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     

Envelope-constrained time-domain deconvolution for transversal-filter equalisers

A deconvolution algorithm is presented for calculating the N tap weights of a transversal-filter equaliser. The procedure attempts to control the size of individual, time-domain response errors rather than simply minimise total mean-square error of the response. A least-square error solution for the tap weights is iteratively modified, using only elementary algebraic matrix operations, in an effort to satisfy tolerance constraints on the envelope of the equalised impulse response. The algorithm is suitable for digital computation.     

Efficiently computed reduced-parameter input-aided MMSE equalizersfor ML detection: a unified approach

A unified approach for computing the optimum settings of a length-N_f input-aided equalizer that minimizes the mean-square error between the equalized channel impulse response and a target impulse response of a given length N_b is presented. This approach offers more insight into the problem, easily accommodates correlation in the input and noise sequences, leads to significant computational savings, and allows us to analyze a variety of constraints on the target impulse response besides the standard unit-tap constraint. In particular, we show that imposing a unit-energy constraint results in a lower mean-square error at a comparable computational complexity. Furthermore, we show that, under the assumed constraint of finite-length filters, the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance. We describe a new characterization of the optimum delay and show how to compute it. Finally, we derive reduced-parameter pole-zero models of the equalizer that achieve the high performance of a long all-zero equalizer at a much lower implementation cost     

Mean-Square Error Optimization of Quadrature Receivers for CPM with Modulation Index 1/2

Detection of continuous phase modulation (CPM) signals can be accomplished using quadrature coherent detectors which include a pair of linear and time-invariant postdetection filters. Performance of the quadrature detectors is highly sensitive to the postdetection filters response. This paper presents a rigorous derivation of an optimum postdetection filter response. The derivation is based on minimizing the mean-square interference subject, to the constraint that the filter noise bandwidth is held constant. The amount of computations involved is fairly small and increases linearly with the receiver observation interval. Performance analysis results for several modulation techniques are presented.     

An adaptive array for interference rejection

An adaptive array that rejects undesired or interfering signals is presented. The array pattern is controlled by an adaptive feedback system based on a steepest descent minimization of mean-square error. Error is defined as the difference between the array output and a locally generated reference signal. Minimization of mean-square error is closely related to maximization of signal-to-noise ratio (SNR). A two-element adaptive array has been built, and its experimental performance is discussed. Typical patterns for various desired and interfering signals are shown, as well as measured transient response. Finally, some experiments showing the array behavior with modulated signals are described. The results show that such an antenna system is capable of automatically rejecting interfering signals, subject only to certain basic constraints. No a priori information about the angles of arrival of the signals is required, Detailed knowledge of the waveforms of the desired and interfering signals is also not needed, although the spectral characteristics of the desired signal must be known.     

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     

Analysis of the convergence behavior of adaptivedistributed-arithmetic echo cancellers

Adaptive distributed-arithmetic echo cancellers are well suited for full-duplex high-speed data transmission. They allow a simpler implementation than adaptive linear transversal filters, since multiplications are replaced by table look-up and shift-and-add operations. Various tradeoffs between the number of operations and the number of memory locations of the look-up tables can be achieved by segmenting the echo canceller delay line into sections of shorter length. Adaptivity is achieved by a decision-directed stochastic gradient algorithm to adjust the contents of the look-up tables. The author adopts the mean-square error criterion to investigate the convergence behavior of adaptive distributed-arithmetic echo cancellers. Under the assumption that the look-up values are statistically independent of the symbols stored in the echo canceller delay line, he obtains an analytical expression for the mean-square error as a function of time. The maximum speed of convergence and the corresponding optimum adaptation gain are also determined. Simulation results for a full-duplex quaternary partial response class-IV system are presented and compared with theoretical results     

Linear Minimum Mean-Square Error Estimators Applied to Channel Equalization

This concise paper investigates various aspects of the application of unbiased linear minimum mean-square error (ULMMSE) estimators to the equalization of channels used for digital data transmission. One application is to the equalization of the channel to a response free from intersymbol interference. Previous results regarding this application are clarified and extended. The other application is to the equalization of the channel to a finite short memory response. This stems from an interest in reducing the complexity of the Viterbi algorithm. Various new results on the optimum ULMMSE equalizer and its performance are presented. In both applications, the optimum ULMMSE equalizer is a stable, realizable, finite dimensional recursive filter.     

