This paper addresses the problem of determining the statistical distribution of the peak-to-average power ratio (PAR) of orthogonal frequency-division multiplexing (OFDM) transmit signals. In practice, transmission systems are amplitude-limited, thus the large peak values of OFDM signals are clipped and nonlinear distortion follows. In order to avoid the resulting degradations, i.e., spectral widening and increased bit-error rate, a systematic construction of OFDM signals without large peaks is desired. The paper provides new results on the PAR distribution and hence on the achievable information rate with OFDM signals that are peak-limited. In particular, it is shown that in the case of phase-shift-keying (PSK) subcarrier modulation, the frequently applied model of Gaussian data coefficients is not appropriate. By solving an integral equation, new analytic expressions for the PAR and the achievable information rate are derived. Comparison with simulation results confirms that the new model is accurate for all ranges of practical interest.

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.

Originally, Barker (1953) presented binary sequences for synchronization purposes in telecommunications. A sequence is called a generalized Barker sequence if the magnitude of all autocorrelation sidelobes is less or equal to one. It is shown that uniform complex sequences up to length 36, meeting the Barker (1953) condition, do exist. Examples are given for length 32-36. The sequences were obtained with a stochastic optimization algorithm, that was run with properly selected starting vectors.