A peak to mean power control scheme: the extended Rudin-Shapiro construction

Orthogonal frequency-division multiplexing (OFDM) signals exhibit a large peak to mean envelope power ratio (PMEPR), which limits their applications. In this paper, a systematic and constructive methodology of efficiently identifying the phase modulated vectors of length 2^k (k any nonnegative number) whose PMEPRs are below 3 dB is proposed. We show that the set of all the identified distinct phase modulated vectors of length 2^k obtained through our scheme is unaccountable. To attain these goals, we develop a novel way to extend the Rudin-Shapiro (RS) construction and utilize it to develop a procedure of efficiently identifying phase modulated vectors of length n=2^k with desired PMEPRs. The principle is illustrated with the specific example of a four carrier signal.