Showing papers on "Adaptive algorithm published in 1973"

Adaptive channel memory truncation for maximum likelihood sequence estimation

Abstract: Maximum likelihood data sequence estimation, implemented by a dynamic programming algorithm known as the Viterbi algorithm (VA), is of considerable interest for data transmission in the presence of severe intersymbol interference and additive Gaussian noise. Unfortunately, the required number of receiver operations per data symbol is an exponential function of the duration of the channel impulse response, resulting in unacceptably large receiver complexity for high-speed PAM data transmission on many channels. We propose a linear prefilter to force the overall impulse response of the channel/prefilter combination to approximate a desired truncated impulse response (DIR) of acceptably short duration. Given the duration of the DIR, the prefilter parameters and the DIR itself can be optimized adaptively to minimize the mean-square error between the output of the prefilter and the desired prefilter output, while constraining the energy in the DIR to be fixed. In this work we show that the minimum mean-square error can be expressed as the minimum eigenvalue of a certain channel-dependent matrix, and that the corresponding eigenvector represents the optimum DIR. An adaptive algorithm is developed and successfully tested. The simulations also show that the prefiltering scheme, used together with the VA for two different channel models, compares favorably in performance with another recently proposed prefiltering scheme. Limiting results for the case where the prefilter is considered to be of infinite length are obtained; it is shown that the optimum DIR of length two must be one of two possible impulse responses related to the duobinary impulse response. Finally we obtain limiting results for the case where the transmitting filter is optimized.

On the design of gradient algorithms for digitally implemented adaptive filters

Abstract: The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic approximation that to achieve the optimum rate of convergence in an adaptive algorithm the step size should be proportional to 1/n , where n is the number of iterations. On closer examination one finds that this result applies only when n is large and is relevant only for analog algorithms. It is shown that as the number of iterations becomes large one should not continually decrease the step size in a digital gradient algorithm. This result is a manifestation of the quantization inherent in any digitally implemented system. A surprising result is that these effects produce a digital residual mean-square error that is minimized by making the step size as large as possible. Since the analog residual error is minimized by taking small step sizes, the optimum step-size sequence reflects a compromise between these competing goals. The performance of a time-varying gain sequence suggested by stochastic approximation is contrasted with the performance of a constant step-size sequence. It is shown that in a digital environment the latter sequence is capable of attaining a smaller residual error.

A reduced adaptive observer for multivariable systems

Abstract: An adaptive observer for multivariable systems is presented for which the dynamic order of the observer is reduced, subject to mild restrictions. The observer structure depends directly upon the multivariable structure of the system rather than a transformation to a single-output system. The number of adaptive gains is at most the sum of the order of the system and the number of input parameters being adapted. Moreover, for the relatively frequent specific cases for which the number of required adaptive gains is less than the sum of system order and input parameters, the number of these gains is easily determined by inspection of the system structure. This adaptive observer possesses all the properties ascribed to the single-input single-output adpative observer. Like the other adaptive observers some restriction is required of the allowable system command input to guarantee convergence of the adaptive algorithm, but the restriction is more lenient than that required by the full-order multivariable observer. This reduced observer is not restricted to cycle systems.

Noise Subtracting Filter Study.

Abstract: : A new approach is presented to the problem of suppressing broadband additive interference corrupting a received signal. The noise cancelling procedure developed for the suppression of such interference is intended for problem situations where a second independent input related to the interfering process but not to the signal itself can be easily obtained. This input is called the 'reference' and is used, after suitable filtering, to cancel the interference in the main or primary input. This filtering process is adaptive and is based on the Least Mean Square algorithm of Widrow and Hoff. The algorithm is applied here so as to minimize the output power of the system on the basis of measurements at the system terminals. The adaptive algorithm requires no a priori knowledge about the properties of the system inputs, but a certain amount of qualitative a priori knowledge is required for the proper design of the built in system parameters. In as much as the required signal itself is not filtered, it remains undistorted by the noise cancelling process. Some aspects of the implementation and practical application of adaptive filters are briefly discussed. The successful application of the noise cancelling concept, using a real-time hybrid adaptive signal processor, in two distinctly different practical situations is described. (Modified author abstract)

The adaptive observer

Abstract: The simple generation of state from available measurements, for use in systems for which the criteria defining the acceptable state behavior mandates a control that is dependent upon unavailable measurement is described as an adaptive means for determining the state of a linear time invariant differential system having unknown parameters A single input output adaptive observer and the reduced adaptive observer is developed The basic ideas for both the adaptive observer and the nonadaptive observer are examined A survey of the Liapunov synthesis technique is taken, and the technique is applied to adaptive algorithm for the adaptive observer

The estimation of non-stationary filtered poisson process intensity using an adaptive algorithm based on the occurrence of peaks

Abstract: A recursive algorithm for estimating the intensity parameter of a non-stationary filtered Poisson process is presented. The algorithm, which is tested on simulated acoustic volume reverberation, adjusts the scatterer density until the number of peaks in a segment of simulated reverberation approaches the number of peaks in a corresponding segment of measured reverberation. Extensions of the algorithm may be useful for assessment of marine resources or for the extraction of process intensity estimates for simulation of radar or sonar scattering.

Stochastic penalty function optimization

Abstract: We investigate a stochastic penalty algorithm, which can be used to find a constrained optimum point for a concave or convex objective function subject to a nonlinear constraint which forms a connected region, even when we do not have the objective function available, but only have a noisy estimate of the objective function. When the constraint consists of one linear equation, we prove convergence to the constrained optimum value and bound the rate of convergence of the algorithm to the constrained optimum value. We then apply this algorithm to the nonlinear problem of automatically making an array of detectors form a beam in a desired direction in space when unknown interfering noise is present so as to maximize the signal-to-noise ratio subject to a constraint on the super-gain ratio.

Adaptive algorithms for communication through time-dispersive channels

Abstract: Linear and nonlinear adaptive algorithms for coping with intersymbol interference and additive noise in high speed data transmission over time-dispersive channels are presented. The algorithms perform the signal detection function and simultaneously, either directly or indirectly, estimate the channel for the purpose of identifying the characteristics of the inter-symbol interference. The stability and the convergence properties of the algorithms are treated as well as their performance capabilities.