Bounds on Error in Signal Parameter Estimation

In this correspondence, the problem of lower bounds on mean-square error in parameter estimation is considered. Lower bounds on mean-square error can be used, for instance, to bound the performances, namely the attainable output signal-to-noise ratio, of pulse modulation transmission systems, such as pulse-position modulation (PPM) or pulse-frequency modulation (PFM). The tightest lower bounds to mean-square error previously known are the Ziv-Zakai bounds; the analysis carried out in this paper, which is based on an inequality first obtained by Kotel'nikov, leads to lower bounds tighter than previously known bounds.     

Pel-recursive motion estimation algorithm

A new pel-recursive motion estimation algorithm for video coding applications is presented. The derivation of the algorithm is based on recursive least-squares estimation that minimises the mean-square prediction error. A comparison with the modified steepest-descent gradient estimation technique algorithm shows significant improvement in terms of mean-square prediction error performance     

Least-squares design of higher order nonrecursive differentiators

A method is described that can be used to design non-recursive linear-phase higher order differentiators that can perform differentiation over any frequency range. The method is based on formulating the absolute mean-square error between the amplitude responses of the practical and ideal differentiator as a quadratic function. The coefficients of the differentiators are obtained by solving a set of linear equations. This method leads to a lower mean-square error and is computationally more efficient than both the eigenfilter method and the method based on the Remez exchange algorithm. Design of differentiators based on minimization of the relative mean-square error is also carried out. Finally, the method is extended to the design of frequency selective higher order differentiators     

Convergence analysis of adaptive linear estimation for dependentstationary processes

The convergence properties of an adaptive linear mean-square estimator that uses a modified LMS algorithm are established for generally dependent processes. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated. It is shown that the mean-square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation. The present findings extend earlier results in the literature obtained for independent and M-dependent input data     

Steady-state error in adaptive mean-square minimization

This paper considers the steady-state mean-square error when an adaptive linear estimator is used on a stationary time series. The estimator weights are adjusted periodically by moving a small increment in the direction of the estimated gradient. Under very general conditions the asymptotic mean-square error is bounded and under more restrictive conditions is evaluated exactly.     

Steady-state analysis of quantized distributed incremental LMS algorithm without Gaussian restriction

In this paper, we analyze the steady-state performance of the distributed incremental least mean-square (DILMS) algorithm when it is implemented in finite-precision arithmetic. Our analysis in this paper does not consider any distribution of input data. We first formulate the update equation for quantized DILMS algorithm, and then we use a spatial-temporal energy conservation argument to derive theoretical expressions that evaluate the steady-state performance of individual nodes in the network. We consider mean-square error, excess mean-square error, and mean-square deviation as the performance criteria. Simulation results are generated by using two types of signals, Gaussian and non-Gaussian distributed signals. As the simulation results show, there is a good match between the theory and simulation.     

Convergence analysis of the sign algorithm for adaptive filtering

We consider the convergence analysis of the sign algorithm for adaptive filtering when the input processes are uncorrelated and Gaussian and a fixed step size μ>0 is used. Exact recursive equations for the covariance matrix of the deviation error are established for any step size μ>0. Asymptotic time-averaged convergence for the mean-absolute deviation error, mean-square deviation error, and for the signal mean-square estimation error are established. These results are shown to hold for arbitrary step size μ>0     

Transmission of an analog signal over a fixed bit-rate channel

The transmission of a nonbandlimited analog signal over a digital channel with a fixed bit-rate is considered. The trade-off between the mean-square error due to quantizing and the mean-square error due to the process of sampling and reconstructing the signal is investigated. Simple approximations to these errors, which are valid in most practical situations, are derived, and simple expressions are obtained from which the optimum sampling interval and number of bits per sample can be calculated. Results for first-, second-, and third-order Butterworth and fiat bandlimited spectra, together with the zero-order hold and the linear point connector, are included. The resulting mean-square error goes to zero with large channel bit-rates in a slower manner than the Shannon limit, which assumes a strictly bandlimited signal and perfect reconstruction.     

A fundamental lower bound to the performance of phase estimatorsover Rician-fading channels

We present a fundamental lower bound to the mean-square error of estimators of the phase of a sine wave passed through a Rician-fading channel. Explicit expressions for the bound with Gaussian and Rayleigh channels are provided. The bound is derived by analyzing the performance of the Bayes minimum mean-square error phase estimator, and therefore represents the best performance attainable by physically realizable phase estimators over a Rician channel     

Uniform Quantizers for Noisy Channels

We consider optimum uniform data quantization for noisy channels. We present a general formulation for natural encoding that results in simple expressions for the mean-square error. Specifically, we show that the optimum location of the center of the quantizer is at the mean of the distribution for all error rates. The optimum levels for quantization and the corresponding mean-square error are presented for Gaussian and uniform data. For the latter the width of the optimum quantizer for noisy channels is shown to be smaller than the entire range of probability distribution.     

