The eigenstructure, the initial convergence, and the steady-state behavior of a phase-splitting fractionally spaced equalizer (PS-FSE) are analyzed. It is shown that the initial convergence rate of a T/3 or, in general, a T/M, PS-FSE employing the least-mean-square (LMS) stochastic gradient adaptive algorithm is half that of a symbol rate equalizer (SRE) or a complex fractionally spaced equalizer (CFSE) with the same time span. It is also shown that the LMS adaptive PS-FSE with symbol rate update converges to a Hilbert transformer followed by a matched filter in cascade with an optimal SRE, and thus forms an optional receiver structure. The LMS PS-FSE is computationally more efficient and introduces less system delay than the CFSE.>

The authors investigated the detection of trellis codes designed for channels that are intersymbol interference free when they operate in the presence of intersymbol interference. A well-structured reduced-state sequence estimation (RSSE) algorithm is described which can achieve the performance of maximum-likelihood sequence estimation (MLSE) with drastically reduced complexity. Well-defined reduced-state trellises are first constructed by merging the states of the ML supertrellis using set partitioning principles. Then the Viterbi algorithm is used to search these trellises. A special case of RSSE, called parallel decision-feedback decoding, uses the encoder trellis, yet on channels with large attenuation distortion it can provide a significantly better performance than linear equalization. The performance of RSSE is examined analytically and through simulation, and then compared to that of MLSE and ideal decision-feedback equalization. It is noted that the performance advantage of RSSE can be obtained without significantly increasing the decoding delay or complicating an adaptive implementation.>

A reduced-state sequence estimator for linear intersymbol interference channels is described. The estimator uses a conventional Viterbi algorithm with decision feedback to search a reduced-state subset trellis that is constructed using set-partitioning principles. The complexity of maximum-likelihood sequence estimation (MLSE) due to the length of the channel memory and the size of the signal set is systematically reduced. An error probability analysis shows that a good performance/complexity tradeoff can be obtained. In particular, the results indicate that the required complexity to achieve the performance of MLSE is independent of the size of the signal set for large enough signal sets. Simulation results are provided for two partial-response systems. A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis.>

Systems modems intended for use in relatively large private networks are characterized by high performance, reliability and flexibility to support network management, and multiple modes of operation and user features. This paper describes a programmable digital signal processor which is teamed with a 16-bit microprocessor in a dual processor architecture satisfying the requirements of high-speed voiceband systems modems. The architecture of the two custom integrated circuits which form the basis of the signal processor is presented. This processor has novel arithmetic, data structure address generation, and program flow-control capabilities, which result in a high utilization of the arithmetic unit and a low program overhead for housekeeping tasks. Some of these features are illustrated by programming examples.

Prior knowledge of the typical signal spectrum at the equalizer input can be used to speed up the convergence of a least mean-square error nonrecursivc equalizer by placing a weighting matrix in the path of the coefficient (tap gain) corrections. When the training sequence is periodic with period equal to the time-spread of the nonrecursive equalizer, the weighting matrix is not only symmetric and Toeplitz, but also circulant. Thus the fast update algorithm can be implemented by inserting a single nonrecursive filter in the path of the periodic input sequence before it is used for computing coefficient correction terms. The stability and convergence of the fast start-up algorithm with "stochastic" update in the presence of noise are examined. In the absence of prior information about the channel characteristics, this fast converging training procedure may be easily extended to a one-shot method of equalizer setup. The one-shot method, which involves estimation of the inverse filter from one period of the received signal, proves to be robust in the presence of noise. Simulation resuits are given for class I partial-response and Nyquist (20 percent roll-off raised cosine) data transmission systems with quadrature amplitude modulation over a dial-up telephone connection.

It is shown that the sensitivity of the performance of least mean-square error (LMS) equalizers to the sampler phase is a function of equalizer length for partial-response systems. An LMS algorithm for the adjustment of sampler phase is derived for partial-response systems. This algorithm does not require the transmission of any pilot tones and is relatively easily implementable by digital circuits. A method of selecting a "good" initial sampler phase is also proposed.

The present structure of adaptive least mean-square error (LMSE) equalizers for data transmission has an unnecessary constraint of a fixed position for the reference tap. This constraint limits their performance. In this paper a gradient-directed method of adjusting the position of the reference tap is developed to minimize the mean-square distortion (MSD). A scheme for implementing this modified equalizer is proposed. Results of computer simulation are shown that indicate that for channels with delay distortion some improvement in performance can be achieved.

Optimum nonlinear receivers for digital signaling over channels with a relatively long impulse response become too complex to be practical. In this paper a suboptimum but simple and practical receiver is proposed for such channels. The receiver consists of a linear adaptive equalizer in cascade with a maximum-likelihood sequence estimator. A general method of finding the error probability of a maximum-likelihood sequence estimator (MLSE) in the presence of correlated noise is developed. An upper bound on the performance of an MLSE is also presented for the case when thc actual channel is different from the channel estimate known to the MLSE. The performance of the proposed receiver is analyzed and results of the analysis and computer simulation are shown for a typical telephone channel.