Simultaneous correlation of complementary set of sequences using a transpose generation approach

Complementary sets of sequences are currently being applied to signal coding, radar, and multi-user systems, among others. Their particular mathematical properties make them adequate for multi-emission and noisy environments. Nowadays sustained efforts are being devoted to reduce the calculations involved in the generation and/or correlation of these signals by means of recursive algorithms. Some authors have proposed efficient algorithms that are based on modular architectures made up of adders, multipliers and delays. This work introduces a new approach to correlation algorithms of complementary sets of sequences, which is based on a transposition of the generation process. This approach allows to notoriously reduce calculations, and enables the simultaneous correlation of M sequences, without adopting time multiplexing schemes or complex parallel implementations. The correlation algorithm is theoretically demonstrated and its calculation performance is evaluated in a hardware reconfigurable platform. A comparison with other algorithms is included, considering the amount of calculations as a function of the length of the sequences.