Simplified Set-Membership Affine Projection Least Mean Fourth Algorithm

The problem of distributed estimation is considered for distributed network. A diffusion model on adaptive affine projection sign algorithm based on least mean fourth algorithm is introduced according to an Adapt-Then-Combine (ATC) design for the distributed framework. Least mean fourth (LMF) algorithm is defined by taking the fourth power of error to against the non-Gaussian environment. An adaptive affine projection sign algorithm based on LMF algorithm is proposed firstly. Then, an ATC diffusion model on adaptive affine projection sign algorithm based on LMF algorithm is presented in terms of the low complexity of sign approach with the order of adaptation and combination, named as ATC-DAPS-LMF. Numerical simulations verify that the proposed algorithm can perform significantly to the conventional affine projection sign algorithm.

Least-Mean Square algorithm, or simply the LMS, is generally one of the most commonly used techniques for optimized solution in adaptive schemes especially in the Gaussian environment. However, least mean fourth (LMF) algorithm and its variants, such as normalized LMF (NLMF), perform better in the non-Gaussian environment. The conventional LMF algorithms usually diverge in non-Gaussian environment with dynamic input. Conventionally, regularization is archived by using a small constant compensation term in the denominator of the learning rate to protect the algorithm from divergence. This paper introduces an efficient time-varying regularized normalized least mean fourth (R-NLMF) algorithm. In the proposed algorithm, the regularization term is made time varying and gradient adaptive according to steepest descent approach. Thus the proposed algorithm adapts its learning rate according to the environment and the input signal dynamics. A similar approach, namely Generalized Normalized Gradient Descent (GNGD) algorithm, has been previously applied to the normalized least mean-square (NLMS) algorithm in the Gaussian environment. However, due to its dependence on NLMS, the GNGD algorithm performance degrades in non-Gaussian environment. In order to overcome this problem, an efficient regularized NLMF algorithm for non-Gaussian environment is proposed. The algorithm shows promising results and achieves faster convergence while maintaining lesser steady-state miss-adjustment. Simulations are carried out to support the theoretical development.

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.

Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations.

Adaptive equalization is undoubtedly one of the cornerstones of digital communication as it allows for fast and reliable data transmission over practical channels that are non-ideal and that are plagued with serious problems such as signal dispersion and non-Gaussian interferences. In such cases, the performance of the well-known least-mean square (LMS) algorithm or that of any of its variants remains sub-optimal at best. As a remedy to this, the least-mean fourth (LMF) algorithm was later proposed but its high computational load was found to be a constraining factor in its practical implementation, particularly for real-time applications. Inspired from a previous work done on the LMS [1], we recently proposed a new algorithm [2], termed LMF-PTQ, combining the power of the LMF with the implementational advantages of the power-of-two quantization scheme. In this work, we demonstrate, through an extensive simulation study, the effectiveness of our proposed LMF-PTQ algorithm in the equalization of a time-varying channel in a CDMA system which suffers from both signal dispersion and non-Gaussian disturbances. The results obtained so far are very encouraging and provide us with ample enthusiasm to investigate the proposed algorithm further.

In this work, the convergence analysis of the variable weight mixed-norm least-mean squares (LMS)-least mean-fourth (LMF) adaptive algorithm is derived. The proposed algorithm minimizes an objective function defined as a weighted sum of the LMS and LMF cost functions, where the weighting factor is time varying and adapts itself to allow the algorithm to keep track of the variations in the environment. As a by-product of this novel approach, new necessary and sufficient conditions for the LMF algorithm have been derived. Furthermore, a more general expression for the excess steady-state error for the LMF algorithm has been derived.

Fast exact variable order affine projection algorithm

In this work, a family of normalized least mean fourth algorithms is presented. Unlike the LMF algorithm, the convergence behavior of these algorithms is independent of the input data correlation statistics. Moreover, the tracking analysis of these algorithms is carried out in the presence of two sources of nonstationarites (carrier frequency offset between transmitter and receiver, and random variations in the environment). Simulation results agree very closely with theory and an enhancement in performance is obtained through the use of these techniques over the LMF algorithm. the step size.

Subband affine projection (SAP) algorithm which combines the advantages of the affine projection algorithm (APA) and subband adaptive filtering (SAF) has been proposed for achieving the improved convergence performance. In this paper, the family of SAP algorithms is presented. Following this, the mean-square performance for this family of SAP algorithms is derived. The derivation process is based on energy conservation arguments and does not limit the regressors to being a specific random distribution. Simulation results illustrate the efficiency for this analysis.

