Peak behavior and information rates for orthonormal systems

High signal peak values are one of the fundamental obstacles to greater efficiency in wireless communications systems. There exist many techniques to reduce signal peak values; however, there have been few theoretical studies of the trade-off between reducing peak values and the resulting cost in other resources. Here we address the trade-off between peak reduction and information rates for two standard systems, OFDM and DS-CDMA, when implementing tone reservation. In particular, we show that when a peak threshold is strictly enforced regardless of the number of carriers, the information rate must tend to zero. We discuss aspects that these two systems share in common, as well as point out a fundamental way in which they differ.