New construction of mutually orthogonal complementary sequence sets

To address the limitations in design methods and the scarcity of construction parameters for mutual orthogonal complementary sequence set (MOCSS), a construction method for MOCSS based on paraunitary (PU) matrices was proposed. The new concept of coefficient paraunitary (CPU) matrices was defined, and by employing matrix multiplication, Kronecker product, and matrix iteration techniques, three types of PU matrices with varying sizes were constructed. Utilizing the equivalence between PU matrices and MOCSS, a series of multi-phase MOCSS with flexible parameter selection were developed, filling the parameter gap in the existing literature. Considering the suppression of peak-to-average power ratio (PAPR) in multi-carrier code division multiple access (MC-CDMA) systems, a class of CPU matrices with low column vector PAPR characteristics was designed using Boolean functions. Experimental results demonstrate that the constructed MOCSS using such CPU matrices effectively controls the column sequence PAPR within the range of below two, while maintaining the flexibility of code capacity and length, providing a variety of signal selection options for the systems.