1. A method of designing a detection and ranging apparatus having an M number of transmitting elements and an N number of receiving elements, the method comprising: decomposing a desired polynomial equation representing an array factor of a K element sensor array into a first polynomial equation representing an array factor of an M element sensor array and a second polynomial equation representing an array factor of an N element sensor array; determining arrangement of the M number of transmitting elements based on the first polynomial equation; and determining arrangement the N number of receiving elements based on the second polynomial equation, wherein K=M×N, or K≧max(M, N).