Optimal finite duration pulses for OFDM

This paper presents pulses of finite duration for use in orthogonal frequency division multiplex (OFDM) using offset QAM modulation, in such a system the pulses will overlap in both frequency and time without intersymbol or interchannel interference. The pulses are generated by an optimization procedure which minimizes the out-of-band energy under the constraints of zero intersymbol and interchannel interference. Low out-of-band energy is important to achieve high bandwidth efficiency, especially when the number of channels is small. The optimization procedure leads to an integral equation which is solved by expanding the pulse in truncated prolate spheroidal wave functions. Examples of optimized pulses and their spectrum are presented for lengths of 2 and 4 symbol intervals.