Robust Adaptive Algorithm for Smart Antenna System With $\alpha$ -Stable Noise

One of the main problems facing beamforming in smart antenna system is the <inline-formula> <tex-math notation="LaTeX">$ {\alpha }$ </tex-math></inline-formula>-stable noise. To address this problem, a novel algorithm, named the recursive continuous logarithmic mixed <inline-formula> <tex-math notation="LaTeX">${p}$ </tex-math></inline-formula>-norm (RCLMP) algorithm, which employs a logarithmic cost, is proposed in this brief. The proposed algorithm combines the logarithmic <inline-formula> <tex-math notation="LaTeX">${p}$ </tex-math></inline-formula>-norms <inline-formula> <tex-math notation="LaTeX">${1}{\leq } p \leq 2$ </tex-math></inline-formula> which does not need the parameter selection and prior knowledge of <inline-formula> <tex-math notation="LaTeX">${\alpha }$ </tex-math></inline-formula>-stable noise, and exhibits good robustness against <inline-formula> <tex-math notation="LaTeX">${\alpha }$ </tex-math></inline-formula>-stable noise. Moreover, we show some <inline-formula> <tex-math notation="LaTeX">${H}^{{\infty }}$ </tex-math></inline-formula> norm bounds for the proposed algorithm. Simulation results show that the RCLMP algorithm outperforms the existing algorithms in terms of interference rejection capability and estimation accuracy.