Extensions to the Analysis of Regenerative Repeaters with Quantized Feedback

In the design of digital communication links, various reasons exist for the removal of low-frequency components during or prior to transmission of a pulse train. In the case of vestigial sideband (VSB) modulation 1 of data over voice-frequency channels, the dc and lowfrequency signal components are removed at the transmitter before modulation and carrier reinsertion. This is required to insure satisfactory carrier recovery at the receiver for relatively low transmitted carrier power. In the T - l Carrier System, 2 the loss of low-frequency information results from transformer coupling of an unbalanced 1S31 1832 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , OCTOBER 1967 repeater to the balanced line. In either event, the effect of low-frequency suppression is to cause the positive impulse response of the overall equalized medium to exhibit an undershoot which gives intersymbol interference. One means of reducing the effect of low-frequency suppression in a regenerative repeater is to feed back a signal in an attempt to cancel the long transient tail. This method of compensation has been called quantized feedback and its use dates back to the 1920's (as noted by Bennett 3 ). We assume that the reader is familiar with Bennett's excellent expository paper. Until recently, analysis of the effects of quantized feedback on average bit error probability in a noisy environment has received essentially no attention. The first to examine this problem were Anderson, Gerrish, and Salz 4 who considered the polar binary case, neglecting signal shaping and assuming perfect matching of the feedback cancellation signal to the input signal tail.