Optimal waveform design for multicarrier transmission through a multipath channel

The optimal pulse shape for the transmission of a multicarrier (MC) signal through a multipath channel is designed. The optimization criterion is the minimization of the maximum power of the interference which is due to the multipath channel. The optimal waveform is obtained by applying the calculus of variations which leads to a set of differential equations (the Euler equations) with boundary conditions and isoperimetric constraints. Results show that half-period sinusoids are extremal waveforms for the optimization problem. Results can be used in the design as well as performance improvement of the multicarrier transmission technique for wireless digital communication systems.