A comparison is made of several self-orthogonalizing adjustment algorithms for linear tapped delay line equalizers. These adaptive algorithms accelerate the rate of convergence of the equalizer tap weights to those which minimize the output mean-squared error of a data transmission system. Accelerated convergence of the estimated gradient algorithm is effected by premultiplying the correction term in the algorithm by a matrix which is an estimate of the inverse of the channel correlation matrix. The various algorithms differ in the manner in which this estimate is sequentially computed. Depending on the degree of complexity available, the equalizer convergence time may be reduced more than an order of magnitude from that required by the simple gradient algorithm.

A new technique, related to the Viterbi algorithm for simultaneous phase jitter tracking and data detection of signals transmitted over the dispersive channel with Gaussian noise is proposed. This technique produces a reliable phase estimate and avoids the poor receiver performance which occurs with Viterbi decoding in the presence of phase jitter due to the use of a phase estimate derived from unreliable preliminary decisions. The effectiveness of this approach is demonstrated through computer simulation of the voiceband channel. It was found that for the case of a typical meeting the combined requirements ofC2andD1conditioning and signaled at 14,400 bits/s, no errors were experienced in a computer simulation run of 2000 symbols compared to a previous run with a less sophisticated phase tracking algorithm which experienced 17 errors in 2000 symbols.

The purpose of this paper is a detailed comparison of the error rate performance of six 8-point signal constellations under the conditions of Gaussian noise alone, or combined with either phase jitter, second order harmonic, or third order harmonic distortion for application to the voiceband telephone channel. An approximate evaluation technique is developed for inclusion of the effects of second and third order harmonic distortion which was found to be in agreement with laboratory performance measurements of several of the signal constellations reported here. A signal constellation, which consists of points in a circle surrounding a single point in the center (denoted the 1-7 constellation), was found to be superior to the other 5 constellations considered under the conditions of Gaussian noise combined with second or third order harmonic distortion. Under the condition of phase jitter not exceeding 1.5 degrees RMS, it is also superior to the other constellations. Thus, it appears that the 1-7 constellation in conjunction with a good phase locked loop would offer superior performance.

The application of QAM receivers employing passband decision feedback equalization or Viterbi algorithm detection is considered for high-speed data transmission in voiceband telephone channels. Analytical results for the Viterbi receiver indicate that it can permit digital data transmission with symbol rates exceeding the nominal bandwidth capabilities of the channel. However, it is also shown that the minimum distance of partial response-type impulse responses can substantially decrease due to small demodulation phase errors. Thus, decision feedback receivers may offer more robust performance on channels with phase jitter.

This paper describes experimental results of simulated 12000 and 14400 bits/s quadrature amplitude-modulated (QAM) systems (which were described in detail in Part I [1] ) operating on real and simulated voiceband channels. These experimental results show that both Viterbi algorithm detection and decision feedback equalization allow digital data transmission at symbol rates exceeding the nominal bandwidth capabilities of typical telephone channels. It is demonstrated in these experiments that the Viterbi algorithm receiver structure tested is less affected by linear distortion than the decision feedback receiver but exhibits greater sensitivity to phase jitter. On conditioned voiceband channels where there may be substantial phase jitter, a reasonable compromise between sensitivity to distortion and noise and sensitivity to phase jitter is made by a modem employing decision feedback equalization and decision-directed carrier phase tracking.

This paper investigates the performance of compromise Viterbi algorithm (VA) and standard equalization techniques by computation and simulation over band-limited channels using fourlevel vestigial sideband (VSB) modulation. Linear channel characteristics from the published telephone channel survey were used as examples of band-limited data transmission channels. One of the principal conclusions drawn from the study is that at data rates of 9600 bits/s and less, the linear characteristics of these channels do not limit performance even with linear equalization. It was found that at this data rate, receivers based on linear equalization are very sensitive to timing and carrier phase over some channels. Thus at 9600 bits/s the decision feedback equalizer was found to be a better choice because it is relatively insensitive to carrier phase and timing considerations. Moreover, at 9600 bits/s no problem with error propagation was encountered with the decision feedback equalizer. As the data rate was increased beyond 9600 bits/s the decision feedback tap gains became large enough to cause severe error propagation. The compromise VA receiver structure was effective at higher data rates and was almost unaffected by channel bandwidth up to 12 000 bits/s.

An adaptive maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite-duration unknown slowly time-varying intersymbol interference and additive white Gaussian noise is developed. Predicted performance and simulation results for specific channels are given.

An estimate of an upper bound on performance in terms of probability of error is developed for maximum-likelihood sequence estimation over channels for which only the pulse response energy and duration are known. This bound is evaluated for channels with a pulse response duration up to 10 signaling intervals, and the related minimum-distance channel codes are presented.