This paper addresses the problem of practically implementing an original sound source localization strategy for mobile robots applications. The proposed method is based on a convex optimization solution to beamforming. It allows the sensing of signals within a direction of arrival and frequency domain of interest while rejecting other data. A precise description of the acquisition chain is proposed and a careful mathematical modeling is given in order to bridge the gap between theory and practical implementation. Simulation results and comparisons with classical filter-sum beamformer techniques are provided at the end of the paper to illustrate the performance of the sensor.