One-dimensional Linear Array Beam Formation

In the analysis of the far-field area of uniform linear array, a method based on amplitude weighting for far-field radiation intensity distribution was proposed which is different from the phase control beam forming. After some mathematical transformation and reasoning, combining with the Fourier transform of pectination-like function, the formula for calculating the weights can be obtained. The simulation validates the correctness of this theory which indicates that it can infinitely approximate to the requested far-field radiation function by increasing the number of the array element. Quantitatively analyzing the wave distribution from the energy point of view, the numerical results show that the precise element number can be calculated according to the requirements of the energy. Combining the amplitude weighting with linear phase control in practice, it has been affirmed that the electric scanning can substitute the mechanical scanning, and the complexity and cost of the phase-shifter and controller in solely can be reduced significantly. This method can be extended to other arrays with periodical topological structure.Based on amplitude weighting, an approaching to function method for one-dimensional uniform linear array beam focusing in near field is proposed. Just assuming that the amplitude distribution function in space to beδ((r|â†')-(r|â†')₀), in which (r|â†')₀ is vector of focal point, the valueof every element radiation amplitude can be calculated by solving a set of homogeneous second-order nonlinear equations. The focusing effect between amplitude weighting and phase control has been compared from four aspects through Maple and the simulation show that the former has fewer side lobe and low energy loss. With the increase in working frequency, the phase-shifter and controller also has a corresponding increase in complexity, but it is comparatively simple to control the array element amplitude, so with the amplitude weighting method it can reduce the cost of the complexity. Moreover, this method can be extended to planar array or other array elements that their radiations have different polarization direction.