# Scalable ESPRIT Processor for Direction-of-Arrival Estimation of Frequency Modulated Continuous Wave Radar

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## Abstract

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## 1. Introduction

## 2. ESPRIT Algorithm for Estimating DOA

#### 2.1. Signal Model

#### 2.2. ESPRIT and MI-ESPRIT Algorithm

#### 2.3. DOA Estimation Technique for Single Target

#### 2.4. Comparison of RMSE Performance According to the Number of Antennas

## 3. Hardware Architecture of Proposed ESPRIT Processor

#### 3.1. Covariance Matrix Module (CMM)

#### 3.2. Eigenvalue Decomposition Module (EDM)

#### 3.3. Least Square Module (LSM)

#### 3.4. Angle Estimation Module (AEM)

## 4. Implementation Results of Proposed ESPRIT Processor

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Subarray structure for estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm.

**Figure 3.**Subarray structure for multiple invariances (MI)-ESPRIT algorithm ($\mathit{M}$ = 8, $\mathit{h}$ = 6, $\mathit{z}$ = 3).

**Figure 4.**Comparison of root mean square error (RMSE) of direction-of-arrival (DOA) according to the number of the snapshot for the target detected in the R-D map.

**Figure 5.**Comparison of RMSE of DOA according to the number of subarrays ($\mathit{h}$) and the number of antennas in subarray ($\mathit{z}$), (

**a**) $\mathit{M}$ = 4, (

**b**) $\mathit{M}$ = 8.

Number of Antenna | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|

Cycle | Conventional | 48 | 150 | 300 | 520 | 780 | 1134 | 1512 |

Proposed | 48 | 100 | 150 | 208 | 260 | 324 | 378 | |

Reduction (%) | 0 | 33 | 50 | 60 | 66 | 71 | 75 |

**Table 2.**Implementation results of proposed ESPRIT processor based on Xilinx Zynq UltraScale+ ZCU104 FPGA.

Parameter | Value | |
---|---|---|

Target FPGA | Xilinx UltraSclae+ ZCU104 | |

Maximum Operating Frequency | 334 MHz | |

LUT | 28,978 | |

FF | 11,279 | |

DSP | 374 | |

Execution Time ($\mathsf{\mu}$s) | $\mathit{M}$ = 2 | 0.39 |

$\mathit{M}$ = 3 | 0.53 | |

$\mathit{M}$ = 4 | 0.67 | |

$\mathit{M}$ = 5 | 0.79 | |

$\mathit{M}$ = 6 | 0.99 | |

$\mathit{M}$ = 7 | 1.48 | |

$\mathit{M}$ = 8 | 1.86 |

[18] | [19] | [30] | [31] | Proposed | ||
---|---|---|---|---|---|---|

Algorithm | ESPRIT | ESPRIT | Cholesky | Bartlett | MI-ESPRIT | |

Number of Antenna | 4 | 4 | 4 | 8 | 2–8 | |

Word Length | 16 | 16 | 16 | 16 | 16 | |

Target FPGA | Virtex-5 | Virtex-5 | Virtex-5 | Virtex-5 | Virtex-5 | |

Maximum Operating Frequency (MHz) | 52.5 | 62.99 | 63.0 | N.A. | 120 | |

Slice Registers | 35,331 | 16,710 | 17,362 | 10,399 | 10,088 | |

LUT | 40,019 | 22,936 | 21,956 | 7,617 | 18,207 | |

DSP | 253 | 240 | 230 | N.A. | 80 | |

Execution Time ($\mathsf{\mu}$s) | 24.38 | 2.49 | 3.08 | 46.34 | 1.87 | |

Processing Rate (Hz) | 41,017 | 401,606 | 324,675 | 21,580 | 535,714 | |

Area Efficiency | Hz/Registers | 1.16 | 24.03 | 18.70 | 2.075 | 53.10 |

Hz/LUT | 1.02 | 17.51 | 14.79 | 2.83 | 29.42 |

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**MDPI and ACS Style**

Jung, Y.; Jeon, H.; Lee, S.; Jung, Y.
Scalable ESPRIT Processor for Direction-of-Arrival Estimation of Frequency Modulated Continuous Wave Radar. *Electronics* **2021**, *10*, 695.
https://doi.org/10.3390/electronics10060695

**AMA Style**

Jung Y, Jeon H, Lee S, Jung Y.
Scalable ESPRIT Processor for Direction-of-Arrival Estimation of Frequency Modulated Continuous Wave Radar. *Electronics*. 2021; 10(6):695.
https://doi.org/10.3390/electronics10060695

**Chicago/Turabian Style**

Jung, Yongchul, Hohyub Jeon, Seongjoo Lee, and Yunho Jung.
2021. "Scalable ESPRIT Processor for Direction-of-Arrival Estimation of Frequency Modulated Continuous Wave Radar" *Electronics* 10, no. 6: 695.
https://doi.org/10.3390/electronics10060695