The approximate formulas for optimal quantized amplitude weights are firstly derived on condition of equally step widths.When step widths are not equal
particle swarm optimization (PSO) algorithm is introduced.The algorithm is modified to cope with the constrained conditions for integer variables
which correspond with step widths.An efficient series-PSO algorithm is proposed to solve the optimization problem.Simulation experiment shows the efficiency of the series-PSO algorithm.Finally
the influence of quantized amplitude weights error to sidelobe level and the design of planar array antennas are discussed.