# A Robust Complex α-Sigmoid Affine Projection Algorithm Under Non-Gaussian Noise

## TL;DR

This paper introduces a new complex-valued adaptive filtering algorithm that performs better in noisy environments with correlated signals.

## Contribution

The novel α-CSAP algorithm uses an α-Sigmoid cost function to improve performance in non-Gaussian noise.

## Key findings

- The α-CSAP algorithm suppresses impulsive noise and reduces computational complexity.
- Theoretical analysis provides a steady-state mean square deviation expression.
- Simulations show superior performance in system identification and beamforming.

## Abstract

To address the performance degradation of traditional adaptive filtering algorithms in environments with correlated input signals and non-Gaussian noise, this paper proposes a complex-valued affine projection algorithm based on the α-Sigmoid cost function (α-CSAP). The algorithm leverages the nonlinear characteristics of the α-Sigmoid function and implicitly achieves variable step-size updates by introducing a normalization factor, which effectively suppresses impulsive noise interference and avoids matrix inversion, thereby reducing computational complexity. Theoretical analysis derives the steady-state mean square deviation (MSD) expression for the algorithm. Simulation results demonstrate that the proposed α-CSAP algorithm exhibits superior performance compared to traditional complex adaptive filtering algorithms in both system identification and beamforming application scenarios.