## Xiaobo Yang## |

Double-precision floating-point algorithm | Proposed algorithm | Fixed-point algorithm |
---|---|---|

-0.56825095 – 0.04081602i | -0.56825103 – 0.04081590i | -0.57323103 – 0.04601546i |

-0.07209626 + 0.36793381i | -0.07209653 + 0.36793400i | -0.07609633 + 0.36203489i |

-0.61224438 + 0.13253420i | -0.61224393 + 0.13253387i | -0.61724392 + 0.13713237i |

0.082773180 – 0.36822792i | 0.08277294 – 0.36822800i | 0.08777204 – 0.36300231i |

The accuracy of the algorithm in this study was equivalent to that of the double-precision floating-point algorithm [11]. However, the double-precision floating-point algorithm can only complete eigenvalue diagonalization in serial mode and requires the square and division of double-precision floating point numbers. The FPGA implementation requires 300 clock-cycles, whereas the algorithm in this study only requires 70 clock-cycles to complete, 230 clock-cycles fewer than those required for similar calculations presented in the literature [11]. The DOA algorithm must traverse all six non-diagonal elements of the complex matrix, and the clock-cycles used in this algorithm are 1,380 fewer than those in [11]. The entire eigenvalue decomposition process was iterated 16 times, and the clock-cycles used in this algorithm were 22,080 less than those in [11]. The amount of computation required by this algorithm is equivalent to that required by the fixed-point algorithm [10].

The spatial spectrum 3D-plot based on fixed DOA estimation is shown in Fig. 4, and the spatial spectral isobars based on fixed DOA estimation are shown in Fig. 5. The spatial spectrum 3D-plot based on the proposed algorithm is shown in Fig. 6, and the spatial spectral isobars based on the proposed algorithm are shown in Fig. 7.

From the simulation results, the estimated elevation and azimuth angles obtained using the proposed algorithm were equal to the set values, and the decomposition accuracy based on the algorithm satisfied the DOA estimation application requirements. The divergence of the DOA estimation results occurred in fixed-point calculations owing to the large implementation errors.

The double-precision floating-point algorithm proposed in [11] can only be implemented serially and uses calculations of squares of double-precision floating-point numbers, which requires at least 300 clock-cycles to diagonalize the matrix using the field-programmable gate array. The proposed algorithm can be completed in 70 clock cycles, and its computational efficiency is 76.67 % higher than that of the double-precision floating-point algorithm proposed in [11], which significantly improves the real-time performance of DOA estimation, while ensuring accuracy.

Although DOA estimation of the MUSIC algorithm can theoretically exceed the Rayleigh limit and achieve the supposed super-resolution, its application is limited in practical engineering owing to the real-time performance and accuracy of the algorithm. Ensuring the efficiency and accuracy of an algorithm in engineering is a key problem. Based on the analysis of the characteristics of the MUSIC algorithm, complex matrix eigenvalue decomposition, and CORDIC algorithm, a high-accuracy algorithm for DOA estimation with high parallelism was presented herein. The algorithm uses parallel construction of an orthogonal unit matrix and the CORDIC algorithm based on a single-precision floating-point number to ensure the efficiency and accuracy of the algorithm, respectively. Monte Carlo simulation verified that the average error of the feature vector of the algorithm was only 0.000001 compared with the double-precision floating-point calculation, whereas that of the fixed-point algorithm was 0.005. The divergence in the DOA estimation results appeared because of large error in the fixed-point calculation. The diagonalization of double-precision floating-point computation matrices requires at least 300 clock cycles, whereas the proposed algorithm performed a similar calculation in only 70 clock cycles, which signifies a notable improvement in the real-time performance and accuracy of the algorithm.

She received B.S. degree in department of electronic Engineer from Hebei Normal University in 2001, M.S. degree in information science from Yanshan University in 2004, She is currently an associate professor in the Department of Electrical and Electronic Engineering, Shijiazhuang University of Applied Technology. Her research interests include communication and signal processing.

