PAM Constellations Minimizing Symbol-error Probability with Constrained Peak-to-average Power Ratios

In most communications systems, the peak-to-average power ratio of a signal must be constrained due to limits in radio-frequency power amplifiers. Constraining the peak-to-average ratio limits the ability to optimize signal constellation shapes to minimize symbol-error probability. This paper presents the shapes of optimal one-dimensional constellations subject to peak-to-average power ratio constraints, and analyzes the effect of this constraint in terms of degraded symbol-error probability. We discuss the optimization challenges introduced by the additional constraint, and approaches to effectively solving for optimal constellations. The results have promising applications to energy-efficient communications systems.