Colloquium - Details
Bachelor-Presentation: Analysis of an Efficient Algorithm for Time-Domain Multichannel System Identification
Momen Elsayed
Monday, October 26, 2026
10:00 PM
IKS 4G | hybrid
This thesis investigates the efficient estimation of impulse responses of multichannel linear time-invariant systems directly from measured input-output data in the time domain. The input signals cannot be freely designed for the identification, so the algorithms must operate on the available data. Formulating the problem as a least-squares estimation leads to convolution matrices with block-Toeplitz structure, which is not exploited by conventional dense-matrix methods.
A block-Toeplitz QR-factorization algorithm based on the approach of Bojanczyk is analyzed, which updates the factorization iteratively from block column to block column by exploiting the shift structure of the matrix. The method is systematically compared with frequency-domain spectrum division and a conventional time-domain MMSE estimator in a simulated system with two inputs and one output, using measured impulse responses and signal-to-noise ratios from −30 dB to 30 dB. In addition, the computational cost is analyzed by a floating-point operation count.
The experiments show that the relative performance of the methods depends strongly on the SNR. At low SNR around 0 dB, all methods reach a system distance of approximately −3 dB, with spectrum division slightly ahead. At high SNR, spectrum division saturates at approximately −5 dB and the conventional MMSE estimator at approximately −13.5 dB, while the Bojanczyk-based estimator reaches approximately −32 dB at 30 dB SNR. Exploiting the block-Toeplitz structure reduces the computational complexity from O(MK²) for a direct economic QR factorization to O(MK) for M ≫ K.
The two MMSE estimators differ in their convolution-matrix construction (full versus valid), which contributes to the observed accuracy difference. These results indicate that structure-exploiting QR-based identification is accurate and efficient for time-domain multichannel system identification at sufficiently high SNR, while its advantage under strong noise and its performance on fully measured experimental data remain to be validated.
