Robust design of Transmit Pulse Shape

This paper considers the design of Transmit Pulse Shapes such that after transmission through a dispersive channel, the distorted pulse at the receiver fits in a prescribed template. The norm of the transmit pulse is minimized so as to reduce the effect of cross-talk at the receiver end. This design problem is formulated as a Quadratic Programming problem with affine functional inequality constraints. In practice, errors in the implementation of the optimal filter cause the received pulse to violate the template constraints. We present a robust formulation which incorporate the uncertainties to ensure that the constraints are satisfied even in the presence of implementation errors. This technique is applied to determine the transmit pulse shape to be programmed on a Siemens FALC54, a T1 Line Interface Unit.