Massive MIMO and Terahertz Communications

Overview

THz-Band Ultra-Massive MIMO System and Channel Modeling

To advance signal processing for THz communications research [1, 2], we developed TeraMIMO , an accurate, open-source MATLAB simulator for stochastic wideband ultra-massive multiple-input multiple-output (UM-MIMO) THz channels. TeraMIMO models critical THz channel statistics, including coherence time, coherence bandwidth, Doppler spread, and root-mean-square (RMS) delay spread. It captures frequency-selective and time-variant THz channels across various communication distances, ranging from nano-communications to short-range indoor and outdoor scenarios, as well as line-of-sight (LoS) links spanning hundreds of meters. The simulator incorporates UM-MIMO array-of-subarrays (AoSA) architectures to analyze spatial effects such as spherical wave propagation and beam-split in wideband THz channels. Additionally, we implemented three molecular absorption models: an exact model based on radiative transfer theory (0.1–10 THz) and two low-complexity approximations (valid up to 450 GHz). TeraMIMO has been validated against measurement-based channel models and ergodic capacity analyses. It includes a user-friendly graphical interface (Figure 1) and comprehensive guides for THz channel generation and analysis [3, 4].

Figure 1: Graphical user interface for TeraMIMO [3, 4].

We also provided a framework for assessing the performance of various single-carrier and multi-carrier THz communication schemes , as illustrated in Figures 2 and 3. This work analyzed the performance and complexity trade-offs of candidate schemes in both the sub-THz and THz bands under different scenarios using TeraMIMO . Specifically, we evaluated spectral efficiencies, peak-to-average power ratio (PAPR) performance, and baseband complexity while accounting for realistic hardware impairment constraints. Our findings highlight discrete Fourier transform-spread orthogonal frequency-division multiplexing (DFT-s-OFDM) as a promising waveform that enhances robustness to THz impairments and phase noise while maintaining low PAPR and overall complexity.

Figure 2: Key performance indicators for THz waveform design .

Figure 3: Single carrier and multicarrier transceiver block diagrams: (a) CP-OFDM, (b) DFT-s-OFDM, (c) SC-FDE, (d) OQAM/FBMC, (e) OTFS, and (f) DFT-s-OTFS .

1. H. Sarieddeen, M. -S. Alouini and T. Y. Al-Naffouri, "An Overview of Signal Processing Techniques for Terahertz Communications," in Proceedings of the IEEE, vol. 109, no. 10, pp. 1628-1665, Oct. 2021. 
2. H. Sarieddeen, N. Saeed, T. Y. Al-Naffouri and M. -S. Alouini, "Next Generation Terahertz Communications: A Rendezvous of Sensing, Imaging, and Localization," in IEEE Communications Magazine, vol. 58, no. 5, pp. 69-75, May 2020. 
3. S. Tarboush, H. Sarieddeen, H. Chen, M. H. Loukil, H. Jemaa, M.-S. Alouini, and T. Y. Al-Naffouri, “TeraMIMO: A channel simulator for wideband ultra-massive MIMO terahertz communications,” IEEE Trans. Veh. Technol., vol. 70, no. 12, pp. 12 325–12 341, 2021. 
4.  https://github.com/SimonTarboush/TeraMIMO  
5. S. Tarboush, H. Sarieddeen, M.-S. Alouini, and T. Y. Al-Naffouri, “Single- versus multicarrier terahertz-band communications: A comparative study,” IEEE Open J. of the Commun. Soc., vol. 3, pp. 1466–1486, August 2022.

Channel Estimation for UM-MIMO THz-Band Communications

As the far-field assumption breaks down for high-frequency UM-MIMO systems, there has been growing interest in near-field communications in recent years. The spherical wave model (SWM) provides an accurate channel representation across all regions, including the near-field, by modeling the curvature of transmitted wavefronts and capturing the magnitude and phase variations of the received signal across antenna elements. The hybrid spherical planar wave model (HSPWM) is particularly well-suited for AoSA architectures, offering a good trade-off between modeling accuracy and complexity, as illustrated in Figure 4. Given the extremely sparse nature of high-frequency channels, compressed sensing (CS) strategies are effective for channel estimation, as they can significantly reduce training overhead. To address the estimation of sparse THz channels for an AoSA architecture, we proposed a method in that leverages prior information to enhance CS-based estimation. This approach utilizes geometric relationships and spatial information extracted from the channel estimates of the first subarray (SA) to improve the estimation of subsequent SAs.

Figure 4: Block diagram of a wideband UM-MIMO THz communication system with an AoSA architecture.