An upper bound on the estimation error in the threshold region

An upper bound on the estimation error in the threshold region (probability of threshold effect and mean-square error) is obtained for nonlinear pulse modulation systems. The problem is viewed in anN-dimensional Euclidean space. The space of all received signals is divided into two regions, corresponding to the two types of error: weak-noise approximation and threshold effect. The threshold region is geometrically upper bounded by a larger region, and the estimation error is obtained as a sum of incompleteGammafunctions. The resulting bound on the mean-square error was found to be quite close for the cases calculated. An extension of the method to PPM system is also presented.     

A Simple Approximation for Minimum Mean-Square Error Symmetric Uniform Quantization

In the context of minimum mean-square error symmetric uniform quantization, we show that for several different distributions on the input signals, log-log plots of step size versus number of output levels and mean-square error versus number of output levels both exhibit nearly linear behavior. This observation results in a straightforward design procedure for symmetric uniform quantization.     

On quantizers for DPCM coding of picture signals

A measure of picture quality for simple element, differentially coded pictures is developed based on certain subjective tests. The measure weights the quantization noise according to its visibility. It is shown that the measure correlates well with the picture quality determined on a standard impairment scale. Optimization of DPCM quantizers is done for this and for the mean-square measure of picture quality. Performance of the following types of quantizers is evaluated in terms of entropy of the quantized output and the picture quality: a) minimum mean-square error quantizers with a fixed number of levels, b) minimum mean-square error quantizers with fixed entropy, c) minimum mean-square subjective distortion quantizers with a fixed number of levels, d) minimum mean-square subjective distortion quantizers with fixed entropy, and e) uniform quantizers. It is concluded that for a fixed number of levels and a fixed word-length coding of the quantizer outputs, the quantizers in c) outperform those in a); and with variable length coding, the quantizers in d) perform better than all of the other quantizers having the same entropy. The sensitivity of the approach to variation of picture content is also investigated.     

On universal quantization

The quantization ofn-dimensional vectors inR^{n}with an arbitrary probability measure, under a mean-square error constraint, is discussed. It is demonstrated that a uniform, one-dimensional quantizer followed by a noiseless digital variable-rate encoder ("entropy encoding") can yield a rate that is, for anyn, no more than0.754bit-per-sample higher than the rate associated with the optimaln-dimensionai quantizer, regardless of the probabilistic characterization of the inputn-vector for the allowable mean-square error.     

Array pattern synthesis with a controlled mean-square sidelobelevel

The author presents a technique for synthesizing an antenna pattern with a controlled mean-square sidelobe level and a smallest possible beamwidth. The basic idea is to minimize the mean-square error between the array response and the desired response over a mainlobe width subject to a mean-square sidelobe constraint. This formulation results in a quadratically constrained minimization problem. An efficient numerical technique to obtain the optimum weights is presented. Numerical results showed that, under high interference-to-white-noise ratio, the new design approach performs better, on the average, than the Chebyshev technique, in terms of interference rejection     

Computer-aided design of FIR filters

A computer-aided technique for designing FIR digital filters with close to linear phase property is presented. The approach is based on a constrained optimisation problem designed to minimise the mean-square error between a desired response and the filter response over a passband of interest subject to a mean-square stopband constraint. Numerical results are presented to illustrate the performance achievable.<>     

Wiener solution of electrical equalizer coefficients in lightwave systems

Electrical dispersion compensation equalizer is a key and cost-effective element in optical communication on-off-keying systems in the presence of chromatic dispersion. Here, for the first time, to the best of the authors? knowledge, an analytical solution is established for the electrical equalizer coefficients in an optical communication system. The solution is based on minimum mean-square error criterion. The analytical results show a perfect match with computer simulation. In addition BER performance comparison with the adaptive least mean square (LMS) method reveals that the analytical solution performs better due to LMS excess mean-square error.     

A Statistical Model for Combining Biased Expert Opinions

A statistical model is developed to combine subjective estimates of an unknown parameter. The maximum likelihood estimator is a weighted geometric mean of adjusted estimates, each being adjusted to remove certain s-biases. The mean-square error of this estimator is compared to that of an unweighted geometric mean of unadjusted estimates; under the assumed model, this unweighted estimator is inferior except when there is no s-bias and when all estimates have the same uncertainty. An s-unbiased version of the maximum likelihood estimator has even smaller mean-square error in an example problem. A simple s-confidence interval estimator is derived.     

Asymptotic a priori estimates for the error in the nonlinear filtering problem (Corresp.)

The minimal mean-square error for the scalar nonlinear filtering problem is considered. Asymptotic lower and upper bounds on the error are derived for the case where the intensity of the observation noise tends to zero.     

The mean-square delayed decision feedback sequence detector

In signal equalization, a detection technique that allows reduction of the number of states of the Viterbi (1979) detector is the delayed decision feedback sequence detector (DDFSD). In order to achieve good performance, it is crucial to operate an appropriate prefiltering of the received sequence before the DDFSD. The main novelty of the paper is performance evaluation of the DDFSD when the feedforward filter of the minimum mean-square error decision feedback equalizer (DFE) is adopted as prefilter. The union upper bound is used to evaluate the probability of first error event and truncation of the sum appearing in the bound to the error sequences that dominate the performance is discussed. It is also shown that the feedforward filter of the minimum mean-square error DFE leads to maximum likelihood sequence detection with a minimum number of states, which seems to be a novel result.