Array processing involves manipulation of signals induced on various antenna elements. Its capabilities of steering nulls to reduce cochannel interferences and pointing independent beams toward various mobiles, as well as its ability to provide estimates of directions of radiating sources, make it attractive to a mobile communications system designer. Array processing is expected to play an important role in fulfilling the increased demands of various mobile communications services. Part I of this paper showed how an array could be utilized in different configurations to improve the performance of mobile communications systems, with references to various studies where feasibility of apt array system for mobile communications is considered. This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them. This paper brings together almost all aspects of array signal processing.

/pdf/application-of-antenna-arrays-to-mobile-communications-ii-52fds1c81j.pdf

Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations

This paper provides a time-domain feedback analysis of gradient-based adaptive schemes. A key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties (along the lines of H/sup /spl infin//-theory and robust filtering). The analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions. It is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes. The feedback structure is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The configuration is further shown to lend itself to analysis via a so-called small gain theorem, thus leading to stability and robustness conditions that require the contractivity of certain operators. Choices for the step-size parameter in order to guarantee faster rates of convergence are also derived, and simulation results are included to demonstrate the theoretical findings. In addition, the time-domain analysis provided in this paper is shown to extend the so-called transfer function approach to a general time-variant scenario without any approximations.

A time-domain feedback analysis of filtered-error adaptive gradient algorithms

Conventional gradient-based adaptive filters, as typified by the well-known LMS algorithm, use an instantaneous estimate of the error-surface gradient to update the filter coefficients. Such a strategy leaves the algorithm extremely vulnerable to impulsive interference. A class of adaptive algorithms employing order statistic filtering of the sampled gradient estimates is presented. These algorithms, dubbed order statistic least mean squares (OSLMS), are designed to facilitate adaptive filter performance close to the least squares optimum across a wide range of input environments from Gaussian to highly impulsive. Three specific OSLMS filters are defined: the median LMS, the average LMS, and the trimmed-mean LMS. The properties of these algorithms are investigated and the potential for improvement demonstrated. Finally, a general adaptive OSLMS scheme in which the nature of the order-statistic operator is also adapted in response to the statistics of the input signal is presented. It is shown that this can facilitate performance gains over a wide range of input data types. >

A class of order statistic LMS algorithms

This letter analyzes the mean-square convergence of a deficient-length least mean-square adaptive filter whose length is less than that of the unknown system and proves that filter length and the envelope of impulse response are the important factors in convergence rate control For the impulse response with an exponential decay envelope, which covers a large set of physical systems, eg, acoustic echo path, an optimal filter length sequence is figured out to achieve the fastest convergence The simulations of an exact exponential decay envelope and of a real-life echo path in a car environment are performed via computer, and the results validate our analysis well

Convergence analysis of a deficient-length LMS filter and optimal-length sequence to model exponential decay impulse response

This paper provides a time-domain feedback analysis of gradient-based adaptive schemes with emphasis on stability and robustness issues. It is shown that an intrinsic feedback structure, mapping the noise sequence and the initial weight guess to the a priori estimation errors and the final weight estimate, can be associated with such schemes. The feedback configuration is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The configuration is further shown to lend itself rather immediately to analysis via a so-called small gain theorem; thus leading to stability conditions that require the contractivity of certain operators.

Time-domain feedback analysis of adaptive gradient algorithms via the small gain theorem

A simple approximation to the behavior of the LMS adaptive filter as a discrete transfer function is developed. This representation is a valid description for both deterministic inputs and for the expected results with random inputs (including correlated inputs). The results are shown to be exact for some classes of input including periodic signals. One result of this analysis is the demonstration that the LMS filter can produce results which are biased from the least-squares solution under the combined conditions of a nonzero mean primary and a correlated reference input.

Simplified analysis of the LMS adaptive filter using a transfer function approximation

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Simplified analysis of the LMS adaptive filter using a transfer function approximation