@InProceedings{8081399,
  author = {A. Lenz and M. S. Stein and A. L. Swindlehurst},
  booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)},
  title = {Analog transmit signal optimization for undersampled delay-Doppler estimation},
  year = {2017},
  pages = {1205-1209},
  abstract = {In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cramer-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore the Pareto region spanned by the optimized analog waveforms. Furthermore, we demonstrate how the framework can be used to reduce the sampling rate at the receiver while maintaining high estimation accuracy. Finally, we verify the practical impact by Monte-Carlo simulations of a channel estimation algorithm.},
  keywords = {Bayes methods;channel estimation;Doppler radar;eigenvalues and eigenfunctions;filtering theory;Fourier transforms;Monte Carlo methods;Pareto optimisation;radar receivers;radar signal processing;signal sampling;synchronisation;analog transmit signal optimization;undersampled delay-Doppler estimation;analog transmit waveform;Bayesian Cramer-Rao lower bound;estimation theoretic design rule;Fourier coefficients;wireless delay-Doppler channel;system optimization problem;channel estimation algorithm;subNyquist conditions;analog prefiltering bandwidth;eigenvalue decomposition;Pareto region;Estimation;Optimization;Bandwidth;Receivers;Signal processing;Europe;Channel estimation;Bayesian Cramer-Rao lower bound;compressive sensing;delay-Doppler estimation;signal optimization;sub-Nyquist sampling;waveform design},
  doi = {10.23919/EUSIPCO.2017.8081399},
  issn = {2076-1465},
  month = {Aug},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2017/papers/1570347482.pdf},
}

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Based on the Bayesian Cramer-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore the Pareto region spanned by the optimized analog waveforms. Furthermore, we demonstrate how the framework can be used to reduce the sampling rate at the receiver while maintaining high estimation accuracy. 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Lenz and M. S. Stein and A. L. Swindlehurst},\n booktitle = {2017 25th European Signal Processing Conference (EUSIPCO)},\n title = {Analog transmit signal optimization for undersampled delay-Doppler estimation},\n year = {2017},\n pages = {1205-1209},\n abstract = {In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cramer-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore the Pareto region spanned by the optimized analog waveforms. 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