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High peak values of transmission signals in wireless communication systems lead to wasteful energy consumption and out-of-band radiation. However, reducing peak values generally comes at the cost of some other resource. We provide a theoretical contribution toward understanding the relationship between peak value reduction and the resulting cost in information rates. In particular, we address the relationship between peak values and the proportion of transmission signals allocated for information transmission when one is using a strategy known as tone reservation. We show that when tone reservation is used in both OFDM and DS-CDMA systems, if a peak-to-average power ratio criterion is always satisfied, then the proportion of transmission signals that may be allocated for information transmission must tend to zero. We investigate properties of these two systems for sets of both finite and infinite cardinalities. We present properties that OFDM and DS-CDMA share in common as well as ways in which they fundamentally differ.

On the Peak-to-Average Power Ratio Reduction Problem for Orthogonal Transmission Schemes