- 1 P. Chen, Z. Wen, L. Li, F Guo, "Performance analysis of classical MUSIC algorithm for DOA estimation,"
*Microprocessors*, vol. 40, no. 6, pp. 40-43, 2019.doi:[[[10.1109/ICCIT51783.2020.9392663]]] - 2 C. W. Zhou, H. Zheng, Y. Gu, Y. Wang, Z. Shi, "Research progress on coprime array signal processing: direction-of-arrival estimation and adaptive beamforming,"
*Journal of Radars*, vol. 8, no. 5, pp. 558-577, 2019.doi:[[[10.12000/JR19068]]] - 3 Y. Zhang, J. Lu, S. Tian, H. Li, "Hypothesis testing based range statistical resolution limit of radar: random-distributed amplitude,"
*Journal of Signal Processing*, vol. 36, no. 10, pp. 1735-1743, 2020.custom:[[[-]]] - 4 W. Wang, M. Zhang, B. Yao, Q. Yin, P. Mu, "Computationally efficient direction-of-arrival estimation of non-circular signal based on subspace rotation technique,"
*Journal on Communications*, vol. 41, no. 11, pp. 198-205, 2021.custom:[[[-]]] - 5 H. Dou, J. Xie, L. Sun, F. Yang, "High precision DOA estimation algorithm for MIMO radar based on covariance fitting,"
*Journal of Beijing University of Technology*, vol. 46, no. 2, pp. 140-146, 2020.custom:[[[-]]] - 6 F. G. Yan, Y. Shen, "Overview of efficient algorithms for super-resolution DOA estimates,"
*Systems Engineering and Electronicsvol, 37*, no. 7, pp. 1465-1475, 2015.custom:[[[-]]] - 7 C. Feng, X. Gong, R. Luo, "Fast DOA estimation based on FFT and golden section,"
*Computer Simulation*, vol. 38, no. 9, pp. 159-163+172, 2021.custom:[[[-]]] - 8 Y. Jiang, M. Y. Feng, Q. Xu, Y. He, "Fast DOA estimation methods for underdetermined wideband signals with a high accuracy,"
*Journal of Xidian University*, vol. 47, no. 2, pp. 91-97+107, 2020.doi:[[[10.19665/j.issn1001-2400.2020.02.013]]] - 9 H. Fan, X. Diao, F. Zhang, Z. Xue, X. Dong, M. Tie, "Analysis and elimination of half-wavelength error in homodyne laser interference signal processing system based on CORDIC algorithm,"
*Acta Metrologica Sinica*, vol. 42, no. 3, pp. 287-293, 2021.custom:[[[-]]] - 10 C. Song, X. Li, Y. Jian, S. Shang, Q. Zheng, "CORDIC algorithm for IQ real-time demodulation and FPGA implementation in radar imaging system,"
*Electronic Measurement Technology*, vol. 43, no. 18, pp. 136-140, 2020.custom:[[[-]]] - 11 J. Chen, J. Zhu, S. Liu, P. Liu, Z. Xu, "Realization of adaptive array covariance matrix feature separation based on FPGA,"
*Navigation Positioning and Timing*, vol. 6, no. 5, pp. 102-108, 2019.custom:[[[-]]] - 12 X. Li, W. Xue, Z. Sun, "High quality method for solving eigenvalues of complex Hermite matrix,"
*Journal of Data Acquisition and Processing*, vol. 20, no. 4, pp. 403-406, 2005.custom:[[[-]]] - 13 M. Garrido, P. Kallstrom, M. Kumm, O. Gustafsson, "CORDIC II: a new improved CORDIC algorithm,"
*IEEE Transactions on Circuits and Systems II: Express Briefs*, vol. 63, no. 2, pp. 186-190, 2015.doi:[[[10.1109/TCSII.2015.2483422]]] - 14 R. Schmidt, "Multiple emitter location and signal parameter estimation,"
*IEEE Transactions on Antennas and Propagation*, vol. 34, no. 3, pp. 276-280, 1986.doi:[[[10.1109/tap.1986.1143830]]] - 15 Q. Zhang, S. Li, Z. Tang, "DOA estimation of coherent sources based on hybrid MUSIC algorithm,"
*Application Research of Computers*, vol. 37, no. 5, pp. 1536-1540, 2019.custom:[[[-]]]