Modular Architecture for Efficient Generation and Correlation of Complementary Set of Sequences

Golay sequences and complementary sets of sequences have been long studied for their application in multisensor and communication systems. The feasibility of these systems strongly depends on the design of an efficient generator and correlator with the aim of reducing the computational load and hardware complexity. Recursive algorithms, which allow efficient architectures, are available in the case of complementary pairs of sequences and complementary sets of four sequences. This work presents a generalization of these algorithms with the purpose of obtaining complementary sets of M sequences with length L, the number of sequences M being a power of two (M=2m), and the length L a power of M (L=2mN) with m,Nisin N-{0}. This fact allows an ideal Kroumlnecker delta function of weight MmiddotL in the addition of the autocorrelation functions of the M sequences of the set. Furthermore, the generation of M different mutually orthogonal sets can be obtained. This fact makes their application suitable in simultaneous multiemission systems. With the proposed algorithm, an effective reduction in the number of operations necessary to implement the correlator can be obtained, if it is compared with the straightforward implementation. Also, a regular structure is provided that allows implementation of the generator and/or the correlator for complementary sets of M sequences, based on the structure for complementary sets of M/2 sequences The sequence length can also be easily extended to any multiple of M. Finally, the generation and correlation of M different mutually orthogonal complementary sets of M sequences can be immediately derived