Crest factors of Shapiro-Rudin sequence based multi-code MC-CDMA signals

The envelope power of MC-CDMA signals usually exhibits wide fluctuations, leading to a high value of the associated crest factor. However, when Shapiro-Rudin based sequences, namely a Shapiro-Rudin (1959) pair, a Shapiro-Rudin based sub-complementary pair and a Shapiro-Rudin based Sivaswamy's (1978) complementary set are used for two- and four-code BPSK modulated MC-CDMA spreading sequences, the crest factor is found to be bounded by 3dB. These sequences belong to the so-called orthogonal complementary set and Walsh-Hadamard sequences constitute a special case of these sets, when the sequence length is equal to the number of codes. When a typical nonlinear power amplifier is used, the low crest factor of the Shapiro-Rudin sequence based multi-code MC-CDMA scheme results in reduced amplifier-induced signal clipping. Hence a reduced power loss is imposed due to clipping in comparison to OFDM and to multicode MC-CDMA schemes based on other spreading sequences, such as Walsh codes, orthogonal Gold codes, Frank (1962) codes and Zadoff-Chu (1972) codes.