Precoding for Multiple-Speed Data Transmission

In conventional pulse amplitude modulation (PAM) data transmission systems (digital or analog), the signal at the receiver input takes the form s(t) = E akf(t - kT0), k= 1 (1) where {ak} are the information symbols, T 0 is the signaling interval, and the signals / { t -- kT0), k = 1, · · · , N, are time translates of each 1633 1 6 4 8 T H E BELL S Y S T E M T E C H N I C A L J O U R N A L , S E P T E M B E R 19(37 other. It is well known 1 that in order for these systems to meet the criterion "Maximize the signal-to-noise ratio in the presence of bandlimited white noise under the constraints of fixed line signal power and no intersymbol interference," the signals should be designed so that the overall channel characteristics are in the Nyquist I class and the overall amplitude characteristics are divided equally between the transmitting and the receiving side. Such a signal design scheme (hereafter referred to as Scheme I) is popular and is used even if the system designer is aware that the channel noise may not be white over the frequency band of interest. This is because the practical determination of the noise statistics and the realization of the corresponding optimum filters for a general communication complex are nearly impossible. A block diagram of Scheme I is shown in Fig. 1. In this paper, a precoding signaling scheme (Scheme II) is presented for multiple-speed analog or digital data transmission. Scheme II also meets the signal-to-noise ratio criterion above. The very distinctive difference between Schemes I and II is that in I the signals f(t -- kTo) are time translates, but in II the signals are not necessarily so.