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The channel estimation problem has been widely discussed in traditional reconfigurable intelligent surface assisted multiple-input multiple-output. However, solutions for channel estimation adapted to beyond diagonal RIS need further study, and few recent works have been proposed to tackle this problem. Moreover, methods that avoid or minimize the use of pilot sequences are of interest. This work formulates a data-driven (semi-blind) joint channel and symbol estimation algorithm for beyond diagonal RIS that avoids a prior pilot-assisted stage while providing decoupled estimates of the involved communication channels. The proposed receiver builds upon a PARATUCK tensor model for the received signal, from which a trilinear alternating estimation scheme is derived. Preliminary numerical results demonstrate the proposed method's performance for selected system setups. The symbol error rate performance is also compared with that of a linear receiver operating with perfect knowledge of the cascaded channel.

Reconfigurable intelligent surface is a potential technology component of future wireless networks due to its capability of shaping the wireless environment. The promising MIMO systems in terms of extended coverage and enhanced capacity are, however, critically dependent on the accuracy of the channel state information. However, traditional channel estimation schemes are not applicable in RIS-assisted MIMO networks, since passive RISs typically lack the signal processing capabilities that are assumed by channel estimation algorithms. This becomes most problematic when physical imperfections or electronic impairments affect the RIS due to its exposition to different environmental effects or caused by hardware limitations from the circuitry. While these real-world effects are typically ignored in the literature, in this paper we propose efficient channel estimation schemes for RIS-assisted MIMO systems taking different imperfections into account. Specifically, we propose two sets of tensor-based algorithms, based on the parallel factor analysis decomposition schemes. First, by assuming a long-term model in which the RIS imperfections, modeled as unknown phase shifts, are static within the channel coherence time we formulate an iterative alternating least squares (ALS)-based algorithm for the joint estimation of the communication channels and the unknown phase deviations. Next, we develop the short-term imperfection model, which allows both amplitude and phase RIS imperfections to be non-static with respect to the channel coherence time. We propose two iterative ALS-based and closed-form higher order singular value decomposition-based algorithms for the joint estimation of the channels and the unknown impairments. Moreover, we analyze the identifiability and computational complexity of the proposed algorithms and study the effects of various imperfections on the channel estimation quality., Comment: arXiv admin note: text overlap with arXiv:2206.03557

Reconfigurable intelligent surface (RIS) is a candidate technology for future wireless networks. It enables to shape the wireless environment to reach massive connectivity and enhanced data rate. The promising gains of RIS-assisted networks are, however, strongly depends on the accuracy of the channel state information. Due to the passive nature of the RIS elements, channel estimation may become challenging. This becomes most evident when physical imperfections or electronic impairments affect the RIS due to its exposition to different environmental effects or caused by hardware limitations from the circuitry. In this paper, we propose an efficient and low-complexity tensor-based channel estimation approach in RIS-assisted networks taking different imperfections into account. By assuming a short-term model in which the RIS imperfections behavior, modeled as unknown amplitude and phase shifts deviations, is non-static with respect to the channel coherence time, we formulate a closed-form higher order singular value decomposition based algorithm for the joint estimation of the involved channels and the unknown impairments. Furthermore, the identifiability and computational complexity of the proposed algorithm are analyzed, and we study the effect of different imperfections on the channel estimation quality. Simulation results demonstrate the effectiveness of our proposed tensor-based algorithm in terms of the estimation accuracy and computational complexity compared to competing tensor-based iterative alternating solutions.

Intelligent reflecting surface (IRS) is an emerging technology for future wireless communications including 5G and especially 6G. It consists of a large 2D array of (semi-)passive scattering elements that control the electromagnetic properties of radio-frequency waves so that the reflected signals add coherently at the intended receiver or destructively to reduce co-channel interference. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. In this paper, we address the receiver design for an IRS-assisted multiple-input multiple-output (MIMO) communication system via a tensor modeling approach aiming at the channel estimation problem using supervised (pilot-assisted) methods. Considering a structured time-domain pattern of pilots and IRS phase shifts, we present two channel estimation methods that rely on a parallel factor (PARAFAC) tensor modeling of the received signals. The first one has a closed-form solution based on a Khatri-Rao factorization of the cascaded MIMO channel, by solving rank-1 matrix approximation problems, while the second one is an iterative alternating estimation scheme. The common feature of both methods is the decoupling of the estimates of the involved MIMO channel matrices (base station-IRS and IRS-user terminal), which provides performance enhancements in comparison to competing methods that are based on unstructured LS estimates of the cascaded channel. Design recommendations for both methods that guide the choice of the system parameters are discussed. Numerical results show the effectiveness of the proposed receivers, highlight the involved trade-offs, and corroborate their superior performance compared to competing LS-based solutions., Comment: arXiv admin note: text overlap with arXiv:2001.06554

Intelligent reflective surface (IRS) is an emergent technology for future wireless communications. It consists of a large 2D array of passive scattering elements that control the electromagnetic properties of radio-frequency waves so that the reflected signals add coherently at the intended receiver or destructively to reduce co-channel interference. The promised gains of IRS-assisted communications depend on the accuracy of the channel state information. In this paper, we propose two novel channel estimation methods for an IRS-assisted multiple-input multiple-output (MIMO) communication system. Assuming a structured time-domain pattern of pilots and IRS phase shifts, we show that the received signal follows a parallel factor (PARAFAC) tensor model that can be exploited to estimate the involved communication channels in closed-form or iteratively. Numerical results corroborate the effectiveness of the proposed channel estimation methods and highlight the involved tradeoffs.