Hybrid Digital Transmission Systems Part I: Joint Optimization of Analog and Digital Repeaters

It is customary in long-haul digital transmission systems to regenerate the digital signal at each point that gain is introduced into the system. This is not necessary, however, and in fact there are circumstances in which it is advantageous to do otherwise. One such circumstance occurs when multilevel pulses are being transmitted and the associated digital repeater* is too complicated and costly to be placed at every gain point. In this case there is merit in interspersing a number of analog repeaters between digital repeaters, even though the digital device must usually be complicated further by the introduction of automatic equalization to compensate for the misalignment which accrues over several analog links in tandem. * A digital repeater is also called a regenerative repeater, 1 a reconstructive repeater, or a regenerator. 1663 1664 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1968 Part I of this study addresses itself to the problem of jointly optimizing the various filters contained in a combination analog-digital or " h y b r i d " multilevel transmission system. T h e criterion used is minimizing the mean-square error between transmitted and received symbols. T h e system studied is general in that: ( i ) the repeater spacing may be nonuniform and the transfer functions of the transmission media may be different, (ii) the noises introduced by the repeaters may not be white and each may have a different spectral density (Hi) the analog repeaters are not constrained to be identical, and (iv) the repeater output power levels are not constrained to be the same.