A Direct Construction of Optimal ZCCS and IGC Code Set With Maximum Column Sequence PMEPR Two For MC-CDMA System
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Multicarrier code-division multiple-access (MCCDMA) combines an orthogonal frequency division multiplexing (OFDM) modulation with a code-division multiple-access (CDMA) scheme and hence exploits the advantages of OFDM as well as CDMA. However, a major drawback in MC-CDMA system is high peak-to-mean envelope power ratio (PMEPR). This problem can be dealt by employing proper codes. A Zcomplementary code set (ZCCS) is a collection of codes with same length and an equal number of constituent sequences or two-dimensional matrices with zero correlation zone (ZCZ) properties. In a ZCCS based MC-CDMA system, the PMEPR is determined by column sequence PMEPR of the codes. The column sequence PMEPR of existing ZCCS by using Boolean function approach is determined by the number of constituents sequences which are the same as the number of sub-carrier in a ZCCS based MC-CDMA system. Although, all existing Boolean function approach is a direct method to construct ZCCS and it is feasible for rapid hardware generation particularly for long ZCCSs, the large number of sub-carrier in an MC-CDMA system degrades the performance of an existing ZCCS based MC-CDMA system. In this paper, we propose a construction of ZCCS with maximum column sequence PMEPR 2 by using generalized Boolean functions (GBFs). The proposed ZCCS is optimal with respect to the theoretical upper bound. Our proposed construction can also generate ZCCS with inter-group complementary property or Inter-group complementary (IGC) code set with maximum column sequence PMEPR 2 whereas the maximum column sequence PMEPR of all existing IGC code set is given by the number of constituent sequences in a code. This work also establishes a link from ZCCS and IGC code set to higer-order Reed-Muller (RM) code.
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