Complementary Sets, Complete Complementary Codes, and Their Applications

Abstract

Due to the ideal autocorrelation property, Golay complementary sets (GCSs) can be applied to orthogonal frequency division multiplexing (OFDM) systems for peak-to-average power ratio (PAPR) reduction. With the additional ideal cross-correlation property, complete complementary codes (CCCs), which consist of mutually orthogonal GCSs, can be employed in code-division multiple access (CDMA) systems to eliminate the multiple-access interference. It has been shown that both GCSs and CCCs can be obtained from cosets of the first-order generalized Reed-Muller codes. In the thesis, a unified work to construct families of complementary sets and CCCs from cosets of the first-order generalized Reed-Muller codes is proposed. Besides generalizing some previous results on GCSs and CCCs, extensions of GCSs and CCCs which have some desirable (even though nonideal) autocorrelation and/or cross-correlation properties are investigated, namely, multiple-shift complementary sets (MSCSs), quasi-complementary sets (QCSs), and quasi complete complementary codes (QCCCs). The relationship between the families of GCSs and generalized Reed-Muller codes is first investigated in the thesis. Direct generic constructions of GCSs, MSCSs, and QCSs from cosets of the first-order generalized Reed-Muller codes are proposed. Upper bounds on PAPRs of families of GCSs are also exploited. Then constructions of CCCs and QCCCs from generalized Reed-Muller codes are provided. A novel application of the constructed QCCCs is proposed in the thesis to employ them as the preamble sequences for cell search in cell-based OFDM systems, due to their good auto-correlation and cross-correlation properties as well as low PAPR values. Simulation results show that the proposed QCCC-based preambles outperform the preambles employed in the WiMAX system, both in terms of PAPR and cell search performance.