The hybrid system is an extension of the state-space system model which allows for random and abrupt changes in the model parameters. In this paper we use the hybrid system to model burst type interference in a direct-sequence spread-spectrum (DS/SS) communication system. The resulting optimum receiver is easily derived but too computationally complex to be practical. Two suboptimal but more practical receivers are presented. In an example, the hybrid system is used to model pulsed narrowband interference. The performance of each suboptimal receiver is evaluated using computer simulations.>

The asymptotic behavior of a Bayes optimal adaptive estimation scheme for a linear discrete-time dynamical system with unknown Markovian noise statistics is investigated. Noise influencing the state equation and the measurement equation is assumed to come from a group of Gaussian distributions having different means and covariances, with transitions from one noise source to another determined by a Markov transition matrix. The transition probability matrix is unknown and can take values only from a finite set. An example is simulated to illustrate the convergence.

In this paper, an adaptive receiver with memory for fading communication channels is considered. The receiver consists of an estimator and a detector. The estimator is a finite-memory MMSE estimator with decision-feedback which minimizes the probability of error of the receiver. Asymptotic approximations are employed to derive an adaptive decision role based on the estimate. An example is presented where the receiver with memory is shown to perform better than an optimum receiver without memory.

A Markov gap model is proposed for real digital communication channels. Analytic properties of the model are investigated and compared with data from VHF and troposcatter channels. The model is also simulated, and the satistics of the simulated data are compared favorably with those of the real data.

A variable length feedback scheme for binary constant antipodal signals with an upper bound on the decision time is proposed. In addition to the noiseless decision feedback channel a noiseless information feedback channel is used for energy saving. The performance of the scheme is derived, and the probability of error as a function of the average energy per symbol is compared to existing systems. Two of the existing systems may be obtained as limiting cases of the combined scheme considered here.

The mean-squared continuous Markov process of the separable class is represented by a nonlinear stochastic differential equation. The representation for the strictly stationary case implies that the process is determined by its autocorrelation function and first-order probability density function. A class of stationary Markov separable processes may be obtained by a zero-memory nonlinear (ZNL) transformation of a wider class of stationary Markov processes. A special case of the multidimensional process is shown to result in a separable process of degreeN. Several examples are considered to illustrate the representation.

A nonlinear filtering scheme with noiseless feedback is presented, based on a consideration of the minimum-mean-squared error filtering of independent signal samples corrupted by additive noise. The explicit solution for the general case is very complex. However, if the signal-to-noise ratio is assumed to be large and the nonlinear estimating filter has zero memory, the problem may be simplified by reducing it to the zero-memory prefiltering problem combined with predictive feedback. The improvement over the linear case without feedback is shown to be the product of the improvements due to the zero-memory non-linearities and the feedback. An example is considered to illustrate the improvements in the error,

This paper is concerned with the minimum mean-squared error (MMSE) nonlinear prediction of a class of random processes. A class of random processes is defined by the property that its MMSE zero-memory predictor is represented by a finite sum of separable terms. Sufficient conditions for the existence of such processes are also considered. The nonlinear predictor is restricted to be composed of a linear filter in parallel with a zero-memory nonlinearity (ZNL) preceded by a variable delay, The optimum predictor is shown to be the solution of linear integral equations with the same kernel as for the optimum linear predictor. The first step of the derivation also yields a simpler scheme which ,only requires the addition of a ZNL to the optimum linear predictor. The improvements in the MMSE of the two nonlinear systems over the linear case are compared and illustrated by a numerical example.

The determination of minimum-mean-squared-error (MMSE) nonlinear filters usually involves formidable mathematical difficulties. These difficulties may be bypassed by restricting attention to special classes of filters or special processes. One such class is Zadeh's classn_{1}, which for the general case also involves mathematical difficulties. In this work two realizations of classn_{1}are used for the MMSE reconstruction and filtering of a sampled signal. The cases where the filter reduces to a zero-memory nonlinearity followed by a linear filter are discussed. A suboptimum scheme composed of a zero-memory nonlinearity followed by a linear filter is considered for the reconstruction and filtering of a subclass of the separable process.

This paper presents an integral representation for the derivation of sampling expansions. The representation uses the theory of self-adjoint differential equations. Different methods of evaluating the resulting triple integral have different physical significances and yield the commonly used approaches to the derivation of sampling expansions. The first- and second-order differential operators are discussed, and the physical interpretation of the first-order case is emphasized.