the convergence rate and robustness against impulse noise. [ABSTRACT FROM AUTHOR]

Estimation in a cooperative and distributed manner in wireless sensor networks (WSNs) has considered much attention in recent years. When this distributed estimation is performed adaptively, the concept of adaptive networks will develop. In such networks, proper selection of the unknown parameter length is an issue in itself. A deficient filter length results in an additional steady-state error while selecting a large length will impose a more computational load on the nodes, which is critical in sensor networks due to the lack of energy resources. This motivates the use of variable tap-length adaptive filters in the context of the adaptive networks. This has been achieved in adaptive networks using the distributed fractional tap-length (FT) algorithm. This algorithm requires proper selection of the length adaptation parameters, such as error width and length adaptation step-size. This paper proposes an automatic method for selecting these parameters. In the proposed method, these parameters are adapted based on the estimated gradient vector. The proposed method is fully distributed and presented in a diffusion strategy. Simulation results show that the proposed algorithm has both the advantage of fast length convergence and an unbiased steady-state tap-length. [ABSTRACT FROM AUTHOR]

A filtering algorithm based on frequency domain spline type, frequency domain spline adaptive filters (FDSAF), effectively reducing the computational complexity of the filter. However, the FDSAF algorithm is unable to suppress non-Gaussian impulsive noises. To suppression non-Gaussian impulsive noises along with having comparable operation time, a maximum correntropy criterion (MCC) based frequency domain spline adaptive filter called frequency domain maximum correntropy criterion spline adaptive filter (FDSAF-MCC) is developed in this paper. Further, the bound on learning rate for convergence of the proposed algorithm is also studied. And through experimental simulations verify the effectiveness of the proposed algorithm in suppressing non-Gaussian impulsive noises. Compared with the existing frequency domain spline adaptive filter, the proposed algorithm has better performance. [ABSTRACT FROM AUTHOR]

This paper aims to extend the proportionate adaptation concept to the design of a class of diffusion normalized subband adaptive filter (DNSAF) algorithms. This leads to four extensions of the algorithm associated with different step-size variations, namely diffusion proportionate normalized subband adaptive filter (DPNSAF), diffusion μ -law PNSAF (DMPNSAF), diffusion improved PNSAF (DIPNSAF) and diffusion improved IPNSAF (DIIPNSAF). Subsequently, steady-state performance, stability conditions and computational complexity of the proposed algorithms are investigated. For each extension the performance has been evaluated using both real and simulated data, where the outcomes demonstrate the accuracy of the theoretical expressions and effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

To better perform distributed estimation, this paper, by combining the Fair cost function and adapt-then-combine scheme at all distributed network nodes, a novel diffusion adaptive estimation algorithm is proposed from an M-estimator perspective, which is called the diffusion Fair (DFair) adaptive filtering algorithm. The stability of the mean estimation error and the computational complexity of the DFair are theoretically analyzed. Compared with the robust diffusion LMS (RDLMS), diffusion Normalized Least Mean M-estimate (DNLMM), diffusion generalized correntropy logarithmic difference (DGCLD), and diffusion probabilistic least mean square (DPLMS) algorithms, the simulation experiment results show that the DFair algorithm is more robust to input signals and impulsive interference. In conclusion, Theoretical analysis and simulation results show that the DFair algorithm performs better when estimating an unknown linear system in the changeable impulsive interference environments. [ABSTRACT FROM AUTHOR]

The widely linear model has attracted much attention due to its good features for non-circular adaptive signal processing in recent years. In this paper, a sparsity-induced augmented complex-valued NLMS algorithm is proposed to promote the performance of the adaptive filter for estimating sparse systems, which is established by incorporating the l 0 -norm regularization into the squared error normalized by the input vector. To address the problem of trade-off between fast convergence rate and low steady-state misalignment, we minimize the variance of the a posteriori error to derive an optimal step-size and then some practical problems are considered. Simulation results are provided to verify the superior performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Due to its low computational burden, the affine-projection-like (APL) adaptive filtering algorithm has been extensively studied for colored signal input. Recently, a robust APL algorithm was designed by adopting the M-estimate cost function in impulsive noise environment; however, its convergence rate is very slow for sparse system identification. This paper proposed a proportionate APL M-estimate (PAPLM) algorithm, which is derived by using the proportionate matrix to heighten the convergence rate. To maintain good steady-state performance of the PAPLM algorithm, a time-varying parameter PAPLM (TV-PAPLM) algorithm is proposed, which uses a modified exponential function to adjust the time-varying parameter according to the ratio of the mean square score function to the system noise variance. Moreover, the steady-state excess mean-square error performance of PAPLM algorithm is analyzed and obtained in detail. Simulation results reveal that the proposed PAPLM and TV-PAPLM algorithms achieve fast convergence rate and good steady-state performance in sparse system identification. [ABSTRACT FROM AUTHOR]