Computational Advances in Multi-Sensor Signal Processing
Final Report Abstract
The current challenges of existing signal processing algorithms for multi-antenna systems include the fact that current multi-antenna system design problems are often unsolvable in terms of the available signal processing methods and tools. There is a promising trend to use advanced new signal processing approaches such as non-linear convex optimization, tensor-based processing, statistical resampling schemes, and techniques using structural properties of signal processing operators and algorithms. But the currently available techniques based on these emerging approaches are still far from the desired quality in terms of performance, optimality, and complexity. All the aforementioned facts motivate the development of new computationally advanced signal processing tools and methods for multi-sensor systems that substantially outperform the current methods in terms of performance, robustness, and computational complexity. Within the project, we have focused on the design of computational advances for multi-dimensional multisensor signal processing using higher-order arrays. We utilize tensors as a main tool to design advanced tensor-based signal processing techniques for multi-dimensional multi-sensor systems. This is due to the fact that it offers several fundamental advantages compared to matrix-based techniques. First of all, multilinear decompositions are essentially unique without additional constraints and allow to separate more components compared to the bilinear (matrix) approaches, which renders them attractive for component separation tasks. Moreover, since the structure of the data is preserved, structured denoising can be applied, which leads to an improved tensor-based signal subspace estimate and can enhance any subspace-based parameter estimation scheme. The major achievements are classified into three fields. i. Multi-sensor subspace estimation using higher-order arrays New multi-dimensional subspace based algorithms using higher-order arrays are designed for enhanced model order selection, robust model order estimation in the presence of brief sensor failures, efficient tensor decompositions such as the higher-order SVD (HOSVD) and joint diagonalization techniques, low-rank decompositions for higher order arrays, HOSVD-based subspace estimates in colored noise and interference scenarios, tensor-based subspace tracking via Kronecker structured projection, tensorbased spatial smoothing, closed-form solutions for parallel factor (PARAFAC) analysis, and iterative dual-symmetric PARAFAC. ii. Analytical performance assessment for HOSVD-based subspace estimates Analytical performance analysis expressions for subspace-based parameter estimation schemes are often based on an asymptotical error analysis of the eigenvectors of the underlying eigenvalue decomposition. A similar treatment for the HOSVD has been derived in this CAMUS project for multi-dimensional HOSVD based algorithms such as R-D standard Tensor-ESPRIT and R-D Unitary Tensor-ESPRIT. iii. Applicable scenarios in multi-sensor systems We have investigated selected application scenarios which offer the potential to benefit greatly from the proposed new tensor-based low-rank techniques. The considering applicable scenarios involve general array geometries, multi-dimensional MIMO channel estimation, blind and semi-blind channel estimation for SIMO, MIMO, OSTBC-based MIMO systems, and electroencephalographic (EEG) source separation.
Publications
- “Tensor-based channel estimation (TENCE) and iterative refinements for twoway relaying with multiple antennas and spatial reuse,” IEEE Trans. on Sigal Processing, vol. 58, issue 11, pp. 5720 - 5735, Nov. 2010
F. Römer and M. Haardt
- “Tensor-based spatial smoothing (TB-SS) using multiple snapshots,” IEEE Trans. on Sigal Processing, vol. 25, pp. 2715 – 2728, May 2010
A. Thakre, M. Haardt, F. Römer, and K. Giridhar
- “Multi-dimensional model order selection,” EURASIP Journal on Advances in Signal Processing, vol. 26, Jul 2011
J. P. C. L. da Costa, F. Römer, M. Haardt, and R. T. de Sousa Jr.
- “A “sequentially drilled” joint congruence (SeDJoCo) transformation with applications in blind source separation and multi-user MIMO systems,” IEEE Transaction on Signal Processing, vol. 60, pp.2744-2757, June 2012
A. Yeredor, B. Song, F. Römer and M. Haardt
- “Multi-way space-time-wave-vector analysis for EEG source separation,” EURASIP Signal Processing, pp. 1021-1031, Apr. 2012
H. Becker, P. Comon, L. Albera, M. Haardt, and I. Merlet
(See online at https://doi.org/10.1016/j.sigpro.2011.10.014) - “A semi-algebraic framework for approximate CP decompositions via simultaneous matrix diagonalizations (SECSI),” in Elsevier Signal Processing, vol. 93, issue 9, pp. 2722 - 2738, Sept. 2013
F. Römer and M. Haardt
(See online at https://doi.org/10.1016/j.sigpro.2013.02.016) - “Multidimensional prewhitening for enhanced signal reconstruction and parameter estimation in colored noise with Kronecker correlation structure,” Elsevier Signal Processing, vol. 93, pp. 3209 – 3226, Nov. 2013
J. P. C. L. da Costa, K. Liu, H. C. So, S. Schwarz, M. Haardt, and F. Römer
(See online at https://doi.org/10.1016/j.sigpro.2013.04.010) - “Analytical performance assessment of multi-dimensional matrix- and tensor-based ESPRIT-type algorithms,” IEEE Transactions on Signal Processing, vol. 62, pp. 2611 – 2625, May 2014
F. Römer, M. Haardt, and G. Del Galdo
(See online at https://doi.org/10.1109/TSP.2014.2313530) - “EEG extended source localization: Tensor-based vs. conventional methods,” NeuroImage, vol. 96, pp. 143 – 157, Aug. 2014
H. Becker, L. Albera, P. Comon, M. Haardt, G. Birot, F. Wendling, M. Gavaret, C. Bnar, and I. Merlet
(See online at https://doi.org/10.1016/j.neuroimage.2014.03.043) - “Tensor subspace Tracking via Kronecker structured projections (TeTraKron) for time-varying multidimensional harmonic retrieval”. EURASIP Journal on Advances in Signal Processing, December 2014, 2014:123
Y. Cheng, F. Roemer, O. Khatib, and M. Haardt
(See online at https://doi.org/10.1186/1687-6180-2014-123)
