# Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise

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## Abstract

**:**

## 1. Introduction

## 2. Tensor Preliminaries and Signal Model

#### 2.1. Tensor Preliminaries

**Definition**

**1**

**Definition**

**2**

**Definition**

**3**

#### 2.2. Signal Model

## 3. Robust Covariance Tensor-based Angle Estimation Method

#### 3.1. Spatial Colored Noise Suppression and Mutual Coupling Elimination

#### 3.2. Tensor-Based Signal Subspace Estimation and Angle Estimation

#### 3.3. Joint DOD and DOA Estimation

- Step.1
- Stack the matched data into a third-order tensor $\mathcal{Y}$ as Equation (9);
- Step.2
- Step.3
- Perform HOSVD of $\mathcal{R}$ to get ${\mathbf{U}}_{ns}$, ($n=1,2,3,4$), and get $\stackrel{~}{\mathbf{R}}$ via Equation (22);
- Step.4
- Perform EVD of ${\mathbf{R}}_{s}$ to get ${\stackrel{~}{\mathbf{U}}}_{s}$, obtain ${\widehat{\mathbf{\Phi}}}_{t}$ and ${\widehat{\mathbf{\Phi}}}_{r}$ via Equation (27), and compute EVD of ${\widehat{\mathbf{\Phi}}}_{t}$ to get ${\mathbf{\Phi}}_{t}$ and $\widehat{\mathbf{T}}$.
- Step.5
- Calculate ${\mathbf{\Phi}}_{r}$ via $\widehat{\mathbf{T}}{\widehat{\mathbf{\Phi}}}_{r}{\widehat{\mathbf{T}}}^{-1}$ and finally get the DODs and DOAs via Equation (28).

## 4. Remarks and Algorithm Analysis

#### 4.1. Related Remarks

**Remark**

**1.**

**Remark**

**2.**

**Remark**

**3.**

#### 4.2. Computation Complexity

## 5. Simulation Results

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Estimation results of the proposed method with $\mathrm{SNR}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$.

**Figure 4.**$\mathrm{RMSE}$ performance comparison versus $\mathrm{SNR}$ in the presence of weak mutual coupling.

**Figure 5.**$\mathrm{PSD}$ performance comparison versus $\mathrm{SNR}$ in the presence of weak mutual coupling.

Method | Computational Complexity |
---|---|

ESPRIT-Like | $\begin{array}{c}{\left(M-2P\right)}^{2}{\left(N-2P\right)}^{2}L+2\left(M-2P-1\right)\left(N-2P\right){K}^{2}+2\left(N-2P-1\right)\left(M-2P\right){K}^{2}\hfill \\ +3{K}^{3}+2{\left(M-2P\right)}^{3}{\left(N-2P\right)}^{3}\hfill \end{array}$ |

PM-Like | $\begin{array}{c}{\left(M-2P\right)}^{2}{\left(N-2P\right)}^{2}L+2\left(M-2P\right)\left(N-2P\right){K}^{2}+2\left(M-2P-1\right)\left(N-2P\right){K}^{2}\hfill \\ +\left(M-2P\right)\left(N-2P\right)K\left(\left(M-2P\right)\left(N-2P\right)-K\right)+2\left(N-2P-1\right)\left(M-2P\right){K}^{2}+3{K}^{3}\hfill \end{array}$ |

HOSVD | $\begin{array}{c}{\left(M-2P\right)}^{2}{\left(N-2P\right)}^{2}K+0.5\left(M-2P-1\right)\left(N-2P\right){K}^{2}\hfill \\ +0.5\left(N-2P-1\right)\left(M-2P\right){K}^{2}+{K}^{3}+2{\left(N-2P\right)}^{3}{\left(M-2P\right)}^{3}\hfill \end{array}$ |

Proposed | $\begin{array}{c}{M}^{2}{N}^{2}\left(L-1\right)+2{(M-2P)}^{2}K+2{(N-2P)}^{2}K+2{(M-2P)}^{2}{(N-2P)}^{2}+\hfill \\ 2\left(M-2P-1\right)\left(N-2P\right){K}^{2}+2\left(N-2P-1\right)\left(M-2P\right){K}^{2}+\hfill \\ 3{K}^{3}+3{(M-2P)}^{3}{(N-2P)}^{3}+{(M-2P)}^{3}{(N-2P)}^{3}\hfill \end{array}$ |

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**MDPI and ACS Style**

Wang, J.; Wang, X.; Xu, D.; Bi, G. Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise. *Sensors* **2018**, *18*, 832.
https://doi.org/10.3390/s18030832

**AMA Style**

Wang J, Wang X, Xu D, Bi G. Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise. *Sensors*. 2018; 18(3):832.
https://doi.org/10.3390/s18030832

**Chicago/Turabian Style**

Wang, Junxiang, Xianpeng Wang, Dingjie Xu, and Guoan Bi. 2018. "Robust Angle Estimation for MIMO Radar with the Coexistence of Mutual Coupling and Colored Noise" *Sensors* 18, no. 3: 832.
https://doi.org/10.3390/s18030832