Second-Order Nonlinearity Estimated and Compensated Diffusion LMS Algorithm: Theoretical Upper Bound, Cramer-Rao Lower bound, and Convergence Analysis
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910370482880512 |
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| author | Zayyani, Hadi Korki, Mehdi |
| author_facet | Zayyani, Hadi Korki, Mehdi |
| contents | In this paper, an algorithm for estimation and compensation of second-order nonlinearity in wireless sensor setwork (WSN) in distributed estimation framework is proposed. First, the effect of second-order nonlinearity on the performance of Diffusion Least Mean Square (DLMS) algorithm is investigated and an upper bound for $l^2$-norm of the error due to nonlinearity is derived mathematically. Second, mean convergence analysis of the DLMS algorithm in presence of second-order nonlinearity is derived. Third, a distributed algorithm is suggested which consists of extra nonlinearity estimation and compensation units. Moreover, considering the second-order nonlinearity, the Cramer-Rao bound (CRB) for estimating both the unknown vector and nonlinearity coefficient vector is calculated, in which the Fisher information matrix is obtained in a closed-form formula. Simulation results demonstrate the effectiveness of the proposed algorithm in improving the performance of distributed estimation in the presence of nonlinear sensors in a WSN. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second-Order Nonlinearity Estimated and Compensated Diffusion LMS Algorithm: Theoretical Upper Bound, Cramer-Rao Lower bound, and Convergence Analysis Zayyani, Hadi Korki, Mehdi Signal Processing In this paper, an algorithm for estimation and compensation of second-order nonlinearity in wireless sensor setwork (WSN) in distributed estimation framework is proposed. First, the effect of second-order nonlinearity on the performance of Diffusion Least Mean Square (DLMS) algorithm is investigated and an upper bound for $l^2$-norm of the error due to nonlinearity is derived mathematically. Second, mean convergence analysis of the DLMS algorithm in presence of second-order nonlinearity is derived. Third, a distributed algorithm is suggested which consists of extra nonlinearity estimation and compensation units. Moreover, considering the second-order nonlinearity, the Cramer-Rao bound (CRB) for estimating both the unknown vector and nonlinearity coefficient vector is calculated, in which the Fisher information matrix is obtained in a closed-form formula. Simulation results demonstrate the effectiveness of the proposed algorithm in improving the performance of distributed estimation in the presence of nonlinear sensors in a WSN. |
| title | Second-Order Nonlinearity Estimated and Compensated Diffusion LMS Algorithm: Theoretical Upper Bound, Cramer-Rao Lower bound, and Convergence Analysis |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2403.11059 |