# Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar

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## Abstract

**:**

## 1. Introduction

## 2. Basic Knowledge of Tensor and Signal Model Based on Tensor

#### 2.1. Basic Knowledge of Tensor

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

#### 2.2. Signal Model Based on Tensor

## 3. Doa and Range Estimation VIA Tensor for FDA-Mimo Radar

#### 3.1. Signal Subspace Estimation VIA HOSVD

#### 3.2. DOA Estimation VIA Tensor-Based Reduced-Dimension Music

#### 3.3. Range Estimation

## 4. Performance Analysis of the Proposed Method

#### 4.1. Computation Complexity

- (1) The HOSVD computation complexity of $\mathcal{X}\in {\mathbb{C}}^{M\times N\times L}$ is $O\left(\phantom{\rule{0.166667em}{0ex}}MNL\right(M+N+L\left)\phantom{\rule{0.166667em}{0ex}}\right)$ in Equation (11);
- (2) The signal subspace estimation needs $O\left(4PLMN\right)$ in Equation (15);
- (3) In Equation (21), the dimensionality reduction of the two-dimensional search requires $O\left({M}^{2}{N}^{2}{P}^{2}(MN+{P}^{2})\right)$;
- (4) The spectrum peak search of DOA estimation in Equation (27) is $O({d}_{\theta}\left(MP\right)!(MP-1))$, where ${d}_{\theta}$ represents the search times within the search DOA, and $(*)!$ stands for factorial;
- (5) Computing the range requires $O(2{M}^{3}P+{M}^{2}P)$;

#### 4.2. Cram$\stackrel{\xb4}{\mathit{e}}$r-Rao Bound

## 5. Numerical Simulations

#### 5.1. Spectrum Peak Search for DOA Estimation

#### 5.2. 2D Point Cloud of the Target Landing Point

#### 5.3. RMSE Performance

#### 5.4. Probability of Successful Detection

#### 5.5. The Simulation Time Versus Trial Number

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Notation | Definition |
---|---|

$\mathcal{Q}$(bold Euler script letter) | tensor |

$\mathit{A}$(bold capital letter) | matrix |

$\mathit{a}$(bold lowercase letter) | vector |

∘ | Hadamard product |

⊗ | Kronecker product |

⊙ | Khatri-Rao product |

${\mathit{I}}_{Q}$ | $Q\times Q$ identity matrix |

${\mathit{0}}_{Q}$ | $Q\times Q$ zero matrix |

${(\xb7)}^{*}$ | conjugate of matrix |

${(\xb7)}^{\mathrm{T}}$ | transpose of matrix |

${(\xb7)}^{\mathrm{H}}$ | conjugation-transpose of matrix |

$\mathrm{diag}(\ast )$ | diagonalization of matrix |

$\mathrm{angle}(\ast )$ | extract phase |

${\mathbb{C}}^{M\times N}$ | $M\times N$ matrix set |

Method | Computation Complexity |
---|---|

Proposed | $O\{4MNL+{M}^{2}{N}^{2}{P}^{2}(MN+{P}^{2})+{d}_{\theta}\left(MP\right)!(MP-1)$ $+2{M}^{3}P+{M}^{2}P+MNL(M+N+L)\}$ |

ESPRIT | $O\{{\left(2MN\right)}^{2}L+{\left(2MN\right)}^{3}+4(5MN-2M-2N){K}^{2}$ $+{K}^{3}(L+M)+MN{K}^{2}+31{K}^{3}\}$ |

MUSIC | $O\{{d}_{\theta}*{d}_{range}\left[{\left(MN\right)}^{2}(2(MN-P)+MN)\right]$ $+{\left(MN\right)}^{2}L+{M}^{2}N+M{N}^{2}\}$ |

Tensor-ESPRIT | $O\{2{\left(MNL\right)}^{3}+MNL(M+N+L)+MLK(N+K)$ $+{K}^{3}(L+M)+MN{K}^{2}+31{K}^{3}\}$ |

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**MDPI and ACS Style**

Xu, T.; Wang, X.; Huang, M.; Lan, X.; Sun, L.
Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar. *Remote Sens.* **2021**, *13*, 3772.
https://doi.org/10.3390/rs13183772

**AMA Style**

Xu T, Wang X, Huang M, Lan X, Sun L.
Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar. *Remote Sensing*. 2021; 13(18):3772.
https://doi.org/10.3390/rs13183772

**Chicago/Turabian Style**

Xu, Tengxian, Xianpeng Wang, Mengxing Huang, Xiang Lan, and Lu Sun.
2021. "Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar" *Remote Sensing* 13, no. 18: 3772.
https://doi.org/10.3390/rs13183772