Arrays of random line arrays with constrained element separations

In previous analyses of random arrays the element position probability density functions (pdf’s) assumed have allowed the possibility of elements being arbitrarily close together. When elements are close enough together for the received noise samples to be correlated, the directivity index (DI) of the array is reduced. In an array of random line arrays this DI reduction can be substantially eliminated by placing a constraint on the minimum interelement spacing allowed on each line. Expressions for the ensemble averages of the pattern function and the power pattern are derived by use of a pdf for each element position that excludes a small region centered on each of the previously chosen element positions on the same line. Calculated power patterns and gain patterns for arrays of random line arrays with constrained and unconstrained separations are compared.