Search

In the past decade, the augmented complex-valued least mean square adaptive filtering algorithm based on the minimum mean square error criterion and widely-linear model has attracted much attentions due to its simplicity and applicability to non-circular signals. However, the system noise with impulse characteristics will dramatically affect the convergence of the augmented complex-valued least mean square algorithm. Recently, a robust widely-linear complex-valued least mean M-estimate algorithm has been proposed, which significantly improves the robustness of the augmented complex-valued least mean square algorithm to impulsive noise. But it should be noted that the widely-linear complex-valued least mean M-estimate algorithm with fixed step size faces the trade-off between convergence speed and steady-state accuracy. To overcome this drawback, a variable step size widely-linear complex-valued least mean M-estimate algorithm is presented in this paper, in which the optimal step size at each iteration is obtained by maximizing the difference between the mean square deviations of the WL-CLMM algorithm at adjacent moments. In order to reveal the statistical convergence behavior of the proposed variable-step-size widely-linear complex-valued least mean M-estimate algorithm to better guide the parameter selection in practical applications. Theoretical transient and steady-state mean-square deviation convergence behaviors of the variable-step-size widely-linear complex-valued least mean M-estimate algorithm are analyzed and the corresponding mean-square deviation expressions are also derived. Computer simulations on system identification and stereophonic acoustic echo cancellation in impulsive noise environments confirm the validity of the analysis results and the performance improvement from the variable step size strategy. [ABSTRACT FROM AUTHOR]

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]

Constrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs. [ABSTRACT FROM AUTHOR]