Design of transmitter and receiver filters for decision feedback equalization

We present the constructive design of finite order equalizer filters for data transmission systems employing decision feedback equalization. Both transmitter design with power constraints and receiver design with ambient noise considerations are treated. Expressions for the filter tap settings which maximize a signal-to-noise ratio are found for both baseband pulse amplitude modulation and quadrature amplitude modulation (QAM) systems. Design examples are given in a passband equivalent (of QAM) formulation for an average toll telephone connection. Neglecting the possibility of error propagation, these examples demonstrate that decision feedback equalization requires fewer taps for acceptable system performance as compared to linear equalization. The problem of postcursor size in a decision feedback equalized response is treated and shown to diminish in importance when a hybrid equalization procedure is imposed on the linear tap adjustment. The price one pays for allowing the linear filter taps to reduce the postcursor sizes in this hybrid equalizer is a lower signal-to-noise ratio.