Linear Array Thinning Exploiting Almost Difference Sets

Codebooks from almost difference sets

In direct spread CDMA systems, codebooks meeting the Welch bounds are used to distinguish among the signals of different users. Recently, constructions of codebooks with difference sets meeting Welch’s bound on the maximum cross-correlation amplitude were developed. In this paper, a generic construction of codebooks using almost difference sets is considered and several classes of codebooks nea...

Genetically-designed Arbitrary Length Almost Difference Sets

When almost all sets are difference dominated

We investigate the relationship between the sizes of the sum and difference sets attached to a subset of {0, 1, ..., N}, chosen randomly according to a binomial model with parameter p(N), with N = o(p(N)). We show that the random subset is almost surely difference dominated, as N → ∞, for any choice of p(N) tending to zero, thus confirming a conjecture of Martin and O’Bryant. Furthermore, we ex...

Almost difference sets and their sequences with optimal autocorrelation

Almost difference sets have interesting applications in cryptography and coding theory. In this paper, we give a wellrounded treatment of known families of almost difference sets, establish relations between some difference sets and some almost difference sets, and determine the numerical multiplier group of some families of almost difference sets. We also construct six new classes of almost di...

A Thinning Method of Linear And Planar Array Antennas To Reduce SLL of Radiation Pattern By GWO And ICA Algorithms

In the recent years, the optimization techniques using evolutionary algorithms have been widely used to solve electromagnetic problems. These algorithms use thinning the antenna arrays with the aim of reducing the complexity and thus achieving the optimal solution and decreasing the side lobe level. To obtain the optimal solution, thinning is performed by removing some elements in an array thro...