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In this paper, cooperative beamforming in the context of wireless sensor networks with random mobile nodes is analyzed. In the first part, we use two dimensional Brownian motion to model mobile nodes, which are assumed to follow Gaussian distribution at every time. The concept of overall outage probability is introduced, and its lower and upper bounds are derived theoretically. In the second part, we extend the Brownian motion to any form and prove the beampattern with minimum mainlobe as well as maximum three-dB sidelobe region can be got simultaneously, then we design a low complexity algorithm to arrange sensor node locations to produce this optimum beampattern. Simulation results show that the overall outage probability and its lower and upper bounds are in good agreement, and compared with uniform and Gaussian distribution, the beampattern produced by the algorithm has sharpest mainbeam and significantly small sidelobe peaks.