Many algorithms have been proposed for multidimensional frequency estimation from a single snapshot or multiple snapshots of data mixture. Most of these algorithms fail when one or more identical frequencies are found in certain dimensions. In this paper, a multidimensional frequency estimation technique from a single datum snapshot is proposed. It applies LU decomposition (Gaussian Elimination) on an eigenvector-based algorithm for multidimensional frequency estimation. This proposed technique is simulated using a MATLAB code. The average root mean square error (RMSE) is investigated as a performance measure of the proposed technique. A comparison between original eigenvector-based (traditional) and the proposed techniques is introduced. The simulation results show that the RMSE of the proposed technique is less than the original one, and it has a more efficient solution for an identical frequency case but at the expense of complexity.
This is a preview of subscription content, log in to check access.
Buy single article
Instant unlimited access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Bülow T, Sommer G (2001) Hypercomplex signals-a novel Extension of the analytic signal to the multidimensional case. IEEE Trans Signal Process 49(11)
Gilli E, Schennach R (2009) Detection of coatings on paper using infra red spectroscopy. Lenzinger Berichte 87:162–167
Cao H, Wu Y, Leshem A (2015) R-D frequency estimation of multidimensional sinusoids based on eigenvalues and eigenvectors. Multidim Syst Sign Process 26:777–786. https://doi.org/10.1007/s11045-014-0277-4
Muir S, Chapin J, Bose V, Steinheider J Distributed antenna systems plus software radio: range extension and other benefits. Vanu, Inc, Cambridge email@example.com
Hua Y (1992) Estimating two-dimensional frequencies by matrix enhancement and matrix pencil. IEEE Trans Signal Process 40(9):2267 2280
Liu J (2007) Eigenvector-based multidimensional frequency estimation: identifiability, performance, and applications. Electronic Theses and Dissertations. Paper 842. https://doi.org/10.18297/etd/842
Andersson F, Carlsson M (2016) Fixed-point algorithms for frequency estimation and structured low rank approximation, arXiv:1601.01242v1 [math.NA]
Haardt M, Hüper K, Moore JB, Nossek JA Simultaneous schur decomposition of several matrices to achieve automatic pairing in multidimensional harmonic retrieval problems. Retrieved on: 03 February 2016
Cheng Q, Yang R, Zhang H (2005) Optimally weighted ESPRIT using uniform circular arrays. Comput Electr Eng 31:272–281
Liu J, Liu X, Ma X Multidimensional frequency estimation with finite snapshots in the presence of identical frequencies. Impact Factor 2.79. https://doi.org/10.1109/TSP.2007.899530. Source: IEEE Xplore
Ino F, Goda K, Matsui M, Hagihara K (2005) Performance study of lu decomposition on the programmable gpu*. In Proceedings of the 12th IEEE international conference high erformance computing, HiPC05, page 83–94, Washington. IEEE Computer Society
Stewart GW (n.d.) Matrix algorithms: basic decompositions (available on Google books)
Trefethen LN, Bau D (n.d.) Numerical linear algebra (available on Google books)
Kozubek B, Hapla J (n.d.) Markopoulos: LINEÁRNÍ ALGEBRA S MATLABEM, http://mi21.vsb.cz/ (in Czech) -MATLAB Help
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Omar, M.M.M., Eskaf, K.A. & Ghreiwati, B.A. Multidimensional frequency estimation using LU decomposition eigenvector–based algorithm. Ann. Telecommun. 75, 17–25 (2020). https://doi.org/10.1007/s12243-019-00723-9
- Eigenvalue decomposition
- Least mean square errors
- Multidimensional frequency estimation
- Singular value decomposition