This paper analyzes an adaptive training algorithm for adjusting the tap weights of a tapped delay line filter to minimize mean-square intersymbol interference for synchronous data transmission. The significant feature of the adjustment procedure is that convergence is guaranteed for all channel response pulses, even for very severe amplitude and phase distortion. The author examines convergence, rate of convergence, and the effect of noisy observations of the received pulses, and he shows that the noisy observations result in a random sequence of tap weight settings whose mean value converges to a suboptimal setting. The mean-square deviation of the tap weights from the suboptimal values is asymptotically bounded with a bound that can be made as small as desired by sufficiently reducing the speed of convergence. The suboptimality arising here results from the use of isolated test pulses for the training signal. However, a training scheme using pseudorandom sequences or the actual data signal does not suffer from the suboptimality effect. Hence, although of possible utility in other pulse shaping applications, the technique presented here appears to be primarily of value in providing a conceptual framework for the closely related but more practical techniques to be examined in the sequel to this paper to be published shortly.

Adaptive equalization of highly dispersive channels for data transmission

A tutorial paper on an adaptive receiver that is suitable for high-speed digital signaling over slowly time-varying, band-limited channels which have impulse responses that are unknown at the receiver is presented. The receiver utilizes a steepest-descent technique for adjusting its parameters to existing channel conditions. A treatment of the speed of adaptation of the receiver is included.

An adaptive receiver for digital signaling through channels with intersymbol interference

A new mean-square-error automatic equalizer for synchronous data transmission is developed. It utilizes Rosen's gradient-projection method to optimize parameters in the discrete frequency domain. The algorithm converges (in the mean) for any channel even in the presence of noise. It is shown that for the channels considered, convergence is faster (in a bounded sense) than for comparable time-domain equalizers.

Automatic equalization using the discrete frequency domain

This paper surveys the literature on communication theory from 1968 to 1973. A large part of this literature, and of this paper, deals with digital communication through linear dispersive channels. Error rate bounds for pulse-amplitude modulation systems, the optimization of linear transmitters and receivers, and adaptive equalization are topics discussed initially. Important results from the literature on non-linear receivers are described next, including decision feedback, maximum-likelihood, and Viterbi algorithm approaches. New results on the conventional digital modulation formats of amplitude, phase, and frequency-shift keying are summarized. The paper concludes with sections describing the literature from this period on nonlinear and non-Gaussian problems, analog communication, and feedback communication.

A survey of the communication theory literature: 1968-1973

A new technique for very fast start-up of adaptive transversal-filter equalizers used in high-speed synchronous data communications is presented. A special training sequence whose period in symbols is equal to the number of equalizer taps is used initially to achieve an open eye pattern. Rapid convergence, even over highly distorted channels, is obtained because an ideal reference sequence is available at the receiver, but it is not necessary to synchronize the ideal reference with the received sequence. The special choice of the training sequence automatically provides the synchronized ideal reference needed for fast convergence, but the resulting equalizer coefficients may be cyclically displaced from their proper positions. After the eye is opened by this process, the equalizer coefficients are rotated to their proper positions, and decision-directed equalization is used with either a longer training sequence or random data to achieve final tap settings. Adjustments during the training period can be made with a gradient-type algorithm or with stochastic adjustment techniques; an exact analysis is possible for both of these schemes. Cyclic equalization is shown to provide perfect equalization at evenly spaced points in the frequency domain.

Cyclic equalization — a new rapidly converging equalization technique for synchronous data communication

Results are reported which are of interest in the automatic adaptive equalization of telephone lines or other narrowbandwidth channels where data transmission is limited primarily by intersymbol interference. We describe an algorithm for adjusting the tap gains of a tapped delay line (TDL) equalizer which converges for all channels to the setting, which minimizes the mean-square error (rose) at the filter output due to both noise and intersymbol interference. This algorithm has been implemented using digital microcircuits and metal-oxide semiconductor (MOS) shift registers to construct a 63 tap all-digital TDL filter covering 19.7 ms. The modulation system used is vestigal sideband with bandwidth 1.6 kHz. The data rate is 3200 pulses/s, or 9600 bit/s with 8 data levels. A description of the hardware realization and performance data over various telephone lines is given.

D. Willim

Papers

Adaptive Equalizer for Pulse Transmission