Root Nyquist Pulses with an Energy Criterion

The design of root-Nyquist pulses with the maximum possible energy concentration of the power spectrum is a fundamental problem is communications engineering. Since the problem is one of global optimization in nature, earlier attempts at a solution have been primarily numerical. Consequently, it is very likely that the proposed design procedures yield solutions that are only locally optimal. In this paper, a detailed analysis of the optimization problem is presented and it is shown that under certain conditions, a globally optimal solution is possible. The global optimization procedure is arrived at by focusing on dual, which is an eigenvalue minimization problem. Numerical results are presented comparing the pulses so obtained with the raised- cosine pulse and the "better than" raised-cosine pulse recently proposed in the literature.