BAYESIAN RECEIVER DESIGN AND BEAMFORMING FOR MULTIUSER MIMO THZ COMMUNICATIONS USING PROBABILISTIC GRAPHICAL MODELS AND GRAPH NEURAL NETWORKS

Context:

Wireless transmissions in sub-THz and THz bands [1] are widely regarded as an enabling technology for future 6G communications, due to the availability of unused spectrum. The short wavelengths enable to pack a large number of antenna elements at the transmitter and receiver side, thus enabling ultra-massive multiple-input multiple-output (UM-MIMO) with the potential of tera-bits per second data rates and precise localization. Besides traditional backhaul links, deploying sub-THz/THz technologies seems relevant for emerging applications such as vehicular [2] and device-to-device communications. Nevertheless, a number of signal processing processing issues remain largely unsolved in order to make affordable sub-THz/THz technologies available. Firstly, MIMO channels in these frequency bands suffer from huge signal-to-noise degradation due to significant path loss and blockage [3], which can partly be compensated using high-gain beamforming. Physical layer waveform design is also an important challenge. It is questionable whether orthogonal frequency division multiplexing (OFDM) used in 4G/5G is still adequate for sub-THz/THz frequency bands due to complexity issues [4,5]. Howewer for the single-carrier (SC) techniques described in [3], the narrowband beamforming model, where signals received over different antenna elements are identical up to a phase shift, may become invalid so that additional time delays need to be compensated [6]. Accurate channel estimation is known to be a difficult task in UM-MIMO settings [7,8] as it usually relies only on pilot symbols to estimate a large number of complex coefficients for growing array sizes. This problem becomes even more complicated in highly dynamic environments induced by user mobility. Finally, low-cost RF implementations incure hardware impairments such as phase noise, I-Q imbalance and amplifier nonlinearities [9], that need proper compensation.

Specific issues will be addressed in this project. Firstly, beam alignment between the transmitter and the receiver is required in order to overcome the overwhelming path loss (otherwise channel estimation would fail). Such mechanisms to establish communication are often time consuming and imperfect [10]. They also do not account for abrupt user appearance/ disappearance caused by blockage. Secondly, accomodating multiuser transmissions requires space division multiple access (SDMA) or beam division multiplexing (BDM) techniques, where groups of users clustered according to the similarity of their angle of departure (AoD) can be resolved [4]. Specific interference cancellation techniques need to be applied in order to cancel inter-group interference [11]. It is worth pointing out that the problem of sub-THz/THz communications with potential beam misalignment or blockage has deep connections with multitarget estimation for direction-of-arrival (DOA) detection and tracking in radar theory [12].

Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic graphical models (PGMs) have been well developed in recent years to mathematically model real-world scenarios in compact graphical representations of variable distributions [13,14]. Graphic neural networks (GNNs) are new inference methods developed in recent years and are attracting increasing attention due to their efficiency and ability in solving inference and learning problems on graph-structured data, see e.g., [15]. These two powerful approaches have different advantages in capturing relationships from observations and how they drive message passing, and they can enrich each other in various tasks. Both GNNs and PGMs are capable of conducting accurate and fast inference on graphs but the major differences between them are how they process relational variables and how they perform message passing in the models.

The possible intersection, and even association, of these two approaches is a promising idea that is spreading in the field of communications theory. PGMs and belief propagation (BP) joint channel equalization and decoding is investigated in e.g., [16,17,18]. In [19,20], GNNs are used for channel decoding. Very recently, [21] has proposed the use of GNNs for joint channel equalization and decoding, one GNN for channel equalization and one GNN for channel decoding. Both GNNs are connected by their variable nodes (VNs) to form a combined factor graph [17] that allows information exchange between equalization and decoding. This is in contrast with [22] where such a combined factor graph is employed in combination with a decision feedback equalizer (DFE) and a channel decoder based on PGMs and BP.

The proposed research project aims to explore when and how combined GNNs and PGMs can improve Bayesian receiver design and beamforming for multiuser MIMO THz communications.

Objectives:

Wireless communications in sub-THz and THz bands are considered a key enabler for future 6G networks due to the abundance of unused spectrum and the potential for ultra-massive MIMO (UM-MIMO) systems that achieve terabit-per-second data rates and precise localization. However, challenges such as severe path loss, blockage, hardware impairments, and the limitations of conventional waveform designs complicate reliable channel estimation, beam alignment, and multiuser transmission. This project focuses on addressing these issues by leveraging probabilistic graphical models (PGMs) and graph neural networks (GNNs) to enhance Bayesian receiver design and beamforming in multiuser THz MIMO systems. By combining the complementary strengths of PGMs and GNNs in modeling relational data and performing efficient message passing, the research aims to develop advanced inference methods for joint channel equalization, decoding, and interference mitigation, ultimately enabling robust and high-capacity THz communications.

Expected Results:

The expected outcomes of the PhD include the production of high-quality scientific work, intended to be disseminated through publications in peer-reviewed journals, as well as through presentations at international conferences and specialized events. In addition, the thesis is expected to yield technical reports, software tools, datasets, or experimental protocols that can support further research. The work may also contribute to collaborations with industrial partners, or the development of new methodologies and algorithms, enhancing both scientific knowledge and practical applications.

