Linear arrays with sensors at integer locations are widely used in array signal processing. This paper considers arrays where sensor locations can be rational numbers. It is demonstrated that such rational arrays have...
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Linear arrays with sensors at integer locations are widely used in array signal processing. This paper considers arrays where sensor locations can be rational numbers. It is demonstrated that such rational arrays have some important advantages over integerarrays. For example, they offer more flexibility and reduced DOA estimation error when a limited number of sensors are to be distributed in a fixed aperture. Sparse and coprime rational arrays are introduced to achieve this. Extensive Monte-Carlo simulations demonstrate that rational arrays can perform close to CRB even at low SNR and a small number of snapshots compared to the integerarrays. Furthermore, they can resolve the closely spaced sources and provide smaller MSE for almost all two-DOA configurations. Next, if the signals are impinging from a restricted spatial scope, rational arrays can better utilize this information and place sensors over a larger aperture while still maintaining unique identifiability property. Results on steering vector invertibility of general rational arrays and unique identifiability with rational coprime arrays are provided. In order to do this, some rational extensions of integer number theoretic concepts such as greatest common divisor and coprimality are required, which are introduced as well. The theoretical results are further extended to arbitrary arrays where sensor locations may even be irrational.
Antenna arrays are critical in enhancing communication reliability and spectral efficiency within cellular networks. Traditional integer-based designs, while simple and robust, impose limitations on performance scalab...
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Antenna arrays are critical in enhancing communication reliability and spectral efficiency within cellular networks. Traditional integer-based designs, while simple and robust, impose limitations on performance scalability. This study explores the underutilized potential of non-integer array configurations for base station deployments. By introducing a novel theoretical framework supported by mathematical derivations and two foundational lemmas, this work demonstrates the superior spectral efficiency and sum-rate capacity achievable with non-integer arrays. Comprehensive MATLAB simulations validate these theoretical predictions across various configurations, fading conditions, and multiuser scenarios. Key findings highlight the consistent performance gains of non-integer arrays over integer-based designs, including improved capacity even under constrained antenna subsets and varying interference conditions. This research paves the way for innovative antenna designs that address the growing demands of next-generation wireless networks, offering practical insights for implementation in high-capacity communication systems.
Rational arrays were recently proposed for direction of arrival (DOA) estimation. In particular, rational coprime arrays were demonstrated to be useful when the aperture and the number of sensors are constrained. In t...
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ISBN:
(纸本)9781665459068
Rational arrays were recently proposed for direction of arrival (DOA) estimation. In particular, rational coprime arrays were demonstrated to be useful when the aperture and the number of sensors are constrained. In this paper, we provide a necessary and sufficient condition for steering vector invertibility of a general rational array. We demonstrate that shrunk rational ULAs can have smaller MSE than integer ULAs when multiple sources impinge from the directions away from the normal to the array. We also propose a new way for generating rational arrays which readily ensures the "rational coprimality condition" for identifiability. arrays generated according to this new way provide better DOA estimation performance compared to previously used rational coprime arrays. Next, the paper provides a detailed performance evaluation for rational coprime arrays in terms of numerical and analytical mean square errors with root-MUSIC. For this, a modification of root-MUSIC for search-ree estimation of DOAs with rational arrays is introduced. It is found that rational coprime arrays have smaller MSE than three possible integerarrays with the same aperture and number of sensors, including ULAs and integer coprime arrays.
Linear arrays used in array processing usually have sensor positions r(i)lambda\2 where lambda is the wavelength of the impinging signals and ri are integers. This paper considers rational arrays, where r(i) are ratio...
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ISBN:
(纸本)9781665405409
Linear arrays used in array processing usually have sensor positions r(i)lambda\2 where lambda is the wavelength of the impinging signals and ri are integers. This paper considers rational arrays, where r(i) are rational numbers. In particular, sparse rational arrays such as coprime rational arrays are introduced. In order to do this, some rational extensions of integer number theoretic concepts such as greatest common divisor and coprime numbers are required, which are introduced as well. The advantages of rational arrays are demonstrated with the help of rational coprime arrays. For example, they improve the accuracy of DOA estimation when the sensors have to be distributed with a fixed aperture constraint.
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