Minimum variance beamforming with soft response constraints

Soft constraints on the beamformer response to the signal are examined in the context of minimum variance beamforming. A quadratic constraint on the beamformer weights is used to control the mean-squared error between a desired response and the actual response in the signal direction. The constraint is purposely chosen to permit distortion of the signal with the goal of achieving improved interference cancellation. Under the assumptions of known signal direction and spectral shape the signal-to-noise ratio is shown to be a nondecreasing function of the mean-square distortion. The distortion presented to the signal is easily computed from the beamformer weights and can be equalized after beamforming if desired. Properties of this beamforming method and its relationship to linear constrained beamforming are discussed. Simulations verify analytic results and illustrate the utility of the soft constrained approach     

Series expansion of wide-sense stationary random processes

This paper presents a general approach to the derivation of series expansions of second-order wide-sense stationary mean-square continuous random process valid over an infinite-time interval. The coefficients of the expansion are orthogonal and convergence is in the mean-square sense. The method of derivation is based on the integral representation of such processes. It covers both the periodic and the aperiodic cases. A constructive procedure is presented to obtain an explicit expansion for a given spectral distribution.     

A Look at Crosstalk in Quadrature-Carrier Modulation Systems

A method is presented for comparing the performance of different quadrature-carrier modulation techniques. It is based on the calculation of the mean-square crosstalk between adjacent digital communications channels. This method was used to determine the crosstalk of a number of constant envelope modulation schemes, including Staggered Quaternary Phase Shift Keying (SQPSK) and Minimum Shift Keying (MSK). The results, as have previous results, show the improved performance of MSK over SQPSK. By utilizing the general equation for mean-square crosstalk as a measure of performance, a search was made for constant envelope modulation methods with reduced crosstalk. A number of methods were found which have better mean-square crosstalk performance than MSK. Finally this paper presents a method for reducing degradation due to crosstalk by using mismatched windows in the standard correlation detector. An example of this technique for detection of MSK signals is analyzed.     

Spreading code optimization and adaptation in CDMA via discrete stochastic approximation

The aim of this paper is to develop discrete stochastic approximation algorithms that adaptively optimize the spreading codes of users in a code-division multiple-access (CDMA) system employing linear minimum mean-square error (MMSE) receivers. The proposed algorithms are able to adapt to slowly time-varying channel conditions. One of the most important properties of the algorithms is their self-learning capability-they spend most of the computational effort at the global optimizer of the objective function. Tracking analysis of the adaptive algorithms is presented together with mean-square convergence. An adaptive-step-size algorithm is also presented for optimally adjusting the step size based on the observations. Numerical examples, illustrating the performance of the algorithms in multipath fading channels, show substantial improvement over heuristic algorithms.     

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.     

Stochastic approximation with a nonstationary regression function (Corresp.)

This correspondence is concerned with a stochastic approximation algorithm having a nonstationary regression function. Convergence conditions and a mean-square error bound are presented. Its possible application to feedback communication is discussed briefly.     

Solution of inverse variation problem in the theory of optimal linear filtering

It is presented is the possibility to solve the inverse variation problem based on the determination of a primary functional by the results of minimum mean-square error in optimal linear filtering of the signal theory.     

Optimum Multielectrode A Posteriori Estimates of Single-Response Evoked Potentials

This paper discusses the design and performance of an optimum linear multielectrode filter for estimating the evoked potential contained in a single scalp-recorded brain response to a visual stimulus. The filter is derived under the criterion of minimum mean-square error and is time varying to allow for the nonstationarity of the brain response. Single-and two-channel filters are designed for simulated and human visual evoked potential data. Cross-correlation matrices required to design the filters are estimated "a posteriori" from multielectrode recordings of the prestimulus electroencephalogram and are derived from a multielectrode model of the evoked potential. Filter performance is evaluated using the criteria of mean-square error, signal bias, noise reduction, and output signal-to-noise ratio. The filter is shown to be very effective at suppressing the ongoing electroencephalogram and emphasizing the underlying evoked potential.     

Monotonic lowpass filters with maximum selectivity

Lowpass filters with no finite zeros and a monotonic magnitude response are discussed. A characteristic function is derived by maximising the mean-square error in the stopband. Analytically, it has been proved that H filters are the most selective of all other filters with monotonic magnitude response.     

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.     

Stochastic convergence analysis of recursive successive over-relaxation algorithm in adaptive filtering

A stochastic convergence analysis of the parameter vector estimation obtained by the recursive successive over-relaxation (RSOR) algorithm is performed in mean sense and mean-square sense. Also, excess of mean-square error and misadjustment analysis of the RSOR algorithm is presented. These results are verified by ensemble-averaged computer simulations. Furthermore, the performance of the RSOR algorithm is examined using a system identification example and compared with other widely used adaptive algorithms. Computer simulations show that the RSOR algorithm has better convergence rate than the widely used gradient-based algorithms and gives comparable results obtained by the recursive least-squares RLS algorithm.     

Improved Lower Bounds on Signal Parameter Estimation

An improved technique for bounding the mean-square error of signal parameter estimates is presented. The resulting bounds are independent of the bias and stronger than previously known bounds.