This paper proposes a pilot decoupling-based two-dimensional channel parameter estimation method for intelligent reflecting surface (IRS)-assisted networks. We exploit the combined effect of Terahertz sparse propagation and the geometrical structure of arrays deployed at the base station, the IRS, and the user equipment to develop a low-complexity channel parameter estimation method. By means of a new pilot design along the horizontal and vertical directions, the overall channel parameter estimation problem is decoupled into different domains. Furthermore, with this decoupling, it is possible to simultaneously sense/estimate the channel parameters and to communicate with the sensed node. Specifically, we formulate two estimators by decoupling the global problem into sub-problems and exploiting the built-in tensor structure of the sensing/estimation problem by means of multiple rank-one approximations for rank-one and low-rank channels. The Cramér-Rao lower bound is derived to assess the performance of the proposed estimators. We show that our two proposed methods yield accurate parameter estimates and outperform state-of-the-art methods in terms of complexity. The tradeoffs between performance and complexity offered by the proposed methods are discussed and numerically assessed.

Intelligent reconfigurable surface IRS are becoming an attractive component of cellular networks due to their ability to shape the propagation environment and thereby improve coverage. While IRS nodes incorporate a great number of phase-shifting elements and a controller entity, the phase shifts are typically determined by the cellular base station (BS) due to its computational capability. Since controlling a large number of phase shifts may become prohibitive in practice, it is important to reduce the control overhead between the BS and the IRS controller. To this end, in this paper, we propose a low-rank modeling approach for the IRS phase shifts. The key idea is to represent the IRS phase shift vector using a low-rank tensor approximation model, where each rank-one component is modeled as the Kronecker product of a predefined number of factors of smaller sizes, obtained via tensor decomposition algorithms. We show that the proposed low-rank models drastically reduce the required feedback requirements associated with the BS-IRS control links. Our simulation results indicate that the proposed method is especially attractive in scenarios with a strong line of sight component, in which case nearly the same spectral efficiency is reached as in the cases with near-optimal phase shifts, but with significantly lower feedback overhead.

In this paper, we propose a rank-one tensor modeling approach that yields a compact representation of the optimum intelligent reconfigurable surface (IRS) phase-shift vector for reducing the feedback overhead. The main idea consists of factorizing the IRS phase-shift vector as a Kronecker product of smaller vectors, namely factors. The proposed phase-shift model allows the network to trade-off between achievable data rate and feedback reduction by controling the factorization parameters. Our simulations show that the proposed phase-shift factorization drastically reduces the feedback overhead, while improving the data rate in some scenarios, compared to the state-of-the-art schemes.

In this work, we propose a two-stage tensor-based receiver for joint channel, phase-noise (PN), and data estimation in MIMO-OFDM systems. First, we cast the received signal at the pilot subcarriers as a third-order PARAFAC model. Based on this model, we propose a closed-form algorithm based on the LS-KRF (Least Squares - Khatri-Rao Factorization) that estimates the channel gains and the phase-noise terms through multiple rank-one factorizations. From the estimated channel, the second stage of the receiver consists of data estimation based on a ZF (Zero-Forcing) receiver that capitalizes on the tensor structure of the received signal at the data subcarriers via a Selective Kronecker Product (SKP) approach. Our numerical simulations show that the proposed receiver achieves an improved performance compared to the state-of-art receivers.

Channel estimation in hybrid analog-digital massive MIMO systems is a challenging problem due to the high channel dimension, low signal-to-noise ratio before beamforming, and reduced number of radio-frequency chains. Compressed sensing based algorithms have been adopted to address these challenges by leveraging the sparse nature of millimeter-wave MIMO channels. In compressed sensing-based methods, the training vectors should be designed carefully to guarantee recoverability. Although using random vectors has an overwhelming recoverability guarantee, it has been recently shown that an optimized update, which could be obtained so that the mutual coherence of the resulting sensing matrix is minimized, can improve the recoverability guarantee. In this paper, we propose an openloop hybrid analog-digital beam-training framework, where a given sensing matrix is decomposed into analog and digital beamformers. The given sensing matrix can be designed efficiently offline to reduce computational complexity. Simulation results show that the proposed training method achieves a lower mutual coherence and an improved channel estimation performance than the other benchmark methods.