Spherical sequences with low aperiodic crosscorrelation

The authors present a new procedure for the generation of non-binary sequences having superior aperiodic crosscorrelation properties to Gold sequences. The proposed procedure randomly extracts points from the surface of a multidimensional sphere, with a posterior selection technique similar to those used in genetic algorithms. A theoretical model is provided, describing the behaviour of these sequences, and several numerical experiments are performed comparing these sequences with those from the literature. It is demonstrated that these sequences outperform both Gold and chaotic generated sequences and approximate the performance of 4-phase sequences in aperiodic crosscorrelation. The sequences have the additional advantages of inherent privacy, due to their random nature and the unlimited number of sequences per set.