Multitone signals with low crest factor

After an introductory discussion of real-valued and complex signals, it is shown that minimizing the crest factor (CF) of multitone signals is closely related to the construction of complex sequences with low sidelobes in their aperiodic autocorrelation function. Inspired by this observation, a lower bound on the achievable CF is derived. Four differing algorithms for the reduction of the CF of complex multitone signals are compared with each other by computer simulation. The preferred algorithm is presented in detail, and its convergence is proven. Examples of multitone signals with up to 15 tones and lower CF than previously reported in the literature are given.