Affine projection algorithms (AP) are widely used to implement active noise control (ANC) systems, due to their fast convergence speed and robustness, nevertheless their high computational cost could restringe their use in real-time applications. For that reason several low cost AP algorithms have been proposed, such as the Error Coded Affine Projection (ECAP) algorithm; however, in order to implement the algorithm in an ANC system is necessary to perform some modifications. In this paper, we present a version of the ECAP algorithm for single-channel ANC systems. The proposal is done using the conventional filtered-x scheme; furthermore, we use an evolutionary method to reduce the projection order of the algorithm during the computation process. Simulation results show a similar convergence speed to the AP algorithm, a lower final residual error and significant computational savings.

The adaptive algorithms have been widely studied in Gaussian environment. However, the impulsive noise and other non-Gaussian noise may largely deteriorate the performance of algorithm in practical applications. To address this problem, in this paper, we propose two novel adaptive algorithms for system identification problem with mixed noise scenarios. Both proposed algorithms are based on the framework of the affine projection (AP) algorithm. The first proposed algorithm, termed as VS-APMCCA, combines variable step-size (VS) strategy and maximum correntropy criterion (MCC) to obtain improved performance. For further performance improvement, the VC-VS-APMCCA is developed, which is based on the variable center (VC) scheme of MCC. The convergence analysis of the VC-VS-APMCCA is conduced. Finally, simulation results demonstrate the superior performance of the VS-APMCCA and VC-VS-APMCCA.

Affine projection (AP) algorithms have demonstrated faster convergence speed than conventional least mean square (LMS) algorithms, thus providing an attractive solution in the active noise control (ANC) field. However, the AP algorithms demand high computational cost, restricting their practical use in real-time ANC applications. Recently, a multichannel filtered-x error-coded affine projection-like (FXECAP-L) algorithm with evolving order has been proposed to reduce the computational burden by maintaining the convergence speed of AP algorithms. In order to obtain an efficient and robust FXECAP-L algorithm with evolving order, the scaling factor and encoder resolution need to be adjusted manually, which is a time-consuming and costly effort that must be carried out by expert designers. To reduce these costs and efforts, we introduce, for the first time, a strategy for automatic adjustment of the scaling factor and encoder resolution that benefits the rapid development of practical ANC applications. To demonstrate its practical use, we applied the proposed strategy for controlling the noise in an acoustic duct. The practical results demonstrate the automatic adjustment of the FXECAP-L algorithm which maintains high convergence speed at the expense of a small compromise in terms of processing time.

Hypotheses made about the behavior of the affine projection algorithm (APA) are investigated by means of carefully designed comparative experiments. These experiments lead us to the properties of the direction vector used in APA. Experiments also show that APA converges faster than NLMS in the case of white noise input, leading us to question that whitening of the direction vector is the explaining factor for the convergence acceleration observed with APA. An alternative hypothesis is offered for why APA may yield faster convergence than NLMS.

In this paper, we provide some insights into the convergence and steady-state behaviors of the sign-error least mean fourth (SLMF), sign-sign least mean fourth (SSLMF), normalized sign-error least mean fourth (NSLMF), and normalized sign-sign least mean fourth (NSSLMF) algorithms for both cases of real- and complex-valued data. Moreover, we also report the equivalence algorithms of the block-based normalized sign-error least mean fourth (BBNSLMF) and block-based normalized sign-sign least mean fourth (BBNSSLMF) algorithms. Finally, simulations are conducted for both cases of real- and complex-valued data to provide us with more insights into the performance of the SLMF, SSLMF, NSLMF, and NSSLMF algorithms.

A novel robust affine projection algorithm (APA) is proposed, which selectively shrinks error components in an error vector according to their individual possibilities of being interrupted by the impulsive noise. In existing robust APAs, if there exists only one error component interrupted by the impulsive noise, all error components of an error vector are shrunk using common step sizes which are inversely proportional to the norm of the error vector. This improper scaling results in performance degradation with a high impulsive noise probability and projection order. In this paper, we derive a modified minimization criterion considering the individual possibilities of error components from a geometric interpretation. For a wide range of impulsive noise probability and a high projection order, the performance of the proposed algorithm is verified in various system identification events including an abrupt system change. The proposed algorithm showed the fastest convergence rate and the lowest steady-state mean square deviation compared to the previous robust APAs and a recent variable step-size affine projection sign algorithm.