A good trade-off performance between the code rate and PMEPR for OFDM signals using generalized Rudin-Shapiro polynomials

Generalized Golay complementary sequences and multiple-shift complementary sequences have recently been introduced to encode orthogonal frequency division multiplexing (OFDM) signals, reducing the peak-to-mean envelope power ratio (PMEPR). Certain classes of these complementary sequences have been identified as a subset of second order cosets of the first order Reed-Muller codes. Since the code rates of these encoding schemes are prohibitively low for a large number of sub-carriers, it is necessary to find an efficient algebraic way to produce sufficient number of codewords such that the code rate of the encoding scheme is high enough. In this paper, we introduce generalized Rudin-Shapiro polynomials, a subset generalized Golay complementary sequences, to encode OFDM signals. In our encoding scheme, a matrix equation recursively produces a sufficient number of Rudin-Shapiro polynomials such that the code rate increases linearly with respect to the PMEPR. Therefore, it offers an excellent trade-off performance between the code rate and the PMEPR.