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Recent advances in space exploration have shown a great need for antennas with high resolution, high gain and low side lobe level (SLL). The last characteristic is of paramount importance especially for the Microwave Power Transmission (MPT) in order to achieve higher transmitting efficiency (TE) and higher beam collection efficiency (BCE). In order to achieve low side lobe levels, statistical methods play an important role. Various interesting properties of a large antenna arrays with randomly, uniformly and combined spacing of elements have been studied, especially the relationship between the required number of elements and their appropriate spacing from one viewpoint and the desired SLL, the aperture dimension, the beamwidth and TE from the other. We propose a new unified approach in searching for reducing SLL by exploiting the interaction of deterministic and stochastic workspaces of proposed algorithms. Our models indicate the side lobe levels in a large area around the main beam and strongly reduce SLL in the entire visible range. A new concept of designing a large antenna array system is proposed. Also, we have proposed a new technique to the beam-control in MPT using syclostationarity. Our theoretic study and simulation results clarify how to deal with the problems of side lobes in designing a large antenna array, which seems to be an important step toward the realization of future SPS/MPT systems.