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.
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