Variable Step-Size Widely Linear Complex-Valued Affine Projection Algorithm and Performance Analysis

Abstract

In this paper, a variable step-size widely linear complex-valued affine projection algorithm (VSS-WLCAPA) is proposed for processing noncircular signals. The variable stepsize (VSS) is derived by minimizing the power of the augmented noise-free a posteriori error vector, which speeds up the convergence and reduces the steady-state misalignment. By exploiting the evolution of the covariance matrix of the weight error vector, we provide insight into the theoretical behavior of the VSS-WLCAPA algorithm. In the analysis, we take into account the dependency between the weight error vector and the noise vector, which is useful for accuracy of the theoretical prediction. To evaluate the mean step-size, the probability density function of the magnitude of the error is derived by employing polar coordinate transformation. Moreover, a special case when the projection order reduces to one is analysed in detail. The presented theoretical analysis is different from existing methodologies for analyzing affine projection algorithms due to the use of the Kronecker product. Simulation results for system identification scenarios demonstrate the merits of the proposed algorithm and verify the accuracy of the theoretical analysis. Wind prediction experiments support the superiority of the proposed VSS-WLCAPA as well.

Adaptive Frequency domain Affine Projection Equalizer of MIMO SC-FDMA Based Overlap-Save Method

“…2. The main part of OLSM is the adaptive affine projection frequency domain equalizer (AAPFDE) [18][19][20][21][22]. This section focuses on finding the weights of AAPFDE and compare them the with the weights of MMSE-FDE.…”

Lawson-Norm Based Adaptive Filter for Channel Estimation and in-Car Echo Cancellation

“…To better understand the devised LNAF algorithm, its stability analysis is presented to get the boundary of learning rate, where the energy conversation method is considered, which has been used for AF analysis for several decades [12], [26].…”

“…This brief brings a Lawson-norm promoted AF (LNAF) algorithm to further enhance AP's convergence and steadystate performance if the system encounters impulsive interferences, and is robust for correlated inputs, and reduces effects from large outliers. Similar to the Lorentzian adaptive filtering (LAF) algorithm [23], motivated by the AP scheme and Lawson-norm [24]- [26], the constructed LNAF algorithm is obtained through taking gradient descent search on a Lawson norm promoting cost function to ensure robustness. The learning rate boundary for achieving stable convergence of the LNAF algorithm is presented and driven.…”

2020 Index IEEE Transactions on Signal Processing Vol. 68

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