### Abstract

Coherent processing of various forms of multidimensional signals is commonplace in radar applications. Space-time adaptive processing in radars is a well-established example of coherent processing involving the domains of space (multiple receiving antenna elements separated spatially) and time (multiple pulse returns at each antenna element). The problem of detecting a subspace signal in a given test data vector can be formulated as a statistical hypothesis testing problem. An approach that has proven effective in dealing with nuisance parameters are invariant hypothesis tests. The general approach is to identify a set of matrices such that the linear transformation of the data by any member of the set leaves the original hypothesis testing problem unchanged, although the original nuisance parameters themselves are changed as a result. In this chapter, the author extended the three signal detectors above to a subspace signal model. Analytical expressions derived include results of signal mismatch errors. The analysis is applied to an example to illustrate the use of subspace detectors to mitigate detection loss resulting from signal mismatch errors.

Original language | English (US) |
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Title of host publication | Modern Radar Detection Theory |

Publisher | Institution of Engineering and Technology |

Pages | 43-83 |

Number of pages | 41 |

ISBN (Electronic) | 9781613532003 |

ISBN (Print) | 9781613531990 |

DOIs | |

State | Published - Jan 1 2016 |

Externally published | Yes |

### Keywords

- Adaptive radar
- Adaptive radar
- Antenna arrays
- Coherent multidimensional signal processing
- Detection loss mitigation
- Invariant hypothesis tests
- Matrix algebra
- Matrix set identification
- Multiple pulse returns
- Multiple receiving antenna elements
- Nuisance parameters
- Radar antennas
- Radar detection
- Receiving antennas
- Set theory
- Signal mismatch errors
- Space-time adaptive processing
- Space-time adaptive processing
- Statistical hypothesis testing problem
- Statistical testing
- Subspace signal detection problem
- Test data vector
- Vectors

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Modern Radar Detection Theory*(pp. 43-83). Institution of Engineering and Technology. https://doi.org/10.1049/SBRA509E_ch3