Abstract
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <formula formulatype="inline"><tex Notation="TeX">$\ell_{1}$</tex> </formula>-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 <formula formulatype="inline"><tex Notation="TeX">$\lambda$</tex></formula> as well as the adaptive step-size <formula formulatype="inline"><tex Notation="TeX">$\mu(k)$</tex> </formula> are derived in detail. Simulation results verify validity and advantages of the proposed algorithms over some existing methods. </para>
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