Optimal finite duration pulses for OFDM

This paper presents pulses of finite duration for use in 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 optimisation procedure which minimise 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 optimisation procedure leads to an integral equation which is solved by expanding the pulse in truncated prolate spheroidal wave functions. Examples of optimised pulses and their spectrum are presented for lengths of 2, 3 and 4 symbol intervals.