ABSTRACT
Large arrays of regularly spaced radiation elements are often prohibitively large, expensive, and can exhibit excessive mutual coupling. Beam width specifications often dictate the length of the array. It is possible to retain the same array length, but thin the number of elements to retain an equivalent beamwidth with a commensurate loss in gain. Periodic thinning of the array element in a uniformly spaced array will create grating lobes, but randomizing the element positions (spacing) can offset this effect. A useful probabilistic approach to thinned array design was formulated by Aggarwal and Lo [19], where the array sidelobe level threshold is described by a probability density function. The probability of power side lobe level being below a threshold is given b:
P = [1 − exp(−α)] exp ( − 2 λ
√ πα
3 exp(−α)
) , (10.26)
where
α = N/SLR L = the linear array level N = the number of elements SLR = the power side lobe level. The N parameter sets an average element spacing for a given array length L. The use of directive radiation
elements can reduce far out side lobe levels. An analysis by Steinberg [20] reveals that the use of directive element can reduce the overall length of the linear array described in Equation 10.26, by the following:
Leff λ
= L/λ√ α(W /λ)
, (10.27)
where
L = the linear array length W /λ = the electrical size of the radiating element.
