Subspace estimation of coherent wideband OFDM signals

Ahcene Bellabas; Tahar Ziani; Ammar Mesloub; Abdelmadjid Maali; Djamel Teguig

doi:10.1515/freq-2024-0238

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Subspace estimation of coherent wideband OFDM signals

Ahcene Bellabas , Tahar Ziani , Ammar Mesloub , Abdelmadjid Maali und Djamel Teguig

Veröffentlicht/Copyright: 25. April 2025

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Abstract

A method for estimating signal and noise subspaces in the context of direction of arrival (DOA) for coherent wideband orthogonal frequency-division multiplexing (OFDM) signals is proposed. It relies on a newly defined matrix, which leverages the orthogonality property of OFDM subcarriers. We mathematically demonstrate that this matrix satisfies adequate subspace decomposition by considering two approximations. Furthermore, through DOA estimation evaluations, we confirm its effectiveness in discerning DOAs even with reduced snapshots and a low signal-to-noise ratio. To validate its feasibility and effectiveness, practical experiments are conducted using a real-world testbed based on USRP-B210 boards, and the results demonstrate the method’s effectiveness.

Keywords: subspace estimation; coherent wideband OFDM signals; DOA estimation; subspace-based techniques

Corresponding author: Ahcene Bellabas, Lab. Antennes et dispositifs micro-ondes, Ecole Militaire Polytechnique, BP 17 Bordj El Bahri, Algiers, Algeria, E-mail: ahcene.bellabas@gmail.com

Acknowledgments

The authors express their sincere gratitude to Professor H.E. Lehtihet for his collaboration, orientation, and invaluable help.

Research ethics: Not applicable.
Informed consent: Not applicable.
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Use of Large Language Models, AI and Machine Learning Tools: None declared.
Conflict of interest: The authors state no conflict of interest.
Research funding: None declared.
Data availability: Not applicable.

Appendix A: Random phase shift elimination

After synchronization and simplifying the scenario by considering a single OFDM symbol and one target, we have the following expressions for the OFDM signal received at the first antenna, denoted as x(t), and the reference signal, denoted as x_ref(t):

(25) x ( t ) = ∑ n = 0 N c − 1 A 1 d T x ( n ) e ȷ 2 π f n ( t − β 1 − τ 0 ) x ref ( t ) = ∑ n = 0 N c − 1 A 1 d T x ( n ) e ȷ 2 π f n ( t − τ 0 )

Here, β₁ represents the delay time associated with the target, A₁ denotes the attenuation, and τ₀ stands for the initial random delay introduced by the USRP-B210 board.

To eliminate the phase random shift, cancellation is performed by multiplying the received signal with the conjugate of the reference signal, as follows:

x ( t ) x ref ( t ) * = ∑ i = 0 N c − 1 A 1 d T x ( i ) e ȷ 2 π f i ( t − β 1 − τ 0 ) × ∑ j = 0 N c − 1 A 1 * d T x * ( j ) e − ȷ 2 π f j ( t − τ 0 ) = | A 1 | 2 ∑ i = 0 N c − 1 d T x ( i ) e − ȷ 2 π f i β 1 × ∑ j = 0 N c − 1 d T x * ( j ) e ȷ 2 π ( f i − f j ) ( t − τ 0 )

Finally, using the orthogonality property, we arrive at the expression:

(26) x ( t ) x ref ( t ) * = | A 1 | 2 ∑ i = 0 N c − 1 | d T x ( i ) | 2 e − ȷ 2 π f i β 1

This cancellation process ensures that the random phase shift introduced by the USRP board is eliminated, preserving the information on the DOA in the computed quantity x(t)x_ref(t)*.

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Received: 2024-07-24

Accepted: 2025-03-31

Published Online: 2025-04-25

Published in Print: 2025-08-26

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subspace estimation; coherent wideband OFDM signals; DOA estimation; subspace-based techniques