This paper describes the problem of carrier recovery for adaptively equalized data communication receivers. A conventional receiver structure that employs baseband equalizers is considered first, and a practical method for jointly adjusting the demodulating carrier and the equalizer is briefly described. The reader is then introduced to an equalizer time delay problem critical to the system's performance. The first remedy for this problem involves the use of dual-mode carrier control loops. A method for designing such loops is presented and its use is illustrated by a conceptual design and a numerical example. The second remedy is to adopt a passband equalizer receiver structure. A tutorial introduction to this concept and a summary of the basic principles involved are presented. This paper concludes by reviewing related timing recovery problems. Joint design approaches such as the maximum likelihood estimate approach and the minimum mean-square error approach will be described and compared.

We analyze the locking properties of a digital rate-locked loop that may be used to synchronize a slave oscillator with a master. Formulating the dynamics of this system by a nonlinear differentialintegral equation, we rigorously prove that in the absence of filtering in the loop the slave oscillator output waveform has periodic zero crossings occurring at exactly the same rate as those of the master oscillator. The main requirement for this is only that the quantization of the staircase comparator in the slave oscillator not be too coarse. A similar proof for a more general loop remains elusive.

A mathematical model is formulated for an optical PCM system. Using the signal-to-noise ratio at the decision circuit as the performance criterion, the optimization of a nonlinear detector is carried out. Closed-form expressions for the jointly optimum electrical filtering and biasing, and for the maximum signal-to-noise ratio are obtained.

This paper is concerned withm-ary communication channels(m \geq 2)having intersymbol interference betweenLtime periods(L \geq 2). Receiver structures are developed for making jointly optimum (minimum probability of error) decisions aboutLconsecutive symbols on the basis of the complete message received. The decision statistics are computed by a sequential procedure, and the number of computations increases only linearly with the message length. The method can be applied to the general problem of making decisions about the states of a discrete-state Markov information source which is observable only through a channel with additive Gaussian or non-Gaussian noise.