Improved architecture of complementary set of sequences correlation by means of an inverse generation approach

Abstract

System coding is a growing trend in all fields of engineering. Many different algorithms have been developed and studied for applications in signal processing, radar and multi-emission systems, among others. One of the most interesting algorithms, among these, is the complementary sets of sequences (CSS) given their potential and simplicity. They are characterised by a distinctive correlation and orthogonality properties. Nowadays, sustained efforts are being devoted toreducing the calculations involved in the generation and/or correlation of these sequences by means of recursive algorithms. Some authors have brought forward efficient algorithms that are based on modular architectures made up of adders, multipliers and delays. This work introduces an inverse generation approach to perform the correlation of CSS. This approach allows one to substantially reduce calculations, and enables the simultaneous correlation of M sequences, adopting neither time-multiplexing schemes nor complex parallel implementations. This is theoretically demonstrated by means of generation and correlation algorithms. An analysis of the performance and efficiency is then conducted in a reconfigurable hardware platform. The proposal represents an advance in the practical application of these sequences in the above-mentioned fields.