Prolate Spheroidal Wave Function in High Data Rate Applications

Growing request for wideband communications requires innovation in power efficiency and signal processing. Without the use of any peak to average power ratio (PAPR) reduction technique, the efficiency of power consumption at the transmitter end becomes very poor. PAPR reduction in this work is accomplished based on using a unique class of functions, prolate spheroidal wave functions (PSWFs). The difficulty arises from the fact that these pulses do not belong to the Nyquist family. A zero forcing equalizer (ZFE) is designed to compensate intersymbol interference (ISI), and its performance is studied under the presence of AWGN. Considering PAPR and ISI as the constraints of communication systems, based on the properties of PSWF, a set of pulses with minimum ISI with respect to a specific amount of PAPR is achieved by defining an optimization problem. The desired level of PAPR is considered to be moved to the constraint set to convert the multi-objective problem into a single objective problem. The results of the numerical optimization of both ISI and PAPR are presented along with a couple of examples of comparison between the resultant pulse and the conventional square root raised cosine. It is shown that by achieving the same level of PAPR of the SRRC, the obtained pulse is a close approximation of SRRC. An implementation based on state variable filters is introduced to realize PSWF for high speed applications. An example based on this approach is presented to compare the finite pole approximation result with the original pulse