Inter-symbol-interference free and inter-carrier-interference free filter design

In this paper, direct optimization approaches are proposed for minimizing the inter-symbol interference (ISI) and the inter-carrier interference (ICI) caused by a truncated prototype filter. Based on the ideal ISI-free and/or ICI-free conditions in the transformed domain, one can define the ISI and/or ICI cost functions of the time-domain samples of the prototype filter. Using the variation technique, a system of nonlinear equations of the time samples of the prototype filter can be established by minimizing the cost function(s). Since the equations are highly non-linear, explicit close form solution is difficult to obtain. We therefore solve the equations using iterative procedures. Using the proposed approaches, numerical results show that the ICI and ISI can be reduced to one-tenth of the original value where the shape of the prototype filter is only slightly altered.