Signal-to-noise ratio of arbitrary power-series envelope detector (Corresp.)

The effect of an arbitrary power-series envelope detector on signal-to-noise ratio (SNR) for non-Gaussian noise is considered. It is found that the insertion of the region of saturation in the input-output characteristic of the power-law envelope detector results in the improvement on the output SNR when input SNR is large.     

Decision theory solutions for nonlinear devices (Corresp.)

Relationships are derived showing that the optimum processor for a process that has been transformed by a memoryless nonlinear device is of the same form as that for the original untransformed process if we replace the measured values of the process by their inversely transformed values.     

Upper bound on the signal-to-noise ratio at the output of a threshold receiver (Corresp.)

An upper bound on the signal-to-noise ratio (SNR) at the output of an estimator-correlator receiver is derived, and the nature of the transmitted signals and random channels that realize this bound is investigated.     

Quantizing for maximum output entropy (Corresp.)

The entropy at the output of a quantizer is equal to the average mutual information between unquantized and quantized random variables. Thus, for a fixed number of quantization levels, output entropy is a reasonable information-theoretic criterion of quantizer fidelity. It is shown that, for a class of signal distributions, which includes the Gaussian, the quantizers with maximum output entropy (MOE) and minimum average error (MAE) are approximately the same within a multiplicative constant.     

On the correlation function of signal plus Gaussian noise passed through nonlinear devices (Corresp.)

This correspondence discusses the transformations between the output autocorrelation functions of functionally related zero-memory nonlinear devices excited by signal plus Gaussian noise. The results are applied to show how output autocorrelation functions can easily be obtained for exponential and half-wave power law devices.     

Duality for the group-coset probability ratio (Corresp.)

From the MacWilliams and Assmus-Mattson identifies, it is shown that Sullivan's lower bound on the ratio of the probability of a group and a coset has a dual relation with the upper bound.     

Some geometric properties of the likelihood ratio (Corresp.)

A fundamental spatial property is noted that relates the likelihood ratio for random signals in Gaussian noise to conditional-mean parameter estimation. This allows a geometric interpretation of the estimation-correlation operation. Some additional properties exhibited by the likelihood ratio are also presented.     

On the design of nonlinear discrete-time predictors (Corresp.)

The problem of minimum mean-squared error prediction of a discrete-time random process using a nonlinear filter consisting of a zero-memory nonlinearity followed by a linear filter is studied. Classes of random processes for which the best predictor is realizable using a nonlinear filter of the above form are discussed. For those random processes for which the best predictor is not realizable using the above nonlinear filter, an iterative procedure is presented for finding a suboptimal nonlinear filter; special attention is directed to the case where the nonlinearity is a polynomial. Also, a noniterative approach based on nonlinear regression is presented.     

On identification of certain nonlinear systems (Corresp.)

In the fields of communication and control there sometimes arises the problem of determining the characteristics of a time-invariant system from discrete records of its input and output during a limited interval of time, where the output data are contaminated with random noise. When this system is linear, we can use the convolution sum to obtain a characterization of the output as a linear combination of past inputs. Hill and McMurtry [4] showed that if we choose a Legendre binary noise sequence as input to a linear system, then the least squares approximation to the characterizing coefficients is expressible in a computationally feasible form, even when a large number of coefficients is involved. In this correspondence we characterize a nonlinear system by a generalization of the convolution sum and show that if we choose Golomb's maximal linear recurring binary-noise sequence [2] as input, then the least squares approximation to the characterizing coefficients is expressible in a computationally feasible form. Thus, the maximal linear recurring sequence occupies the same role in investigating certain nonlinear systems that the Legendre sequence occupies in investigating linear systems.     

Three theorems on the moments of the monopulse ratio (Corresp.)

The monopulse ratio is treated under conditions of multiple nonfluctuating targets and correlated Gaussian interference between the difference and sum channels. Three theorems concerning the mean, the variance, and the first absolute central     

On lower bounds for the nonlinear filtering problem (Corresp.)

The system modeldx_{t}=m(x_{t})dt+sigma_{o}dw_{t}and the observationdy_{t}=h(x_{t})dt+rho dv_{t}are considered, and a lower bound on the error for the least-square estimate of a function ofx_{t}, sayz(x_{t}), is derived. This bound is then applied to derive a lower bound on the error in estimatingx_{t}in the case where the constantsigma_{o}in the equation for the system dynamics is replaced bysigma (x_{t}).     

On estimating signal-to-noise ratio using the sample correlation coefficient (Corresp.)

Two versions of a Gaussian signal, corrupted by independent Gaussian noises, are available for estimating the signal-to-noise power ratio. This correspondence demonstrates that the sample correlation coefficient can be used to construct an unbiased estimator that is asymptotically efficient.     

A likelihood ratio formula for spherically invariant processes (Corresp.)

This correspondence provides a likelihood ratio formula for equivalent spherically invariant measures on a real and separable Hilbert space.     

Further results on decoders forQ-ary output channels (Corresp.)

Decoders for channels with an alphabetAand an output alphabetAprime supseteq Aare given. It is shown that, whenA =     

Analysis of a new nonlinear filter and tracking methodology (Corresp.)

A recursive nonlinear filter and tracking methodology is developed for a class of partially observable processes with an approximating model which is linear in the unobservable states and initially has the unobservables conditionally Gaussian with respect to the observations. The usual model smoothness is not required, and applications to simulated tracking problems show the filter to be considerably more accurate than the modified second-order filter which in a general sense includes the extended Kalman filter.     

Generalized minimum distance decoding algorithms forQary output channels (Corresp.)

A new condition for a generalized minimum distance decoder to guarantee correct decoding is developed. Based on this condition, decoding algorithms for block codes, product codes, and completely orthogonalizable codes onQary output channels are presented. The results of computer simulations comparing the performance of these decoding algorithms with several other soft-decision decoding algorithma are also presented.     

On noiseless source coding with specified encoder output symbol frequencies (Corresp.)

A method is presented for generating prefix-condition codes in which the relative frequencies of the encoder output symbols are close to a previously specified probability distribution. A Kraft-like inequality is developed for this purpose.