On the Compactness of OFDM and Hermite Signals

In this letter, the compactness of the orthogonal frequency division multiplexing (OFDM) and orthogonal Hermite signals is compared by measuring their time-bandwidth products (TBPs). In a theory, it has been shown that the Hermite functions provided the minimum possible TBP among all orthogonal functions; however, this minimum is obtained from the root mean square sense, which is not useful for most communication applications. For instance, an OFDM system that usually employs rectangular pulses in time domain, the whole time duration of the pulses, is considered. In this letter, we use pulse energy criterion, i.e., 99% of the energy, in our measurements, and propose an empirical model as well as a theoretical equation for the TBP of these signals and show that the Hermite signals will still be more compact than OFDM signals. To make a fair comparison, we employ Hermite functions in an orthogonal signal multiplexing system as in OFDM, where trigonometric waveforms are employed as orthogonal basis.