Optimization of the pulse shape of OFDM systems Using the Arrow-Hurwicz Algorithm

Orthogonal frequency division multiplexing (OFDM) has been used in various wireless communication systems. For these OFDM systems, the elementary pulse has to guarantee orthogonality with its time-frequency shifted versions. However, the time and frequency dispersion of the wireless channel leads to the loss of this orthogonality, producing inter-symbol and inter-channel interference. In order to reduce these interferences, a good localization of the pulse shape is required. In this paper, we investigate the optimization of the OFDM pulse shape for time and frequency dispersive channels. We consider the same envelope functions in transmission and reception. The proposed pulse shape is expressed as a linear combination of the most localized Hermite functions. The optimization, with respect to the signal-to-interference ratio (SIR), is carried out using the Arrow-Hurwicz algorithm. Simulations show that OFDM optimized systems can be outperform conventional OFDM systems.