Profile and skills required:

Any PhD candidate should have:
- a research-oriented MSc. degree in applied mathematics/statistics, electrical engineering, telecommunications engineering or equivalent, with excellent study records, and possibly one or two publications in conference proceedings and/or international journals;
- a strong background in mathematics and statistics, and a deep knowledge in at least one of the following fields: information theory, communication theory, signal processing for communications, artificial intelligence, machine learning, statistical learning ;
- a demonstrated ability to work hard and autonomously;
- strong programming skills in one of the following languages: MATLAB, C/C++, or python;
- very good communication skills (French or English), both oral and written;
- a strong motivation for research and a taste for analytical and theoretical subjects.

Bibliography:

[1] J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications”, Journal of Applied Physics, vol. 107, no. 11, 2010.
[2] V. Petrov et al., “On unified vehicular communications and radar sensing in millimeter-wave and low terahertz bands,” IEEE Wireless Communications, vol. 26, no. 3, pp. 146–153, Jun. 2019.
[3] H. Sarieddeen, M. -S. Alouini and T. Y. Al-Naffouri, “An overview of signal processing techniques for terahertz communications,” Proceedings of the IEEE, vol. 109, no. 10, pp. 1628–1665, Oct. 2021.
[4] C. Lin and G. Y. L. Li, “Terahertz communications: An array-of-subarrays solution,” IEEE Communications Magazine, vol. 54, no. 12, pp. 124–131, Dec. 2016.
[5] H. Sarieddeen, N. Saeed, T. Y. Al-Naffouri and M.-S. Alouini, “Next generation terahertz communications: A rendez-vous of sensing, imaging, and localization,” arXiv preprint, 2020.
[6] B. Wang et al., “Spatial-wideband effect in massive MIMO with application in mmwave systems,” IEEE Communications Magazine, vol. 56, no. 12, pp. 134–141, Dec. 2018.
[7] S. Nie and I. F. Akyildiz, “Deep kernel learning-based channel estimation in ultra-massive MIMO communications at 0.06-10 THz,” Proc. 2019 IEEE Globecom Workshops (GC Wkshps), 2019, pp. 1–6.
[8] J. Tan and L. Dai, “Wideband channel estimation for THz massive MIMO,” China Communications, vol. 18, no. 5, pp. 66–80, May 2021.
[9] T. Mao, Q. Wang and Z. Wang, “Receiver design for the low-cost teraHertz communication system with hardware impairment,” Proc. 2020 IEEE International Conference on Communications (ICC), 2020, pp. 1–5.
[10] C. Liu, M. Li, S. V. Hanly, I. B. Collings and P. Whiting, “Millimeter wave beam alignment: Large deviations analysis and design insights,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 7, pp. 1619–1631, Jul. 2017.
[11] H. Sarieddeen, A. Abdallah, M. M. Mansour, M. -S. Alouini and T. Y. Al-Naffouri, “Terahertz-band MIMO-NOMA: Adaptive superposition coding and subspace detection,” IEEE Open Journal of the Communications Society, vol. 2, pp. 2628–2644, 2021.
[12] A. Saucan, T. Chonavel, C. Sintes and J. Le Caillec, “Marked poisson point process PHD filter for DOA tracking,” Proc. 2015 23rd European Signal Processing Conference (EUSIPCO), 2015, pp. 2621–2625.
[13] Bishop, 2006.
[14] Koller and Friedman, 2009.
[15] Kipf and Welling, 2016.
[16] Colavolpe and Germi, 2005.
[17] Kschischang, Frey and Loeliger, 2001.
[18] Loeliger, Dauwels, Hu, Korl, Ping, and Kschischang, 2007.
[19] Nachmani, Be'ery and Burshtein, 2016.
[20] Satorras and Welling, 2021.
[21] Clausius, Geiselhart, Tandler and ten Brink, 2025.
[22] Henkel, Islam and Leghari, 2019

L2S is a joint research unit (UMR 8506) combining the French National Centre for Scientific Research (CNRS), CentraleSupélec, and Paris-Saclay University. L2S is primarily affiliated with the Institute of Information Sciences and their Interactions (INS2I) and also has a secondary affiliation with the CNRS Institute of Engineering and Systems Sciences (INSIS). The laboratory comprises over 100 permanent academic staff and is organized into three clusters of comparable size: “Automation and Systems,” “Signal and Statistics,” and “Telecoms and Networks.” Its scientific activities span several disciplines, including applied and fundamental mathematics, which underpin signal processing, information theory, cryptography, and digital theory, as well as physics, which uses mathematical tools to describe and predict the evolution of systems and is the origin of the theory of electromagnetism. The necessary equipment and materials for the proper conduct of the PhD will be provided by L2S.

Any PhD candidate should have:
- a research-oriented MSc. degree in applied mathematics/statistics, electrical engineering, telecommunications engineering or equivalent, with excellent study records, and possibly one or two publications in conference proceedings and/or international journals;
- a strong background in mathematics and statistics, and a deep knowledge in at least one of the following fields: information theory, communication theory, signal processing for communications, artificial intelligence, machine learning, statistical learning ;
- a demonstrated ability to work hard and autonomously;
- strong programming skills in one of the following languages: MATLAB, C/C++, or python;
- very good communication skills (French or English), both oral and written;
- a strong motivation for research and a taste for analytical and theoretical subjects.