A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems
Unimodular sequences with good correlation and spectral properties are desirable in numerous applications such as active remote sensing and communication systems. Therefore, designing sequences with stopband and correlation sidelobe constraints has gained a lot of attention in the last few decades....
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9834335/ |
| _version_ | 1811311693367607296 |
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| author | Kubilay Savci |
| author_facet | Kubilay Savci |
| author_sort | Kubilay Savci |
| collection | DOAJ |
| description | Unimodular sequences with good correlation and spectral properties are desirable in numerous applications such as active remote sensing and communication systems. Therefore, designing sequences with stopband and correlation sidelobe constraints has gained a lot of attention in the last few decades. In this paper, we propose a fast and efficient iterative algorithm to design unimodular and sparse frequency waveforms with low aperiodic/periodic autocorrelation sidelobes and desired stopband properties. In our approach, the bi-objective optimization problem which minimizes both the integrated sidelobe level (ISL) of the autocorrelation function and the power density in the spectral stopbands is first turned into an unconstrained single objective optimization problem and then is treated as a nonlinear large-scale problem. For the solution of the problem, we develop an algorithm based on Limited Memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) Quasi-Newton optimization method. Unlike most gradient based algorithms which employ line searches to deduce the step length, owing to L-BFGS method, unit step length is taken as a general rule to avoid the cost of computation at every iteration with very few exceptions. The calculation of gradient is based on Fast Fourier Transform and Hadamard product operations and thus the algorithm is fast and computationally efficient. Moreover, the algorithm is space efficient and its low-memory feature makes it possible to generate long sequences. Several numerical examples are presented to validate the efficacy of the proposed method and to show its superiority over other state-of-art algorithms. |
| first_indexed | 2024-04-13T10:23:26Z |
| format | Article |
| id | doaj.art-e1f82f4616b643d4996c3dae5d18794b |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-13T10:23:26Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e1f82f4616b643d4996c3dae5d18794b2022-12-22T02:50:25ZengIEEEIEEE Access2169-35362022-01-0110770117702910.1109/ACCESS.2022.31928489834335A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing SystemsKubilay Savci0https://orcid.org/0000-0003-1839-2340Department of Electrical-Electronics Engineering, Koc University, Istanbul, TurkeyUnimodular sequences with good correlation and spectral properties are desirable in numerous applications such as active remote sensing and communication systems. Therefore, designing sequences with stopband and correlation sidelobe constraints has gained a lot of attention in the last few decades. In this paper, we propose a fast and efficient iterative algorithm to design unimodular and sparse frequency waveforms with low aperiodic/periodic autocorrelation sidelobes and desired stopband properties. In our approach, the bi-objective optimization problem which minimizes both the integrated sidelobe level (ISL) of the autocorrelation function and the power density in the spectral stopbands is first turned into an unconstrained single objective optimization problem and then is treated as a nonlinear large-scale problem. For the solution of the problem, we develop an algorithm based on Limited Memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) Quasi-Newton optimization method. Unlike most gradient based algorithms which employ line searches to deduce the step length, owing to L-BFGS method, unit step length is taken as a general rule to avoid the cost of computation at every iteration with very few exceptions. The calculation of gradient is based on Fast Fourier Transform and Hadamard product operations and thus the algorithm is fast and computationally efficient. Moreover, the algorithm is space efficient and its low-memory feature makes it possible to generate long sequences. Several numerical examples are presented to validate the efficacy of the proposed method and to show its superiority over other state-of-art algorithms.https://ieeexplore.ieee.org/document/9834335/Waveform designsequence designautocorrelationintegrated sidelobe levelspectral stopbandsparse frequency waveform |
| spellingShingle | Kubilay Savci A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems IEEE Access Waveform design sequence design autocorrelation integrated sidelobe level spectral stopband sparse frequency waveform |
| title | A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems |
| title_full | A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems |
| title_fullStr | A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems |
| title_full_unstemmed | A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems |
| title_short | A Limited Memory BFGS Based Unimodular Sequence Design Algorithm for Spectrum-Aware Sensing Systems |
| title_sort | limited memory bfgs based unimodular sequence design algorithm for spectrum aware sensing systems |
| topic | Waveform design sequence design autocorrelation integrated sidelobe level spectral stopband sparse frequency waveform |
| url | https://ieeexplore.ieee.org/document/9834335/ |
| work_keys_str_mv | AT kubilaysavci alimitedmemorybfgsbasedunimodularsequencedesignalgorithmforspectrumawaresensingsystems AT kubilaysavci limitedmemorybfgsbasedunimodularsequencedesignalgorithmforspectrumawaresensingsystems |