ABSTRACT
The Dominant Mode Rejection (DMR) algorithm is a variant of the classical Minimum Variance Distortionless Response (MVDR) algorithm. In DMR, the algorithm estimates the ensemble covariance matrix (ECM) by averaging the noise subspace eigenvalues from the sample covariance matrix (SCM), which is a low-rank approximation of the true covariance matrix. Compared to MVDR, DMR performs better in suppressing strong interference sources and small snapshot processing. However, DMR faces challenges. Accurate estimation of the dimension of the dominant mode subspace is crucial for its performance. Both overestimation and underestimation of this subspace dimension can impact the algorithm's effectiveness. Additionally, the computational complexity of DMR primarily lies in the eigenvalue decomposition of the data covariance matrix. As the number of array elements increases, the computational burden grows significantly. To address these issues, this study employs Lanczos-type iteration and random approximation to achieve rapid decomposition of the dominant mode subspace. During the Lanczos recursion, the algorithm assesses and estimates the dimension of the dominant mode space. Furthermore, to mitigate the impact of subspace dimension estimation, the Marchenko-Pastur distribution is used to estimate the median of the SCM eigenvalues, replacing the mean value. These techniques not only reduce computational overhead but also enhance white noise gain, resulting in a more robust algorithm against array perturbations.
- H. L. V. Trees, Detection, Estimation, and Modulation Theory: Part IV. Hoboken: John Wiley & Sons, 2005, oCLC: 475926535.Google Scholar
- K. E. Wage and J. R. Buck, Snapshot Performance of the Dominant Mode Rejection Beamformer, IEEE Journal of Oceanic Engineering, vol. 39, no. 2, pp. 212–225, Apr. 2014.Google ScholarCross Ref
- J. Capon, High-resolution frequency-wavenumber spectrum analysis, Proceedings of the IEEE, vol. 57, no. 8, pp. 1408–1418, 1969.Google ScholarCross Ref
- D. A. Abraham and N. L. Owsley, Beamforming with dominant mode rejection[C], Washington, DC: IEEE Oceans 1990 Conf. Proc., 1990, 470-475.Google Scholar
- Wage, Kathleen E. and John R. Buck. Experimental Evaluation of a Universal Dominant Mode Rejection Beamformer. 2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM). 2018, 119-123.Google ScholarCross Ref
- Wage, Kathleen E. and John R. Buck. SINR loss of the dominant mode rejection beamformer. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 2015, 2499-2503.Google Scholar
- Buck, John R. The blended dominant mode rejection adaptive beamformer. Journal of the Acoustical Society of America 143. 2018, 1723-1723.Google Scholar
- SHAO Pengfei, ZOU Lina. Subarray smoothing DMR beamforming under the background of colored Gaussian noise[J]. Technical Acoustics, 2019, 38(1): 105-109.Google Scholar
- LOU Wanxiang, HUANG Di. A beam-space dominant mode rejection algorithm[J]. Technical Acoustics, 2020, 39(3): 385-388.Google Scholar
- Xu G, Cho Y, Kailath T. Application of fast subspace decomposition to signal processing and communication problems[J]. IEEE Trans. Signal Processing, 1994, 42(6): 1453-1461.Google ScholarDigital Library
- Xu G, Kailath T. Fast subspace decomposition. IEEE Trans. Signal Processing, 1994, 42(3): 539-551.Google ScholarDigital Library
- C. Hulbert and K. Wage, Random Matrix Theory Predictions of Dominant Mode Rejection Beamformer Performance, in IEEE Open Journal of Signal Processing, vol. 3, pp. 229-245, 2022.Google ScholarCross Ref
- Wage, Kathleen E. and John R. Buck. Random matrix theory analysis of the dominant mode rejection beamformer. Journal of the Acoustical Society of America 132. 2012, 2007-2007.Google Scholar
- D. Campos Anchieta, J. R. Buck. Improving the Robustness of the Dominant Mode Rejection Beamformer With Median Filtering, in IEEE Access, vol. 10, pp. 120146-120154, 2022.Google ScholarCross Ref
- Hulbert, Christopher C. and Kathleen E. Wage. Random Matrix Theory Analysis of the Dominant Mode Rejection Beamformer White Noise Gain with Overestimated Rank. 2020 54th Asilomar Conference on Signals, Systems, and Computers. 2020, 490-495.Google Scholar
- Parlett B N. The Symmetric Eigenvalue Problem[M]. Prentice -Hall, Englewood Cliffs, NJ: 1980.Google Scholar
- A. Bovik, T. Huang, and D. Munson, A generalization of median filtering using linear combinations of order statistics, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 31, no. 6, pp. 1342–1350, Dec. 1983.Google ScholarCross Ref
- P. Gandhi and S. Kassam, Analysis of CFAR processors in nonhomogeneous background, IEEE Transactions on Aerospace and Electronic Systems, vol. 24, no. 4, pp. 427–445, Jul. 1988.Google ScholarCross Ref
Index Terms
- A Robust Fast Dominant Mode Rejection Algorithm
Recommendations
Indirect Dominant Mode Rejection: A Solution to Low Sample Support Beamforming
Part IUnder conditions of low sample support, a low-rank solution of the minimum variance distortionless response (MVDR) equations can yield a higher output signal-to-interference-plus-noise ratio (SINR) than the full-rank MVDR beamformer. In this paper, we ...
A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems
Banded Toeplitz systems of linear equations arise in many application areas and have been well studied in the past. Recently, significant advancement has been made in algorithm development of fast parallel scalable methods to solve tridiagonal Toeplitz ...
Stochastic Preconditioning for Diagonally Dominant Matrices
This paper presents a new stochastic preconditioning approach for large sparse matrices. For the class of matrices that are rowwise and columnwise irreducibly diagonally dominant, we prove that an incomplete $\rm{LDL^T}$ factorization in a symmetric ...
Comments