Kronecker sequences for spread-spectrum communication

Abstract

The paper considers the correlation properties of sets of sequences in which each sequence is constructed by taking the Kronecker product (or tensor product) of two short sequences. It is shown that if the short sequences are carefully chosen then the correlation properties of such sets are nearly as good as those of sequences of comparable length that have been obtained by other means. Furthermore, it is much easier to optimise the phases of these sequences because of the structure that they inherit from the Kronecker product operation. This structure also enhances the ease of synchronisation for such sequences. If the signal/noise ratio is large, the time required to synchronise to Kronecker sequences is significantly less than the time required to synchronise to other sequences of comparable lengths. Thus, the Kronecker sequences allow one to achieve rapid acquisition at the expense of a very small deterioration in some of the correlation properties.