In practice, a mobile user may move back and forth between the near-field and far-field regions of a system, as illustrated in Figure 5. This dynamic behavior gives rise to a cross-field communication problem , where it is first necessary to determine whether the user is in the near-field or far-field region and subsequently take appropriate actions. Channel estimation strategies exist for both regions, but selecting the most suitable strategy at any given time or location requires accurate determination of the user’s region. Thus, dynamic strategies are essential to leverage the benefits of both near-field and far-field regions while minimizing computational complexity. To address this, we propose a novel model selection metric that analyzes variations in received signal power as an indicator of the user’s region . Additionally, we introduced a reduced dictionary method applicable to all estimation strategies. The method minimizes the search space by focusing on angles or distances estimated during an initial search, overcoming the limitations of one-size-fits-all estimation and beamforming techniques, which are suboptimal. The cross-field problem is conceptualized as a classification task to determine whether near-field or far-field approaches should be employed. To enhance the accuracy of region selection, we propose using a hidden Markov model (HMM) that processes an ensemble of region estimates based on the metric introduced in .

Figure 5: Illustration of cross-field communication problem .

6. S. Tarboush, A. Ali, and T. Y. Al-Naffouri, “Compressive estimation of near field channels for ultra massive-MIMO wideband THz systems,” in IEEE Int. Conf. Acoustics, Speech, and Signal Process. (ICASSP), 2023, pp. 1–5. 
7. S. Tarboush, A. Ali, and T. Y. Al-Naffouri, “Cross-field channel estimation for ultra massive-MIMO THz systems,” IEEE Trans. Wireless Commun.,, vol. 23, no. 8, pp. 8619–8635, 2024. 
8. S. Tarboush, A. Ali, and T. Y. Al-Naffouri, “Near or far: On determining the appropriate channel estimation strategy in cross-field communication,” in Proc. IEEE 13rd Sensor Array and Multichannel Sig. Process. Workshop (SAM), 2024. 

Data Detection and Decoding in THz-Band UM-MIMO Systems

Recent advances in electronic and photonic technologies have enabled efficient signal generation and transmission at THz frequencies. However, as the gap in THz operating devices narrows, the demand for circuits capable of achieving terabit-per-second (Tbps) data rates continues to grow. Achieving such data rates requires processing thousands of information bits per clock cycle at state-of-the-art digital baseband processing clock frequencies of just a few GHz. In , we proposed a framework that leverages the structured subspaces of THz channels to provide pseudo-soft information (PSI) for low-complexity detection and decoding at the receiver, as illustrated in Figure 6. Additionally, we introduced a method to map bits to transmission resources using shorter codewords, enabling greater parallelization across all baseband processing blocks [9, 10]. This noise-centric framework reduces soft decoding complexity across multiple THz-band carriers, achieving significant computational gains with minimal performance trade-offs .

UM-MIMO data detection becomes increasingly challenging under high-frequency constraints and massive array dimensions. Achieving high data rates requires parallelizable transceiver architectures to overcome hardware limitations. Subspace detectors, which we analyzed in , offer promising solutions for this challenge.

For optimal data detection, we conducted a performance analysis of outdoor point-to-point THz links by deriving closed-form expressions for bit-error probability, outage probability, and ergodic capacity while accounting for Mixture Gamma (MG) fading and misalignment effects. The MG distribution, adopted in , demonstrates excellent fitting properties for THz small-scale fading and is versatile enough to model various fading scenarios, including Rayleigh, Rice, and Nakagami-m. 

Furthermore, in previous works, we analyzed the performance of THz-band MIMO detection under UM-MIMO spatial modulation and non-orthogonal multiple-access scenarios [14, 15].

Figure 6: Block diagram of a wideband UM-MIMO THz communication system adopting an AoSA architecture with source parallelizability and pseudo-soft information .

