Peak value estimation of band-limited signals from their samples with applications to the crest-factor problem in OFDM

Two problems are addressed in this paper. One is to provide an upper bound on the peak value of complex, bounded band-limited signals (band-limited in the generalized sense, e.g. multi-carrier signals) given the peak value of the samples and the oversampling rate. This problem has significant relevance to OFDM system design. It is shown that the bounds are sharp for all practical rates by constructing band-limited signals taking on this bound. The proof also provides a local characterization of band-limited signals in the neighborhood of an extremum. The second problem is to bound the error in the reconstructed signal given small errors in the samples. It is shown that oversampling can provide robust recovery in the sense that small errors in the samples lead to small errors in the reconstructed signal. An upper bound is derived relating the peak error in the samples and the peak error in the signals. Furthermore, both problems are shown to be coupled and put in a unifying context. The bounds are compared and applied to problems concerning OFDM.