Applications of Golay Complementary Sequences in Mc-cdma and Compressed Sensing

This thesis consists of two separate topics involved with Golay complementary sequences. In the first part, we present results of an experimental investigation where the distribution of peak-to-average power ratio (PAPR) in downlink MC-CDMA systems is modeled by the generalized extreme value (GEV) distribution. Two orthogonal sets of sequences, WalshHadamard and Golay complementary sequences, are used in spreading processes in the system. Then the parameters of the GEV distribution are estimated for the PAPR distribution. Through intensive numerical results, it is shown that the GEV distribution is an accurate model of the PAPR distribution of MC-CDMA systems. Also, the statistically estimated GEV distribution parameters for the PAPR reveal that when the number of subcarriers increases, the PAPR distributions converge to the Gumbel distribution. In the second part of this thesis, a new (N , K) partial Fourier codebook is constructed, associated with a binary sequence obtained by an element-wise multiplication of a pair of binary Golay complementary sequences. In the codebook, N = 2 for a positive integer m, and K is approximately N 4 . It is shown that the maximum magnitude of inner products between distinct code vectors is nontrivially bounded in the codebook, which is approximately up to √ 6 times the Welch bound equality for large N = 2 with odd m. Finally, the new codebook is employed as a deterministic sensing matrix for compressed sensing, where its recovery performance is tested through numerical experiments.