Worst Case and Expected Peak-to-Average Power Ratio for Orthonormal Systems

We present several results that show, according to several criteria, that the large peaks that occur in OFDM are common to all orthonormal systems that are uniformly bounded. In particular, worst case peak-to-average values are always at least the square-root of the number of signals, and the expected peak value of a signal always increases logarithmically with the number of signals. The same growth also occurs for single-user signals with the appropriate normalization. Further, we investigate peak-to-average power properties of the prolate spheroidal wave functions and the Walsh functions, which are used in DS-CDMA.