Robust Minimum $\ell _{1}$ -Norm Adaptive Beamformer Against Intermittent Sensor Failure and Steering Vector Error

A robust adaptive beamformer is described to mitigate against steering vector error and intermittent sensor(s) failure which exists in the form of impulsive noise in the received signal of failed sensor(s). This new beamformer iteratively minimizes the l ₁ -norm of the beamformer´s output, subject to a prespecified set of quadratic constraints which target on attenuating the influence caused by steering vector error. To solve the proposed optimization problem, gradient descent algorithm is adopted. The choice of the Lagrange multiplier ?? as well as the adaptive step-size ??(k) are derived in detail. Simulation results verify validity and advantages of the proposed algorithms over some existing methods.