Mutually orthogonal complementary pairs for OFDM-CDMA systems

Two novel recursion constructions of mutually orthogonal complementary pairs (MOCPs) are respectively presented on the basis of concatenation and interleaving operations. For the proposed set consisting of MOCPs, the zero-shift cross-correlation function between any two complementary pairs is equal to zero, that is, all of complementary pairs in MOCPs set are orthogonal to each other, as suggested by the set´s name. The constructed MOCPs set can possess maximum set size since the number of complementary pairs in MOCPs set is equal to processing gain (or the length of complementary pair). Different from the previous researches, any two adjacent complementary pairs in the constructed MOCPs set are mates of each other and then ideal aperiodic correlation properties can be obtained for such two adjacent complementary pairs. In addition, the peak-to-average power ratio (PAPR) of the proposed MOCPs set can be limited to 3dB since each complementary pair has ideal aperiodic auto-correlation function. The proposed two constructions of MOCPs set are quite suitable for OFDM-CDMA systems, where not only larger system capacity but also lower PAPR can be obtained.