  Applying a sparse constraint on the beam pattern has been suggested to
suppress the sidelobe of the minimum variance distortionless response (MVDR)
beamformer recently. To further improve the performance, we add a mixed norm
constraint on the beam pattern. It matches the beam pattern better and
encourages dense distribution in mainlobe and sparse distribution in sidelobe.
The obtained beamformer has a lower sidelobe level and deeper nulls for
interference avoidance than the standard sparse constraint based beamformer.
Simulation demonstrates that the SINR gain is considerable for its lower
sidelobe level and deeper nulling for interference, while the robustness
against the mismatch between the steering angle and the direction of arrival
(DOA) of the desired signal, caused by imperfect estimation of DOA, is
maintained too.
