Maximum Array Gain Versus Optimum Pattern

Abstract

In the design of arrays, there is a tradeoff between obtaining the maximum array gain on one hand and an optimum pattern on the other. An array was chosen, and the amplitude shading coefficients were calculated to produce the maximum array gain. Next the Tchebyscheff polynomials were used to obtain the amplitude shading coefficients which result in an optimum intensity pattern. Then the array gains and intensity patterns were calculated for each procedure and for a surface generated ambient and an isotropic noise field. The beam width of the patterns (for the same side lobe levels) and the array gains, as obtained by the two methods, were compared at each element spacing. For the cases of a linear, five-element, evenly spaced array at spacings of d/λ=1/8, 2/8, ⋯, 6/8 and both noise models, the two procedures produced minor differences. The maximum differences were that the Tchebyscheff procedure produced a main beam about 112° narrower but resulted in 12 dB less of array gain. For d/λ=7/8 and 1, differences were greater.