Communication in time-frequency spread media using adaptive equalization

Abstract

In high-speed communication through a medium with time-frequency spread (such as in HF ionospheric, sonic underwater, and voice-quality telephone line transmission), the transmission speed and system errors are determined by an overall system variance (or equivalent noise). This overall variance comprises: 1) the intersymbol interference variance from time spread (or dispersion in the unit impulse response of the medium); 2) the variance from frequency spread (or dispersion it the CW response of the medium); and 3) the variance from channel noise at the receiver. In order to mitigate intersymbol variance from time spread, after discussing some early and limited attempts, a review is made of the general synthesis of the infinite and finite Wiener optimal networks or equalizers using delay lines with feedforward and/or feedback taps (or their shift register digital network counterpart). Also considered are optimal finite feedforward delay line approximations to the Wiener networks, synthesized nonsequentially and sequentially using a steepest descent evolutionary network synthesis, resulting in a monotonically decreasing and convergent overall variance. Applications of these networks are shown in the transmission of speeded-up analog facsimile pictures over unconditioned voice-quality telephone lines. It is shown that the received smeared picture can be refocused or de-smeared, or its time spread mitigated, to allow overall satisfactory high-speed picture transmission. Moreover, in over-the-horizon HF ionospheric analog and/or data transmission, time spread occurs in the form of discrete multi-path reception, such as the familiar ghosts observed in television. A particularly stringent multipath comprises two equal or nearly equal magnitude paths, a situation which is actually observed in HF ionospheric communication between two ships at sea. For this case it is shown that serial data transmission with pulses thin enough to resolve the multipath achieves, with optimal equalization, an irreducible bit error ratio (BER) which is a number of orders of magnitude less than the irreducible BER of the parallel data transmission method used in all contemporary HF modems (modulators and demodulators). Design curves are given showing the intersymbol interference variance from time spread as a function of the number of taps it the delay line correction networks, along with the variance arising from channel noise, and the optimal allocation of both variances for minimal overall BER with a given number of taps for the finite realizable correction networks. Because of frequency spread, the ever-changing unit or impulse response of the medium (e.g., HF ionospheric) causes the correction or equalization networks to become aged, giving rise to frequency spread variance. This is formulated both for determinate and for random changes of the medium unit response. For transmission media having simultaneous time spread and frequency spread, the equivalent overall variance is a simple function of the time-frequency spread product of the medium. These formulas are applied to find the overall minimal BER as a function of the time-frequency product for a contemporary parallel data modem and for a new serial adaptive data transmission system (ADAPTICOM) which periodically in real time and with digital techniques rejuvenates the time spread digital correction networks. It is shown that the transmission limit of communication of the parallel data modem is for a time-frequency spread product of about 1/2000, while that for the new serial adaptive data modem is about ten times larger, or 1/200. As a result, new communication channels are opened up for serial adaptive transmission, such as the HF spectrum below the maximum usable frequency (MUF).