Design of time-limited pulses

An approach for designing time-limited transmit pulses is proposed. In the approach, a time-limited pulse is represented by a weighted sum of cosine functions whose frequencies are integer multiples of one over the time duration of the transmit pulse. The weighting coefficients are derived to minimize the mean square error of received symbols for a given symbol timing offset, while restricting the out-of-band energy to a predefined level. The minimization is numerically performed by using the Zoutendijk's feasible direction method. Performance comparison results are presented showing that the pulses derived by this approach not only have smaller mean square errors, but also smaller symbol error probabilities for BPSK signaling compared to the time-truncated versions of conventional square-root Nyquist pulses.