### Abstract

We consider the problem of source separation of a signal whose elements consist of chirp scattered returns and sinusoidal tones overlapping in time and frequency. Due to the application, both signals are assumed to be highly non-stationary with their parameters rapidly changing. Such a mixture may occur when a device with a single antenna is spectrally constrained while simultaneously communicating information and sensing the environment. Another application is to mitigate interference between two devices which must share the spectrum. We consider a formulation where the chirp scattered returns are modeled as a convolution and the sinusoidal tones are modeled as sparse in the overcomplete inverse discrete Fourier domain. The objective function which is a combination of basis pursuit denoising and deconvolution is formulated with a/i-norm regularizer for each signal. A fast transform based iterative algorithm to obtain the solution is presented and the major steps for deriving the solution are outlined. Simulation results are provided where the non-linear separation algorithm yields a significant improvement in signal reconstruction relative to the standard matched-filter.

Original language | English (US) |
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Title of host publication | 2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, CoSeRa 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 163-167 |

Number of pages | 5 |

ISBN (Electronic) | 9781509029204 |

DOIs | |

State | Published - Nov 15 2016 |

Event | 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, CoSeRa 2016 - Aachen, Germany Duration: Sep 19 2016 → Sep 23 2016 |

### Publication series

Name | 2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, CoSeRa 2016 |
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### Other

Other | 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, CoSeRa 2016 |
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Country | Germany |

City | Aachen |

Period | 9/19/16 → 9/23/16 |

### ASJC Scopus subject areas

- Instrumentation
- Signal Processing

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## Cite this

*2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, CoSeRa 2016*(pp. 163-167). [7745721] (2016 4th International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing, CoSeRa 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CoSeRa.2016.7745721