On the Transmitted Power in Generalized Partial Response

The advantages with regard to noise enhancement of certain suboptimum nonlinear techniques for "equalization" of linear distortion on channels used for digital data transmission have recently received considerable attention. These nonlinear schemes fall into two classes: decision feedback and nonlinear precoding. Yet each of these methods has an associated peculiarity which has impeded attempts to give firm bounds on performance. Thus, for decision feedback error propagation has caused the analytical pains, while for nonlinear precoding of an
L
-level alphabet the unknown increase in transmitter power has been culpable. The former problem has recently received successful attention by one of the present authors and some colleagues. Here we address the concomitant problem for nonlinear precoding and its extension to quadrature amplitude modulation (QAM) and show that the transmitted normalized power
P
satisfies
(L^{2} - 1)/3 \leq P \leq (L^{2} - 1)/3 + 1
.