9. H. Sarieddeen, H. Jemaa, S. Tarboush, C. Studer, M.-S. Alouini, and T. Y. Al-Naffouri, “Bridging the complexity gap in Tbps-achieving THz-band baseband processing,” IEEE Wireless Commun., vol. 31, no. 5, pp. 287-294, 2024. 
10. H. Jemaa, H. Sarieddeen, S. Tarboush, M.-S. Alouini, and T. Y. Al-Naffouri, “THz-band, Tbps MIMO Communications: A Joint Data Detection and Decoding Framework,” in IEEE 100th Vehicular Technology Conference (VTC2024-Fall), 2024. 
11. H. Jemaa, H. Sarieddeen, M.-S. Alouini, and T. Y. Al-Naffouri, “THz-band, Tbps MIMO Communications: A Joint Data Detection and Decoding Framework,” in Asilomar Conf. on Signals, Systems, and Computers, pp. 665–669, 2022. 
12. H. Jemaa, S. Tarboush, H. Sarieddeen, M.-S. Alouini, and T. Y. Al-Naffouri, “Performance Analysis of Outdoor THz Links under Mixture Gamma Fading with Misalignment,” IEEE Commun. Lett., vol. 28, no. 11, pp. 2668-2672, 2024. 
13. H. Sarieddeen, M. -S. Alouini and T. Y. Al-Naffouri, "Terahertz-Band Ultra-Massive Spatial Modulation MIMO," in IEEE Journal on Selected Areas in Communications, vol. 37, no. 9, pp. 2040-2052, Sept. 2019. 
14. A. Magbool, H. Sarieddeen, N. Kouzayha, M. -S. Alouini and T. Y. Al-Naffouri, "Terahertz-band Non-orthogonal Multiple Access: System- and Link-level Considerations," in IEEE Wireless Communications, vol. 30, no. 1, pp. 142-149, February 2023. 
15. 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," in IEEE Open Journal of the Communications Society, vol. 2, pp. 2628-2644, 2021.

Physically Consistent Modeling of Reconfigurable Intelligent Surfaces

Reconfigurable intelligent surfaces (RISs) enable real-time smart manipulation of electromagnetic (EM) waves, allowing control over the propagation channel to reduce power consumption and hardware costs. Conventional nearly-passive RISs, however, have limited signal processing capabilities and range (half-space coverage). Active RISs, utilizing reflection-type amplifiers, address these limitations by overcoming the restricted capacity gains of passive RISs and mitigating the multiplicative fading effect .

Physically consistent signal processing bridges the gap between theory and practice by accounting for realistic design constraints. Circuit theory, particularly through multiport network theory , provides a robust framework for equivalent-circuit modeling. For instance, it models expected mutual coupling (MC) in densely packed reconfigurable surfaces, where unit cell spacing is less than the traditional half-wavelength. Significant progress has been made in incorporating MC into RIS-assisted communication systems and their variants. Models based on the scattering matrix (S-parameters) have been developed for various RIS types and were recently validated through experimental measurements in our work .

Few studies address channel estimation and beamforming under different RIS configurations with physically aware models, including MC. Our recent work evaluated channel estimation bounds in the presence of MC, revealing that closer integration of RIS unit cells significantly degrades estimation accuracy. Furthermore, we formulated the sparse channel estimation problem in using a physically consistent model based on scattering parameters derived from circuit theory, as illustrated in Figure 7. The main contribution is the development of a low-complexity CS-based channel estimation strategy and a novel algorithm combining successive convex approximation (SCA) and the Neumann series. This algorithm optimally solves the joint problem of RIS configuration and base station combiner design based on the estimated equivalent channel.

Figure 7: Illustration of a RIS-assisted uplink SIMO communication system in the presence of mutual coupling between RIS unit cells .

16. Z. Zhang, L. Dai, X. Chen, C. Liu, F. Yang, R. Schober, and H. V. Poor, “Active RIS vs. passive RIS: Which will prevail in 6G?” IEEE Trans. Commun., vol. 71, no. 3, pp. 1707–1725, 2022.  
17. M. T. Ivrlac and J. A. Nossek, “The multiport communication theory,” ? IEEE Circuits Syst. Mag., vol. 14, no. 3, pp. 27–44, 2014. 
18. M. T. Ivrlac and J. A. Nossek, “Toward a circuit theory of communication,” IEEE Trans. Circuits Syst. I: Reg. Papers, vol. 57, no. 7, pp. 1663–1683, 2010. 
19. M. Di Renzo and P. del Hougne, “Multiport network theory for modeling and optimizing reconfigurable metasurfaces,” arXiv preprint arXiv:2411.19685, 2024. 
20. P. Zheng, R. Wang, A. Shamim, and T. Y. Al-Naffouri, “Mutual coupling in RIS-aided communication: Model training and experimental validation,” IEEE Trans. Wireless Commun., 2024, accepted. 
21. P. Zheng, X. Ma, and T. Y. Al-Naffouri, “On the impact of mutual coupling on RIS-assisted channel estimation,” IEEE Wireless Commun. Lett., vol. 13, no. 5, pp. 1275–1279, 2024. 
22. P. Zheng, S. Tarboush, H. Sarieddeen, and T. Y. Al-Naffouri, “Mutual coupling-aware channel estimation and beamforming for RIS-assisted communications,” arXiv preprint arXiv:2410.04110, 2024.