A Novel Construction of Complementary Sequences Set from Complementary Sequences Pairs

The construction of complementary sets (CSs) of non-power of two length have raised lots of concerns due to the practical application in orthogonal frequency-division multiplexing (OFDM) systems. Recently, some works have been reported on construction of CSs with lengths non-power of two using the concatenation or insertion method of the sequences in Golay pair or set. In this paper, we achieved a construction of CSs of lengths $M+N$ for set size 4 based on Golay pair of lengths $M$ and $N$ , where $M$ and $N$ are lengths for which $q$ -ary complementary pairs exists. Also, we achieved a construction of CSs of set size 8 and sequence lengths $M+P$ or $P+P^{\prime}$ , where $M$ is length of $q$ -ary complementary pairs, $P$ and $P^{\prime}$ are lengths of $q$ -ary or complementary sets of size 4 exists. The presented designs can easily be extended to a set size of $2^{n+1}$ by recursive method. One important contribution of our work is that our constructions generalise some the previously reported constructions along with generating CSs under less constraints.