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The non-uniform distribution of the weight vector of the elements in an antenna array has attracted much attention in order to obtain such as the desired beam pattern, null locations, and performance objectives. This topic has been of interest for many decades. Several mathematical models and optimization algorithms have been developed to achieve a controllable sidelobe level. However, few researchers have considered the effect of the non-uniform distribution on the aperture efficiency. This paper presents a comprehensive study and proposes accurate mathematical modelling of the aperture efficiency of an antenna array which is divided into two components: power-loss efficiency (which dominates total aperture efficiency) and power-distribution efficiency to gain a better understanding. The paper also shows how the sidelobe level of an antenna array is linked to these efficiencies and how they can be improved. It is proved that the aperture efficiency exponentially decays when lowering the sidelobe level. However, it converges to a certain value when the sidelobes vanish. Moreover, a validation example through simulations is presented to verify the mathematical modelling of the aperture efficiency.

Aperture Efficiency of Non-Uniform Antenna Arrays With Controlled Sidelobe Level